Universe | An Open Access Journal from MDPI

<!DOCTYPE html> <html lang="en" xmlns:og="http://ogp.me/ns#" xmlns:fb="https://www.facebook.com/2008/fbml"> <head> <meta charset="utf-8"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <meta content="mdpi" name="sso-service" /> <meta content="width=device-width, initial-scale=1.0" name="viewport" /> <title>Universe | An Open Access Journal from MDPI</title><link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/font-awesome.min.css?eb190a3a77e5e1ee?1732694169"> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/jquery.multiselect.css?f56c135cbf4d1483?1732694169"> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/chosen.min.css?d7ca5ca9441ef9e1?1732694169"> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/main2.css?69b39374e6b554b7?1732694169"> <link rel="mask-icon" href="https://pub.mdpi-res.com/img/mask-icon-128.svg?c1c7eca266cd7013?1732694169" color="#4f5671"> <link rel="apple-touch-icon" sizes="180x180" href="https://pub.mdpi-res.com/icon/apple-touch-icon-180x180.png?1732694169"> <link rel="apple-touch-icon" sizes="152x152" href="https://pub.mdpi-res.com/icon/apple-touch-icon-152x152.png?1732694169"> <link rel="apple-touch-icon" sizes="144x144" href="https://pub.mdpi-res.com/icon/apple-touch-icon-144x144.png?1732694169"> <link rel="apple-touch-icon" sizes="120x120" href="https://pub.mdpi-res.com/icon/apple-touch-icon-120x120.png?1732694169"> <link rel="apple-touch-icon" sizes="114x114" href="https://pub.mdpi-res.com/icon/apple-touch-icon-114x114.png?1732694169"> <link rel="apple-touch-icon" sizes="76x76" href="https://pub.mdpi-res.com/icon/apple-touch-icon-76x76.png?1732694169"> <link rel="apple-touch-icon" sizes="72x72" href="https://pub.mdpi-res.com/icon/apple-touch-icon-72x72.png?1732694169"> <link rel="apple-touch-icon" sizes="57x57" href="https://pub.mdpi-res.com/icon/apple-touch-icon-57x57.png?1732694169"> <link rel="apple-touch-icon" href="https://pub.mdpi-res.com/icon/apple-touch-icon-57x57.png?1732694169"> <link rel="apple-touch-icon-precomposed" href="https://pub.mdpi-res.com/icon/apple-touch-icon-57x57.png?1732694169"> <link rel="manifest" href="/manifest.json"> <meta name="theme-color" content="#ffffff"> <meta name="application-name" content=" "/> <link rel="apple-touch-startup-image" href="https://pub.mdpi-res.com/img/journals/universe-logo-sq.png?8600e93ff98dbf14"> <link rel="apple-touch-icon" href="https://pub.mdpi-res.com/img/journals/universe-logo-sq.png?8600e93ff98dbf14"> <meta name="msapplication-TileImage" content="https://pub.mdpi-res.com/img/journals/universe-logo-sq.png?8600e93ff98dbf14"> <link rel="icon" type="image/png" sizes="32x32" href="https://pub.mdpi-res.com/img/journals/universe-logo-sq.png?8600e93ff98dbf14"> <link rel="icon" type="image/png" sizes="96x96" href="https://pub.mdpi-res.com/img/journals/universe-logo-sq.png?8600e93ff98dbf14"> <link rel="icon" type="image/png" sizes="16x16" href="https://pub.mdpi-res.com/img/journals/universe-logo-sq.png?8600e93ff98dbf14"> <link rel="icon" type="image/png" sizes="192x192" href="https://pub.mdpi-res.com/img/journals/universe-logo-sq.png?8600e93ff98dbf14"> <meta name="title" content="Universe"> <meta name="description" content="Universe, an international, peer-reviewed Open Access journal." /> <link rel="image_src" href="https://pub.mdpi-res.com/img/journals/universe-logo.png?8600e93ff98dbf14" /> <meta property="og:title" content="Universe" /> <meta property="og:type" content="website" /> <meta property="og:url" content="https://www.mdpi.com/journal/universe" /> <meta property="og:description" content="Universe, an international, peer-reviewed Open Access journal." /> <meta property="og:image" content="https://pub.mdpi-res.com/img/journals/universe-logo-social.png?8600e93ff98dbf14" /> <style> h2, #abstract .related_suggestion_title { } .batch_articles a { color: #000; } a, .batch_articles .authors a, a:focus, a:hover, a:active, .batch_articles a:focus, .batch_articles a:hover, li.side-menu-li a { } span.label a { color: #fff; } #main-content a.title-link:hover, #main-content a.title-link:focus, #main-content div.generic-item a.title-link:hover, #main-content div.generic-item a.title-link:focus { } #main-content #middle-column .generic-item.article-item a.title-link:hover, #main-content #middle-column .generic-item.article-item a.title-link:focus { } .art-authors a.toEncode { color: #333; font-weight: 700; } #main-content #middle-column ul li::before { } .accordion-navigation.active a.accordion__title, .accordion-navigation.active a.accordion__title::after { } .accordion-navigation li:hover::before, .accordion-navigation li:hover a, .accordion-navigation li:focus a { } .relative-size-container .relative-size-image .relative-size { } .middle-column__help__fixed a:hover i, } input[type="checkbox"]:checked:after { } input[type="checkbox"]:not(:disabled):hover:before { } #main-content .bolded-text { } #main-content .hypothesis-count-container { } #main-content .hypothesis-count-container:before { } .full-size-menu ul li.menu-item .dropdown-wrapper { } .full-size-menu ul li.menu-item > a.open::after { } #title-story .title-story-orbit .orbit-caption { #background: url('/img/design/000000_background.png') !important; background: url('/img/design/ffffff_background.png') !important; color: rgb(51, 51, 51) !important; } #main-content .content__container__orbit { background-color: #000 !important; } #main-content .content__container__journal { color: #fff; } .html-article-menu .row span { } .html-article-menu .row span.active { } .accordion-navigation__journal .side-menu-li.active::before, .accordion-navigation__journal .side-menu-li.active a { color: rgba(13,52,73,0.75) !important; font-weight: 700; } .accordion-navigation__journal .side-menu-li:hover::before , .accordion-navigation__journal .side-menu-li:hover a { color: rgba(13,52,73,0.75) !important; } .side-menu-ul li.active a, .side-menu-ul li.active, .side-menu-ul li.active::before { color: rgba(13,52,73,0.75) !important; } .side-menu-ul li.active a { } .result-selected, .active-result.highlighted, .active-result:hover, .result-selected, .active-result.highlighted, .active-result:focus { } .search-container.search-container__default-scheme { } nav.tab-bar .open-small-search.active:after { } .search-container.search-container__default-scheme .custom-accordion-for-small-screen-link::after { color: #fff; } @media only screen and (max-width: 50em) { #main-content .content__container.journal-info { color: #fff; } #main-content .content__container.journal-info a { color: #fff; } } .button.button--color { } .button.button--color:hover, .button.button--color:focus { } .button.button--color-journal { position: relative; background-color: rgba(13,52,73,0.75); border-color: #fff; color: #fff !important; } .button.button--color-journal:hover::before { content: ''; position: absolute; top: 0; left: 0; height: 100%; width: 100%; background-color: #ffffff; opacity: 0.2; } .button.button--color-journal:visited, .button.button--color-journal:hover, .button.button--color-journal:focus { background-color: rgba(13,52,73,0.75); border-color: #fff; color: #fff !important; } .button.button--color path { } .button.button--color:hover path { fill: #fff; } #main-content #search-refinements .ui-slider-horizontal .ui-slider-range { } .breadcrumb__element:last-of-type a { } #main-header { } #full-size-menu .top-bar, #full-size-menu li.menu-item span.user-email { } .top-bar-section li:not(.has-form) a:not(.button) { } #full-size-menu li.menu-item .dropdown-wrapper li a:hover { } #full-size-menu li.menu-item a:hover, #full-size-menu li.menu.item a:focus, nav.tab-bar a:hover { } #full-size-menu li.menu.item a:active, #full-size-menu li.menu.item a.active { } #full-size-menu li.menu-item a.open-mega-menu.active, #full-size-menu li.menu-item div.mega-menu, a.open-mega-menu.active { } #full-size-menu li.menu-item div.mega-menu li, #full-size-menu li.menu-item div.mega-menu a { border-color: #9a9a9a; } div.type-section h2 { font-size: 20px; line-height: 26px; font-weight: 300; } div.type-section h3 { margin-left: 15px; margin-bottom: 0px; font-weight: 300; } .journal-tabs .tab-title.active a { } </style> <link rel="alternate" type="application/rss+xml" title="MDPI Publishing - Latest articles" href="https://www.mdpi.com/rss"> <link rel="alternate" type="application/rss+xml" title="MDPI Publishing - Universe - Latest Articles" href="/rss/journal/universe"> <meta name="google-site-verification" content="PxTlsg7z2S00aHroktQd57fxygEjMiNHydKn3txhvwY"> <meta name="facebook-domain-verification" content="mcoq8dtq6sb2hf7z29j8w515jjoof7" /> <script id="Cookiebot" data-cfasync="false" src="https://consent.cookiebot.com/uc.js" data-cbid="51491ddd-fe7a-4425-ab39-69c78c55829f" type="text/javascript" async></script>  <script type="text/plain" data-cookieconsent="statistics"> (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-WPK7SW5'); </script> <script type="text/plain" data-cookieconsent="statistics"> _linkedin_partner_id = "2846186"; window._linkedin_data_partner_ids = window._linkedin_data_partner_ids || []; window._linkedin_data_partner_ids.push(_linkedin_partner_id); </script><script type="text/javascript"> (function(){var s = document.getElementsByTagName("script")[0]; var b = document.createElement("script"); b.type = "text/javascript";b.async = true; b.src = "https://snap.licdn.com/li.lms-analytics/insight.min.js"; s.parentNode.insertBefore(b, s);})(); </script> <script type="text/plain" data-cookieconsent="statistics" data-cfasync="false" src="//script.crazyegg.com/pages/scripts/0116/4951.js" async="async" ></script> </head> <body> <div id="menuModal" class="reveal-modal reveal-modal-new reveal-modal-menu" aria-hidden="true" data-reveal role="dialog"> <div class="menu-container"> <div class="UI_NavMenu"> <div class="content__container " > <div class="custom-accordion-for-small-screen-link " > <h2>Journals</h2> </div> <div class="target-item custom-accordion-for-small-screen-content show-for-medium-up"> <div class="menu-container__links"> <div style="width: 100%; float: left;"> <a href="/about/journals">Active Journals</a> <a href="/about/journalfinder">Find a Journal</a> <a href="/about/journals/proposal">Journal Proposal</a> <a href="/about/proceedings">Proceedings Series</a> </div> </div> </div> </div> <a href="/topics"> <h2>Topics</h2> </a> <div class="content__container " > <div class="custom-accordion-for-small-screen-link " > <h2>Information</h2> </div> <div class="target-item custom-accordion-for-small-screen-content show-for-medium-up"> <div class="menu-container__links"> <div style="width: 100%; max-width: 200px; float: left;"> <a href="/authors">For Authors</a> <a href="/reviewers">For Reviewers</a> <a href="/editors">For Editors</a> <a href="/librarians">For Librarians</a> <a href="/publishing_services">For Publishers</a> <a href="/societies">For Societies</a> <a href="/conference_organizers">For Conference Organizers</a> </div> <div style="width: 100%; max-width: 250px; float: left;"> <a href="/openaccess">Open Access Policy</a> <a href="/ioap">Institutional Open Access Program</a> <a href="/special_issues_guidelines">Special Issues Guidelines</a> <a href="/editorial_process">Editorial Process</a> <a href="/ethics">Research and Publication Ethics</a> <a href="/apc">Article Processing Charges</a> <a href="/awards">Awards</a> <a href="/testimonials">Testimonials</a> </div> </div> </div> </div> <a href="/authors/english"> <h2>Editing Services</h2> </a> <div class="content__container " > <div class="custom-accordion-for-small-screen-link " > <h2>Initiatives</h2> </div> <div class="target-item custom-accordion-for-small-screen-content show-for-medium-up"> <div class="menu-container__links"> <div style="width: 100%; float: left;"> <a href="https://sciforum.net" target="_blank" rel="noopener noreferrer">Sciforum</a> <a href="https://www.mdpi.com/books" target="_blank" rel="noopener noreferrer">MDPI Books</a> <a href="https://www.preprints.org" target="_blank" rel="noopener noreferrer">Preprints.org</a> <a href="https://www.scilit.net" target="_blank" rel="noopener noreferrer">Scilit</a> <a href="https://sciprofiles.com" target="_blank" rel="noopener noreferrer">SciProfiles</a> <a href="https://encyclopedia.pub" target="_blank" rel="noopener noreferrer">Encyclopedia</a> <a href="https://jams.pub" target="_blank" rel="noopener noreferrer">JAMS</a> <a href="/about/proceedings">Proceedings Series</a> </div> </div> </div> </div> <div class="content__container " > <div class="custom-accordion-for-small-screen-link " > <h2>About</h2> </div> <div class="target-item custom-accordion-for-small-screen-content show-for-medium-up"> <div class="menu-container__links"> <div style="width: 100%; float: left;"> <a href="/about">Overview</a> <a href="/about/contact">Contact</a> <a href="https://careers.mdpi.com" target="_blank" rel="noopener noreferrer">Careers</a> <a href="/about/announcements">News</a> <a href="/about/press">Press</a> <a href="http://blog.mdpi.com/" target="_blank" rel="noopener noreferrer">Blog</a> </div> </div> </div> </div> </div> <div class="menu-container__buttons"> <a class="button UA_SignInUpButton" href="/user/login">Sign In / Sign Up</a> </div> </div> </div> <div id="captchaModal" class="reveal-modal reveal-modal-new reveal-modal-new--small" data-reveal aria-label="Captcha" aria-hidden="true" role="dialog"></div> <div id="actionDisabledModal" class="reveal-modal" data-reveal aria-labelledby="actionDisableModalTitle" aria-hidden="true" role="dialog" style="width: 300px;"> <h2 id="actionDisableModalTitle">Notice</h2> <form action="/email/captcha" method="post" id="emailCaptchaForm"> <div class="row"> <div id="js-action-disabled-modal-text" class="small-12 columns"> </div> <div id="js-action-disabled-modal-submit" class="small-12 columns" style="margin-top: 10px; display: none;"> You can make submissions to other journals <a href="https://susy.mdpi.com/user/manuscripts/upload">here</a>. </div> </div> </form> <a class="close-reveal-modal" aria-label="Close"> <i class="material-icons">clear</i> </a> </div> <div id="rssNotificationModal" class="reveal-modal reveal-modal-new" data-reveal aria-labelledby="rssNotificationModalTitle" aria-hidden="true" role="dialog"> <div class="row"> <div class="small-12 columns"> <h2 id="rssNotificationModalTitle">Notice</h2> <p> You are accessing a machine-readable page. In order to be human-readable, please install an RSS reader. </p> </div> </div> <div class="row"> <div class="small-12 columns"> <a class="button button--color js-rss-notification-confirm">Continue</a> <a class="button button--grey" onclick="$(this).closest('.reveal-modal').find('.close-reveal-modal').click(); return false;">Cancel</a> </div> </div> <a class="close-reveal-modal" aria-label="Close"> <i class="material-icons">clear</i> </a> </div> <div id="drop-article-label-openaccess" class="f-dropdown medium" data-dropdown-content aria-hidden="true" tabindex="-1"> <p> All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited. For more information, please refer to <a href="https://www.mdpi.com/openaccess">https://www.mdpi.com/openaccess</a>. </p> </div> <div id="drop-article-label-feature" class="f-dropdown medium" data-dropdown-content aria-hidden="true" tabindex="-1"> <p> Feature papers represent the most advanced research with significant potential for high impact in the field. A Feature Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for future research directions and describes possible research applications. </p> <p> Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive positive feedback from the reviewers. </p> </div> <div id="drop-article-label-choice" class="f-dropdown medium" data-dropdown-content aria-hidden="true" tabindex="-1"> <p> Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal. <div style="margin-top: -10px;"> <div id="drop-article-label-choice-journal-link" style="display: none; margin-top: -10px; padding-top: 10px;"> </div> </div> </p> </div> <div id="drop-article-label-resubmission" class="f-dropdown medium" data-dropdown-content aria-hidden="true" tabindex="-1"> <p> Original Submission Date Received: <span id="drop-article-label-resubmission-date"></span>. </p> </div> <div id="container"> <noscript> <div id="no-javascript"> You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled. </div> </noscript> <div class="fixed"> <nav class="tab-bar show-for-medium-down"> <div class="row full-width collapse"> <div class="medium-3 small-4 columns"> <a href="/"> <img class="full-size-menu__mdpi-logo" src="https://pub.mdpi-res.com/img/design/mdpi-pub-logo-black-small1.svg?da3a8dcae975a41c?1732694169" style="width: 64px;" title="MDPI Open Access Journals"> </a> </div> <div class="medium-3 small-4 columns right-aligned"> <div class="show-for-medium-down"> <a href="#" style="display: none;"> <i class="material-icons" onclick="$('#menuModal').foundation('reveal', 'close'); return false;">clear</i> </a> <a class="js-toggle-desktop-layout-link" title="Toggle desktop layout" style="display: none;" href="/toggle_desktop_layout_cookie"> <i class="material-icons">zoom_out_map</i> </a> <a href="#" class="js-open-small-search open-small-search"> <i class="material-icons show-for-small only">search</i> </a> <a title="MDPI main page" class="js-open-menu" data-reveal-id="menuModal" href="#"> <i class="material-icons">menu</i> </a> </div> </div> </div> </nav> </div> <section class="main-section"> <header> <div class="full-size-menu show-for-large-up"> <div class="row full-width"> <div class="large-1 columns"> <a href="/"> <img class="full-size-menu__mdpi-logo" src="https://pub.mdpi-res.com/img/design/mdpi-pub-logo-black-small1.svg?da3a8dcae975a41c?1732694169" title="MDPI Open Access Journals"> </a> </div> <div class="large-8 columns text-right UI_NavMenu"> <ul> <li class="menu-item"> <a href="/about/journals" data-dropdown="journals-dropdown" aria-controls="journals-dropdown" aria-expanded="false" data-options="is_hover: true; hover_timeout: 200">Journals</a> <ul id="journals-dropdown" class="f-dropdown dropdown-wrapper dropdown-wrapper__small" data-dropdown-content aria-hidden="true" tabindex="-1"> <li> <div class="row"> <div class="small-12 columns"> <ul> <li> <a href="/about/journals"> Active Journals </a> </li> <li> <a href="/about/journalfinder"> Find a Journal </a> </li> <li> <a href="/about/journals/proposal"> Journal Proposal </a> </li> <li> <a href="/about/proceedings"> Proceedings Series </a> </li> </ul> </div> </div> </li> </ul> </li> <li class="menu-item"> <a href="/topics">Topics</a> </li> <li class="menu-item"> <a href="/authors" data-dropdown="information-dropdown" aria-controls="information-dropdown" aria-expanded="false" data-options="is_hover:true; hover_timeout:200">Information</a> <ul id="information-dropdown" class="f-dropdown dropdown-wrapper" data-dropdown-content aria-hidden="true" tabindex="-1"> <li> <div class="row"> <div class="small-5 columns right-border"> <ul> <li> <a href="/authors">For Authors</a> </li> <li> <a href="/reviewers">For Reviewers</a> </li> <li> <a href="/editors">For Editors</a> </li> <li> <a href="/librarians">For Librarians</a> </li> <li> <a href="/publishing_services">For Publishers</a> </li> <li> <a href="/societies">For Societies</a> </li> <li> <a href="/conference_organizers">For Conference Organizers</a> </li> </ul> </div> <div class="small-7 columns"> <ul> <li> <a href="/openaccess">Open Access Policy</a> </li> <li> <a href="/ioap">Institutional Open Access Program</a> </li> <li> <a href="/special_issues_guidelines">Special Issues Guidelines</a> </li> <li> <a href="/editorial_process">Editorial Process</a> </li> <li> <a href="/ethics">Research and Publication Ethics</a> </li> <li> <a href="/apc">Article Processing Charges</a> </li> <li> <a href="/awards">Awards</a> </li> <li> <a href="/testimonials">Testimonials</a> </li> </ul> </div> </div> </li> </ul> </li> <li class="menu-item"> <a href="/authors/english">Editing Services</a> </li> <li class="menu-item"> <a href="/about/initiatives" data-dropdown="initiatives-dropdown" aria-controls="initiatives-dropdown" aria-expanded="false" data-options="is_hover: true; hover_timeout: 200">Initiatives</a> <ul id="initiatives-dropdown" class="f-dropdown dropdown-wrapper dropdown-wrapper__small" data-dropdown-content aria-hidden="true" tabindex="-1"> <li> <div class="row"> <div class="small-12 columns"> <ul> <li> <a href="https://sciforum.net" target="_blank" rel="noopener noreferrer"> Sciforum </a> </li> <li> <a href="https://www.mdpi.com/books" target="_blank" rel="noopener noreferrer"> MDPI Books </a> </li> <li> <a href="https://www.preprints.org" target="_blank" rel="noopener noreferrer"> Preprints.org </a> </li> <li> <a href="https://www.scilit.net" target="_blank" rel="noopener noreferrer"> Scilit </a> </li> <li> <a href="https://sciprofiles.com" target="_blank" rel="noopener noreferrer"> SciProfiles </a> </li> <li> <a href="https://encyclopedia.pub" target="_blank" rel="noopener noreferrer"> Encyclopedia </a> </li> <li> <a href="https://jams.pub" target="_blank" rel="noopener noreferrer"> JAMS </a> </li> <li> <a href="/about/proceedings"> Proceedings Series </a> </li> </ul> </div> </div> </li> </ul> </li> <li class="menu-item"> <a href="/about" data-dropdown="about-dropdown" aria-controls="about-dropdown" aria-expanded="false" data-options="is_hover: true; hover_timeout: 200">About</a> <ul id="about-dropdown" class="f-dropdown dropdown-wrapper dropdown-wrapper__small" data-dropdown-content aria-hidden="true" tabindex="-1"> <li> <div class="row"> <div class="small-12 columns"> <ul> <li> <a href="/about"> Overview </a> </li> <li> <a href="/about/contact"> Contact </a> </li> <li> <a href="https://careers.mdpi.com" target="_blank" rel="noopener noreferrer"> Careers </a> </li> <li> <a href="/about/announcements"> News </a> </li> <li> <a href="/about/press"> Press </a> </li> <li> <a href="http://blog.mdpi.com/" target="_blank" rel="noopener noreferrer"> Blog </a> </li> </ul> </div> </div> </li> </ul> </li> </ul> </div> <div class="large-3 columns text-right full-size-menu__buttons"> <div> <a class="button button--default-inversed UA_SignInUpButton" href="/user/login">Sign In / Sign Up</a> <a class="button button--default js-journal-active-only-link js-journal-active-only-submit-link UC_NavSubmitButton" href=" https://susy.mdpi.com/user/manuscripts/upload?journal=universe " data-disabledmessage="new submissions are not possible.">Submit</a> </div> </div> </div> </div> <div class="header-divider"> </div> <div class="search-container hide-for-small-down row search-container__homepage-scheme"> <form id="basic_search" style="background-color: inherit !important;" class="large-12 medium-12 columns " action="/search" method="get"> <div class="row search-container__main-elements"> <div class="large-2 medium-2 small-12 columns text-right1 small-only-text-left"> <div class="show-for-medium-up"> <div class="search-input-label"> </div> </div> <span class="search-container__title">Search<span class="hide-for-medium"> for Articles</span><span class="hide-for-small">:</span></span> </div> <div class="custom-accordion-for-small-screen-content"> <div class="large-2 medium-2 small-6 columns "> <div class=""> <div class="search-input-label">Title / Keyword</div> </div> <input type="text" placeholder="Title / Keyword" id="q" tabindex="1" name="q" value="" /> </div> <div class="large-2 medium-2 small-6 columns "> <div class=""> <div class="search-input-label">Author / Affiliation / Email</div> </div> <input type="text" id="authors" placeholder="Author / Affiliation / Email" tabindex="2" name="authors" value="" /> </div> <div class="large-2 medium-2 small-6 columns "> <div class=""> <div class="search-input-label">Journal</div> </div> <select id="journal" tabindex="3" name="journal" class="chosen-select"> <option value="">All Journals</option> <option value="acoustics" > Acoustics </option> <option value="amh" > Acta Microbiologica Hellenica (AMH) </option> <option value="actuators" > Actuators </option> <option value="admsci" > Administrative Sciences </option> <option value="adolescents" > Adolescents </option> <option value="arm" > Advances in Respiratory Medicine (ARM) </option> <option value="aerobiology" > Aerobiology </option> <option value="aerospace" > Aerospace </option> <option value="agriculture" > Agriculture </option> <option value="agriengineering" > AgriEngineering </option> <option value="agrochemicals" > Agrochemicals </option> <option value="agronomy" > Agronomy </option> <option value="ai" > AI </option> <option value="air" > Air </option> <option value="algorithms" > Algorithms </option> <option value="allergies" > Allergies </option> <option value="alloys" > Alloys </option> <option value="analytica" > Analytica </option> <option value="analytics" > Analytics </option> <option value="anatomia" > Anatomia </option> <option value="anesthres" > Anesthesia Research </option> <option value="animals" > Animals </option> <option value="antibiotics" > Antibiotics </option> <option value="antibodies" > Antibodies </option> <option value="antioxidants" > Antioxidants </option> <option value="applbiosci" > Applied Biosciences </option> <option value="applmech" > Applied Mechanics </option> <option value="applmicrobiol" > Applied Microbiology </option> <option value="applnano" > Applied Nano </option> <option value="applsci" > Applied Sciences </option> <option value="asi" > Applied System Innovation (ASI) </option> <option value="appliedchem" > AppliedChem </option> <option value="appliedmath" > AppliedMath </option> <option value="aquacj" > Aquaculture Journal </option> <option value="architecture" > Architecture </option> <option value="arthropoda" > Arthropoda </option> <option value="arts" > Arts </option> <option value="astronomy" > Astronomy </option> <option value="atmosphere" > Atmosphere </option> <option value="atoms" > Atoms </option> <option value="audiolres" > Audiology Research </option> <option value="automation" > Automation </option> <option value="axioms" > Axioms </option> <option value="bacteria" > Bacteria </option> <option value="batteries" > Batteries </option> <option value="behavsci" > Behavioral Sciences </option> <option value="beverages" > Beverages </option> <option value="BDCC" > Big Data and Cognitive Computing (BDCC) </option> <option value="biochem" > BioChem </option> <option value="bioengineering" > Bioengineering </option> <option value="biologics" > Biologics </option> <option value="biology" > Biology </option> <option value="blsf" > Biology and Life Sciences Forum </option> <option value="biomass" > Biomass </option> <option value="biomechanics" > Biomechanics </option> <option value="biomed" > BioMed </option> <option value="biomedicines" > Biomedicines </option> <option value="biomedinformatics" > BioMedInformatics </option> <option value="biomimetics" > Biomimetics </option> <option value="biomolecules" > Biomolecules </option> <option value="biophysica" > Biophysica </option> <option value="biosensors" > Biosensors </option> <option value="biotech" > BioTech </option> <option value="birds" > Birds </option> <option value="blockchains" > Blockchains </option> <option value="brainsci" > Brain Sciences </option> <option value="buildings" > Buildings </option> <option value="businesses" > Businesses </option> <option value="carbon" > C </option> <option value="cancers" > Cancers </option> <option value="cardiogenetics" > Cardiogenetics </option> <option value="catalysts" > Catalysts </option> <option value="cells" > Cells </option> <option value="ceramics" > Ceramics </option> <option value="challenges" > Challenges </option> <option value="ChemEngineering" > ChemEngineering </option> <option value="chemistry" > Chemistry </option> <option value="chemproc" > Chemistry Proceedings </option> <option value="chemosensors" > Chemosensors </option> <option value="children" > Children </option> <option value="chips" > Chips </option> <option value="civileng" > CivilEng </option> <option value="cleantechnol" > Clean Technologies (Clean Technol.) </option> <option value="climate" > Climate </option> <option value="ctn" > Clinical and Translational Neuroscience (CTN) </option> <option value="clinbioenerg" > Clinical Bioenergetics </option> <option value="clinpract" > Clinics and Practice </option> <option value="clockssleep" > Clocks & Sleep </option> <option value="coasts" > Coasts </option> <option value="coatings" > Coatings </option> <option value="colloids" > Colloids and Interfaces </option> <option value="colorants" > Colorants </option> <option value="commodities" > Commodities </option> <option value="complications" > Complications </option> <option value="compounds" > Compounds </option> <option value="computation" > Computation </option> <option value="csmf" > Computer Sciences & Mathematics Forum </option> <option value="computers" > Computers </option> <option value="condensedmatter" > Condensed Matter </option> <option value="conservation" > Conservation </option> <option value="constrmater" > Construction Materials </option> <option value="cmd" > Corrosion and Materials Degradation (CMD) </option> <option value="cosmetics" > Cosmetics </option> <option value="covid" > COVID </option> <option value="crops" > Crops </option> <option value="cryo" > Cryo </option> <option value="cryptography" > Cryptography </option> <option value="crystals" > Crystals </option> <option value="cimb" > Current Issues in Molecular Biology (CIMB) </option> <option value="curroncol" > Current Oncology </option> <option value="dairy" > Dairy </option> <option value="data" > Data </option> <option value="dentistry" > Dentistry Journal </option> <option value="dermato" > Dermato </option> <option value="dermatopathology" > Dermatopathology </option> <option value="designs" > Designs </option> <option value="diabetology" > Diabetology </option> <option value="diagnostics" > Diagnostics </option> <option value="dietetics" > Dietetics </option> <option value="digital" > Digital </option> <option value="disabilities" > Disabilities </option> <option value="diseases" > Diseases </option> <option value="diversity" > Diversity </option> <option value="dna" > DNA </option> <option value="drones" > Drones </option> <option value="ddc" > Drugs and Drug Candidates (DDC) </option> <option value="dynamics" > Dynamics </option> <option value="earth" > Earth </option> <option value="ecologies" > Ecologies </option> <option value="econometrics" > Econometrics </option> <option value="economies" > Economies </option> <option value="education" > Education Sciences </option> <option value="electricity" > Electricity </option> <option value="electrochem" > Electrochem </option> <option value="electronicmat" > Electronic Materials </option> <option value="electronics" > Electronics </option> <option value="ecm" > Emergency Care and Medicine </option> <option value="encyclopedia" > Encyclopedia </option> <option value="endocrines" > Endocrines </option> <option value="energies" > Energies </option> <option value="esa" > Energy Storage and Applications (ESA) </option> <option value="eng" > Eng </option> <option value="engproc" > Engineering Proceedings </option> <option value="entropy" > Entropy </option> <option value="environsciproc" > Environmental Sciences Proceedings </option> <option value="environments" > Environments </option> <option value="epidemiologia" > Epidemiologia </option> <option value="epigenomes" > Epigenomes </option> <option value="ebj" > European Burn Journal (EBJ) </option> <option value="ejihpe" > European Journal of Investigation in Health, Psychology and Education (EJIHPE) </option> <option value="fermentation" > Fermentation </option> <option value="fibers" > Fibers </option> <option value="fintech" > FinTech </option> <option value="fire" > Fire </option> <option value="fishes" > Fishes </option> <option value="fluids" > Fluids </option> <option value="foods" > Foods </option> <option value="forecasting" > Forecasting </option> <option value="forensicsci" > Forensic Sciences </option> <option value="forests" > Forests </option> <option value="fossstud" > Fossil Studies </option> <option value="foundations" > Foundations </option> <option value="fractalfract" > Fractal and Fractional (Fractal Fract) </option> <option value="fuels" > Fuels </option> <option value="future" > Future </option> <option value="futureinternet" > Future Internet </option> <option value="futurepharmacol" > Future Pharmacology </option> <option value="futuretransp" > Future Transportation </option> <option value="galaxies" > Galaxies </option> <option value="games" > Games </option> <option value="gases" > Gases </option> <option value="gastroent" > Gastroenterology Insights </option> <option value="gastrointestdisord" > Gastrointestinal Disorders </option> <option value="gastronomy" > Gastronomy </option> <option value="gels" > Gels </option> <option value="genealogy" > Genealogy </option> <option value="genes" > Genes </option> <option value="geographies" > Geographies </option> <option value="geohazards" > GeoHazards </option> <option value="geomatics" > Geomatics </option> <option value="geometry" > Geometry </option> <option value="geosciences" > Geosciences </option> <option value="geotechnics" > Geotechnics </option> <option value="geriatrics" > Geriatrics </option> <option value="glacies" > Glacies </option> <option value="gucdd" > Gout, Urate, and Crystal Deposition Disease (GUCDD) </option> <option value="grasses" > Grasses </option> <option value="hardware" > Hardware </option> <option value="healthcare" > Healthcare </option> <option value="hearts" > Hearts </option> <option value="hemato" > Hemato </option> <option value="hematolrep" > Hematology Reports </option> <option value="heritage" > Heritage </option> <option value="histories" > Histories </option> <option value="horticulturae" > Horticulturae </option> <option value="hospitals" > Hospitals </option> <option value="humanities" > Humanities </option> <option value="humans" > Humans </option> <option value="hydrobiology" > Hydrobiology </option> <option value="hydrogen" > Hydrogen </option> <option value="hydrology" > Hydrology </option> <option value="hygiene" > Hygiene </option> <option value="immuno" > Immuno </option> <option value="idr" > Infectious Disease Reports </option> <option value="informatics" > Informatics </option> <option value="information" > Information </option> <option value="infrastructures" > Infrastructures </option> <option value="inorganics" > Inorganics </option> <option value="insects" > Insects </option> <option value="instruments" > Instruments </option> <option value="iic" > Intelligent Infrastructure and Construction </option> <option value="ijerph" > International Journal of Environmental Research and Public Health (IJERPH) </option> <option value="ijfs" > International Journal of Financial Studies (IJFS) </option> <option value="ijms" > International Journal of Molecular Sciences (IJMS) </option> <option value="IJNS" > International Journal of Neonatal Screening (IJNS) </option> <option value="ijpb" > International Journal of Plant Biology (IJPB) </option> <option value="ijt" > International Journal of Topology </option> <option value="ijtm" > International Journal of Translational Medicine (IJTM) </option> <option value="ijtpp" > International Journal of Turbomachinery, Propulsion and Power (IJTPP) </option> <option value="ime" > International Medical Education (IME) </option> <option value="inventions" > Inventions </option> <option value="IoT" > IoT </option> <option value="ijgi" > ISPRS International Journal of Geo-Information (IJGI) </option> <option value="J" > J </option> <option value="jal" > Journal of Ageing and Longevity (JAL) </option> <option value="jcdd" > Journal of Cardiovascular Development and Disease (JCDD) </option> <option value="jcto" > Journal of Clinical & Translational Ophthalmology (JCTO) </option> <option value="jcm" > Journal of Clinical Medicine (JCM) </option> <option value="jcs" > Journal of Composites Science (J. Compos. Sci.) </option> <option value="jcp" > Journal of Cybersecurity and Privacy (JCP) </option> <option value="jdad" > Journal of Dementia and Alzheimer's Disease (JDAD) </option> <option value="jdb" > Journal of Developmental Biology (JDB) </option> <option value="jeta" > Journal of Experimental and Theoretical Analyses (JETA) </option> <option value="jfb" > Journal of Functional Biomaterials (JFB) </option> <option value="jfmk" > Journal of Functional Morphology and Kinesiology (JFMK) </option> <option value="jof" > Journal of Fungi (JoF) </option> <option value="jimaging" > Journal of Imaging (J. Imaging) </option> <option value="jintelligence" > Journal of Intelligence (J. Intell.) </option> <option value="jlpea" > Journal of Low Power Electronics and Applications (JLPEA) </option> <option value="jmmp" > Journal of Manufacturing and Materials Processing (JMMP) </option> <option value="jmse" > Journal of Marine Science and Engineering (JMSE) </option> <option value="jmahp" > Journal of Market Access & Health Policy (JMAHP) </option> <option value="jmp" > Journal of Molecular Pathology (JMP) </option> <option value="jnt" > Journal of Nanotheranostics (JNT) </option> <option value="jne" > Journal of Nuclear Engineering (JNE) </option> <option value="ohbm" > Journal of Otorhinolaryngology, Hearing and Balance Medicine (JOHBM) </option> <option value="jop" > Journal of Parks </option> <option value="jpm" > Journal of Personalized Medicine (JPM) </option> <option value="jpbi" > Journal of Pharmaceutical and BioTech Industry (JPBI) </option> <option value="jor" > Journal of Respiration (JoR) </option> <option value="jrfm" > Journal of Risk and Financial Management (JRFM) </option> <option value="jsan" > Journal of Sensor and Actuator Networks (JSAN) </option> <option value="joma" > Journal of the Oman Medical Association (JOMA) </option> <option value="jtaer" > Journal of Theoretical and Applied Electronic Commerce Research (JTAER) </option> <option value="jvd" > Journal of Vascular Diseases (JVD) </option> <option value="jox" > Journal of Xenobiotics (JoX) </option> <option value="jzbg" > Journal of Zoological and Botanical Gardens (JZBG) </option> <option value="journalmedia" > Journalism and Media </option> <option value="kidneydial" > Kidney and Dialysis </option> <option value="kinasesphosphatases" > Kinases and Phosphatases </option> <option value="knowledge" > Knowledge </option> <option value="labmed" > LabMed </option> <option value="laboratories" > Laboratories </option> <option value="land" > Land </option> <option value="languages" > Languages </option> <option value="laws" > Laws </option> <option value="life" > Life </option> <option value="limnolrev" > Limnological Review </option> <option value="lipidology" > Lipidology </option> <option value="liquids" > Liquids </option> <option value="literature" > Literature </option> <option value="livers" > Livers </option> <option value="logics" > Logics </option> <option value="logistics" > Logistics </option> <option value="lubricants" > Lubricants </option> <option value="lymphatics" > Lymphatics </option> <option value="make" > Machine Learning and Knowledge Extraction (MAKE) </option> <option value="machines" > Machines </option> <option value="macromol" > Macromol </option> <option value="magnetism" > Magnetism </option> <option value="magnetochemistry" > Magnetochemistry </option> <option value="marinedrugs" > Marine Drugs </option> <option value="materials" > Materials </option> <option value="materproc" > Materials Proceedings </option> <option value="mca" > Mathematical and Computational Applications (MCA) </option> <option value="mathematics" > Mathematics </option> <option value="medsci" > Medical Sciences </option> <option value="msf" > Medical Sciences Forum </option> <option value="medicina" > Medicina </option> <option value="medicines" > Medicines </option> <option value="membranes" > Membranes </option> <option value="merits" > Merits </option> <option value="metabolites" > Metabolites </option> <option value="metals" > Metals </option> <option value="meteorology" > Meteorology </option> <option value="methane" > Methane </option> <option value="mps" > Methods and Protocols (MPs) </option> <option value="metrics" > Metrics </option> <option value="metrology" > Metrology </option> <option value="micro" > Micro </option> <option value="microbiolres" > Microbiology Research </option> <option value="micromachines" > Micromachines </option> <option value="microorganisms" > Microorganisms </option> <option value="microplastics" > Microplastics </option> <option value="minerals" > Minerals </option> <option value="mining" > Mining </option> <option value="modelling" > Modelling </option> <option value="mmphys" > Modern Mathematical Physics </option> <option value="molbank" > Molbank </option> <option value="molecules" > Molecules </option> <option value="mti" > Multimodal Technologies and Interaction (MTI) </option> <option value="muscles" > Muscles </option> <option value="nanoenergyadv" > Nanoenergy Advances </option> <option value="nanomanufacturing" > Nanomanufacturing </option> <option value="nanomaterials" > Nanomaterials </option> <option value="ndt" > NDT </option> <option value="network" > Network </option> <option value="neuroglia" > Neuroglia </option> <option value="neurolint" > Neurology International </option> <option value="neurosci" > NeuroSci </option> <option value="nitrogen" > Nitrogen </option> <option value="ncrna" > Non-Coding RNA (ncRNA) </option> <option value="nursrep" > Nursing Reports </option> <option value="nutraceuticals" > Nutraceuticals </option> <option value="nutrients" > Nutrients </option> <option value="obesities" > Obesities </option> <option value="oceans" > Oceans </option> <option value="onco" > Onco </option> <option value="optics" > Optics </option> <option value="oral" > Oral </option> <option value="organics" > Organics </option> <option value="organoids" > Organoids </option> <option value="osteology" > Osteology </option> <option value="oxygen" > Oxygen </option> <option value="parasitologia" > Parasitologia </option> <option value="particles" > Particles </option> <option value="pathogens" > Pathogens </option> <option value="pathophysiology" > Pathophysiology </option> <option value="pediatrrep" > Pediatric Reports </option> <option value="pets" > Pets </option> <option value="pharmaceuticals" > Pharmaceuticals </option> <option value="pharmaceutics" > Pharmaceutics </option> <option value="pharmacoepidemiology" > Pharmacoepidemiology </option> <option value="pharmacy" > Pharmacy </option> <option value="philosophies" > Philosophies </option> <option value="photochem" > Photochem </option> <option value="photonics" > Photonics </option> <option value="phycology" > Phycology </option> <option value="physchem" > Physchem </option> <option value="psf" > Physical Sciences Forum </option> <option value="physics" > Physics </option> <option value="physiologia" > Physiologia </option> <option value="plants" > Plants </option> <option value="plasma" > Plasma </option> <option value="platforms" > Platforms </option> <option value="pollutants" > Pollutants </option> <option value="polymers" > Polymers </option> <option value="polysaccharides" > Polysaccharides </option> <option value="populations" > Populations </option> <option value="poultry" > Poultry </option> <option value="powders" > Powders </option> <option value="proceedings" > Proceedings </option> <option value="processes" > Processes </option> <option value="prosthesis" > Prosthesis </option> <option value="proteomes" > Proteomes </option> <option value="psychiatryint" > Psychiatry International </option> <option value="psychoactives" > Psychoactives </option> <option value="psycholint" > Psychology International </option> <option value="publications" > Publications </option> <option value="qubs" > Quantum Beam Science (QuBS) </option> <option value="quantumrep" > Quantum Reports </option> <option value="quaternary" > Quaternary </option> <option value="radiation" > Radiation </option> <option value="reactions" > Reactions </option> <option value="realestate" > Real Estate </option> <option value="receptors" > Receptors </option> <option value="recycling" > Recycling </option> <option value="rsee" > Regional Science and Environmental Economics (RSEE) </option> <option value="religions" > Religions </option> <option value="remotesensing" > Remote Sensing </option> <option value="reports" > Reports </option> <option value="reprodmed" > Reproductive Medicine (Reprod. Med.) </option> <option value="resources" > Resources </option> <option value="rheumato" > Rheumato </option> <option value="risks" > Risks </option> <option value="robotics" > Robotics </option> <option value="ruminants" > Ruminants </option> <option value="safety" > Safety </option> <option value="sci" > Sci </option> <option value="scipharm" > Scientia Pharmaceutica (Sci. Pharm.) </option> <option value="sclerosis" > Sclerosis </option> <option value="seeds" > Seeds </option> <option value="sensors" > Sensors </option> <option value="separations" > Separations </option> <option value="sexes" > Sexes </option> <option value="signals" > Signals </option> <option value="sinusitis" > Sinusitis </option> <option value="smartcities" > Smart Cities </option> <option value="socsci" > Social Sciences </option> <option value="siuj" > Société Internationale d’Urologie Journal (SIUJ) </option> <option value="societies" > Societies </option> <option value="software" > Software </option> <option value="soilsystems" > Soil Systems </option> <option value="solar" > Solar </option> <option value="solids" > Solids </option> <option value="spectroscj" > Spectroscopy Journal </option> <option value="sports" > Sports </option> <option value="standards" > Standards </option> <option value="stats" > Stats </option> <option value="stresses" > Stresses </option> <option value="surfaces" > Surfaces </option> <option value="surgeries" > Surgeries </option> <option value="std" > Surgical Techniques Development </option> <option value="sustainability" > Sustainability </option> <option value="suschem" > Sustainable Chemistry </option> <option value="symmetry" > Symmetry </option> <option value="synbio" > SynBio </option> <option value="systems" > Systems </option> <option value="targets" > Targets </option> <option value="taxonomy" > Taxonomy </option> <option value="technologies" > Technologies </option> <option value="telecom" > Telecom </option> <option value="textiles" > Textiles </option> <option value="thalassrep" > Thalassemia Reports </option> <option value="therapeutics" > Therapeutics </option> <option value="thermo" > Thermo </option> <option value="timespace" > Time and Space </option> <option value="tomography" > Tomography </option> <option value="tourismhosp" > Tourism and Hospitality </option> <option value="toxics" > Toxics </option> <option value="toxins" > Toxins </option> <option value="transplantology" > Transplantology </option> <option value="traumacare" > Trauma Care </option> <option value="higheredu" > Trends in Higher Education </option> <option value="tropicalmed" > Tropical Medicine and Infectious Disease (TropicalMed) </option> <option value="universe" selected='selected'> Universe </option> <option value="urbansci" > Urban Science </option> <option value="uro" > Uro </option> <option value="vaccines" > Vaccines </option> <option value="vehicles" > Vehicles </option> <option value="venereology" > Venereology </option> <option value="vetsci" > Veterinary Sciences </option> <option value="vibration" > Vibration </option> <option value="virtualworlds" > Virtual Worlds </option> <option value="viruses" > Viruses </option> <option value="vision" > Vision </option> <option value="waste" > Waste </option> <option value="water" > Water </option> <option value="wild" > Wild </option> <option value="wind" > Wind </option> <option value="women" > Women </option> <option value="world" > World </option> <option value="wevj" > World Electric Vehicle Journal (WEVJ) </option> <option value="youth" > Youth </option> <option value="zoonoticdis" > Zoonotic Diseases </option> </select> </div> <div class="large-2 medium-2 small-6 columns "> <div class=""> <div class="search-input-label">Article Type</div> </div> <select id="article_type" tabindex="4" name="article_type" class="chosen-select"> <option value="">All Article Types</option> <option value="research-article">Article</option> <option value="review-article">Review</option> <option value="rapid-communication">Communication</option> <option value="editorial">Editorial</option> <option value="abstract">Abstract</option> <option value="book-review">Book Review</option> <option value="brief-communication">Brief Communication</option> <option value="brief-report">Brief Report</option> <option value="case-report">Case Report</option> <option value="clinicopathological-challenge">Clinicopathological Challenge</option> <option value="article-commentary">Comment</option> <option value="commentary">Commentary</option> <option value="concept-paper">Concept Paper</option> <option value="conference-report">Conference Report</option> <option value="correction">Correction</option> <option value="creative">Creative</option> <option value="data-descriptor">Data Descriptor</option> <option value="discussion">Discussion</option> <option value="Entry">Entry</option> <option value="essay">Essay</option> <option value="expression-of-concern">Expression of Concern</option> <option value="extended-abstract">Extended Abstract</option> <option value="field-guide">Field Guide</option> <option value="guidelines">Guidelines</option> <option value="hypothesis">Hypothesis</option> <option value="interesting-image">Interesting Images</option> <option value="letter">Letter</option> <option value="books-received">New Book Received</option> <option value="obituary">Obituary</option> <option value="opinion">Opinion</option> <option value="perspective">Perspective</option> <option value="proceedings">Proceeding Paper</option> <option value="project-report">Project Report</option> <option value="protocol">Protocol</option> <option value="registered-report">Registered Report</option> <option value="reply">Reply</option> <option value="retraction">Retraction</option> <option value="note">Short Note</option> <option value="study-protocol">Study Protocol</option> <option value="systematic_review">Systematic Review</option> <option value="technical-note">Technical Note</option> <option value="tutorial">Tutorial</option> <option value="viewpoint">Viewpoint</option> </select> </div> <div class="large-1 medium-1 small-6 end columns small-push-6 medium-reset-order large-reset-order js-search-collapsed-button-container"> <div class="search-input-label"> </div> <input type="submit" id="search" value="Search" class="button button--dark button--full-width searchButton1 US_SearchButton" tabindex="12"> </div> <div class="large-1 medium-1 small-6 end columns large-text-left small-only-text-center small-pull-6 medium-reset-order large-reset-order js-search-collapsed-link-container"> <div class="search-input-label"> </div> <a class="main-search-clear search-container__link" href="#" onclick="openAdvanced(''); return false;">Advanced<span class="show-for-small-only"> Search</span></a> </div> </div> </div> <div class="search-container__advanced" style="margin-top: 0; padding-top: 0px; background-color: inherit; color: inherit;"> <div class="row"> <div class="large-2 medium-2 columns show-for-medium-up"> </div> <div class="large-2 medium-2 small-6 columns "> <div class=""> <div class="search-input-label">Section</div> </div> <select id="section" tabindex="5" name="section" class="chosen-select"> <option value=""></option> </select> </div> <div class="large-2 medium-2 small-6 columns "> <div class=""> <div class="search-input-label">Special Issue</div> </div> <select id="special_issue" tabindex="6" name="special_issue" class="chosen-select"> <option value=""></option> </select> </div> <div class="large-1 medium-1 small-6 end columns "> <div class="search-input-label">Volume</div> <input type="text" id="volume" tabindex="7" name="volume" placeholder="..." value="" /> </div> <div class="large-1 medium-1 small-6 end columns "> <div class="search-input-label">Issue</div> <input type="text" id="issue" tabindex="8" name="issue" placeholder="..." value="" /> </div> <div class="large-1 medium-1 small-6 end columns "> <div class="search-input-label">Number</div> <input type="text" id="number" tabindex="9" name="number" placeholder="..." value="" /> </div> <div class="large-1 medium-1 small-6 end columns "> <div class="search-input-label">Page</div> <input type="text" id="page" tabindex="10" name="page" placeholder="..." value="" /> </div> <div class="large-1 medium-1 small-6 columns small-push-6 medium-reset order large-reset-order medium-reset-order js-search-expanded-button-container"></div> <div class="large-1 medium-1 small-6 columns large-text-left small-only-text-center small-pull-6 medium-reset-order large-reset-order js-search-expanded-link-container"></div> </div> </div> </form> <form id="advanced-search" class="large-12 medium-12 columns"> <div class="search-container__advanced"> <div id="advanced-search-template" class="row advanced-search-row"> <div class="large-2 medium-2 small-12 columns show-for-medium-up"> </div> <div class="large-2 medium-2 small-3 columns connector-div"> <div class="search-input-label"><span class="show-for-medium-up">Logical Operator</span><span class="show-for-small">Operator</span></div> <select class="connector"> <option value="and">AND</option> <option value="or">OR</option> </select> </div> <div class="large-3 medium-3 small-6 columns search-text-div"> <div class="search-input-label">Search Text</div> <input type="text" class="search-text" placeholder="Search text"> </div> <div class="large-2 medium-2 small-6 large-offset-0 medium-offset-0 small-offset-3 columns search-field-div"> <div class="search-input-label">Search Type</div> <select class="search-field"> <option value="all">All fields</option> <option value="title">Title</option> <option value="abstract">Abstract</option> <option value="keywords">Keywords</option> <option value="authors">Authors</option> <option value="affiliations">Affiliations</option> <option value="doi">Doi</option> <option value="full_text">Full Text</option> <option value="references">References</option> </select> </div> <div class="large-1 medium-1 small-3 columns"> <div class="search-input-label"> </div> <div class="search-action-div"> <div class="search-plus"> <i class="material-icons">add_circle_outline</i> </div> </div> <div class="search-action-div"> <div class="search-minus"> <i class="material-icons">remove_circle_outline</i> </div> </div> </div> <div class="large-1 medium-1 small-6 large-offset-0 medium-offset-0 small-offset-3 end columns"> <div class="search-input-label"> </div> <input class="advanced-search-button button button--dark search-submit" type="submit" value="Search"> </div> <div class="large-1 medium-1 small-6 end columns show-for-medium-up"></div> </div> </div> </form> </div> <div class="header-divider"> </div> <div class="breadcrumb row full-row"> <div style="position: absolute; right: 40px; z-index: 10; top: 5px;"> <div class="iflogo1"> <a href="https://www.scopus.com/sourceid/21100903488" target="_blank" rel="noopener noreferrer" style="text-decoration: none;"> <img src="https://pub.mdpi-res.com/img/journal_indexing_logos/CS_no_number.svg?62107aae53c39662?1732694169" class="iflogo2"> <div class="iflogo1__citescore-number">4.3</div> </a> </div> <div class="iflogo1"> <a href="/journal/universe/stats" target="_blank" rel="noopener noreferrer" style="text-decoration: none;"> <img src="https://pub.mdpi-res.com/img/journal_indexing_logos/IF_no_number.svg?af8a884fb765d812?1732694169" class="iflogo2"> <div class="iflogo1__if-number">2.5</div> </a> </div> </div> <div class="breadcrumb__element"> <a href="/about/journals">Journals</a> </div> <div class="breadcrumb__element"> <a href="#">Universe</a> </div> </div> </header> <div id="main-content" class=""> <div class="row full-width" data-equalizer="three-columns"> <div id="middle-column" class="content__column large-6 large-push-3 medium-6 medium-push-3 small-12 columns end middle-bordered"> <div id="js-small-main-top-container"> </div> <div class="content__container content__container__orbit content__container__orbit__separate"> <div id="title-story" class=""> <ul class="title-story-orbit" data-orbit> <li > <a href="/2218-1997/10/8/316"> <img src="https://pub.mdpi-res.com/title_story/title_story_17292374027796.jpg?1732694169" alt="Prospects for Time-Domain and Multi-Messenger Science with AXIS" /> <div class="orbit-caption"> Prospects for Time-Domain and Multi-Messenger Science with AXIS </div> </a> </li> <li class="hidden"> <a href="/2218-1997/10/9/349"> <img src="https://pub.mdpi-res.com/title_story/title_story_17292372747604.jpg?1732694169" alt="Characterisation of the Atmosphere in Very High Energy Gamma-Astronomy for Imaging Atmospheric Cherenkov Telescopes" /> <div class="orbit-caption"> Characterisation of the Atmosphere in Very High Energy Gamma-Astronomy for Imaging Atmospheric Cherenkov Telescopes </div> </a> </li> <li class="hidden"> <a href="/2218-1997/10/7/296"> <img src="https://pub.mdpi-res.com/title_story/title_story_17292369100971.jpg?1732694169" alt="Lorentzian Quantum Cosmology from Effective Spin Foams" /> <div class="orbit-caption"> Lorentzian Quantum Cosmology from Effective Spin Foams </div> </a> </li> <li class="hidden"> <a href="/2218-1997/10/7/293"> <img src="https://pub.mdpi-res.com/title_story/title_story_17292364723295.jpg?1732694169" alt="Isospin QCD as a Laboratory for Dense QCD" /> <div class="orbit-caption"> Isospin QCD as a Laboratory for Dense QCD </div> </a> </li> </ul> </div> </div> <div class="content__container"> Congratulations to Prof. Roger Penrose, Advisory Board member of <em>Universe</em>, for receiving the Nobel Prize in Physics 2020. </div> <div class="content__container"> <div class="custom-accordion-for-small-screen-link show-for-small-only"> <h2 class="no-padding-left no-margin">Journal Description</h2> </div> <div class="custom-accordion-for-small-screen-content show-for-medium-up"> <div class="journal__description"> <h1> <em>Universe</em> </h1> <div class="journal__description__content"> <em>Universe</em> is a <a href="https://www.mdpi.com/editorial_process">peer-reviewed</a> open access journal focused on principles and new discoveries in the universe. <em>Universe</em> is published monthly online by MDPI.<br /> <ul> <li><strong><span class="label openaccess"><a title="Open Access" href="https://www.mdpi.com/openaccess">Open Access</a></span></strong>— free for readers, with <a href="https://www.mdpi.com/journal/universe/apc">article processing charges (APC)</a> paid by authors or their institutions.</li> <li><strong>High Visibility:</strong> indexed within <a href="https://www.scopus.com/sourceid/21100903488">Scopus</a>, <a href="https://mjl.clarivate.com/search-results?issn=2218-1997&hide_exact_match_fl=true&utm_source=mjl&utm_medium=share-by-link&utm_campaign=search-results-share-this-journal">SCIE (Web of Science)</a>, <a href="https://ui.adsabs.harvard.edu/search/filter_bibstem_facet_fq_bibstem_facet=AND&filter_bibstem_facet_fq_bibstem_facet=bibstem_facet%3A%22Univ%22&fq=%7B!type%3Daqp%20v%3D%24fq_bibstem_facet%7D&fq_bibstem_facet=(bibstem_facet%3A%22Univ%22)&q=pub%3A%22universe%22&sort=date%20desc%2C%20bibcode%20desc&p_=0" target="_blank" rel="noopener noreferrer">Astrophysics Data System</a>, <a href="https://inspirehep.net/">INSPIRE</a>, <a href="https://sso.cas.org/as/authorization.oauth2?response_type=code&client_id=scifinder-n&redirect_uri=https%3A%2F%2Fscifinder-n.cas.org%2Fpa%2Foidc%2Fcb&state=eyJ6aXAiOiJERUYiLCJhbGciOiJkaXIiLCJlbmMiOiJBMTI4Q0JDLUhTMjU2Iiwia2lkIjoianMiLCJzdWZmaXgiOiJUYWozcGUu">CAPlus / SciFinder</a>, <a href="https://www.theiet.org/publishing/inspec/inspec-content-coverage/">Inspec</a>, and <a href="https://www.mdpi.com/journal/universe/indexing">other databases</a>.</li> <li><strong><strong>Journal Rank: </strong></strong>JCR - Q2 (Astronomy and Astrophysics) / CiteScore - Q2 (<em>General Physics and Astronomy</em>)</li> <li><strong>Rapid Publication:</strong> manuscripts are peer-reviewed and a first decision is provided to authors approximately 21.8 days after submission; acceptance to publication is undertaken in 3.7 days (median values for papers published in this journal in the first half of 2024).</li> <li><strong>Recognition of Reviewers:</strong> reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.</li> <li><strong>Companion journal: <em><a href="https://www.mdpi.com/journal/astronomy">Astronomy</a>.</em></strong></li> </ul> </div> <div style="margin-bottom: 15px;"> <strong>Impact Factor:</strong> 2.5 (2023); 5-Year Impact Factor: 2.3 (2023) </div> <div> <a href="/journal/universe/imprint" class="UI_JournalImprintsInfoButton"> <i class="material-icons spaced-link">subject</i> Imprint Information </a>    <a href="/journal/universe/universe_flyer.pdf" class="UD_JournalFlyer"> <i class="material-icons spaced-link">get_app</i> Journal Flyer </a>     <a class="oa-link" href="https://www.mdpi.com/about/openaccess"> <i class="material icons spaced-link"></i> Open Access </a>     <strong> ISSN: 2218-1997 </strong> </div> <div style="clear: both;"></div> </div> </div> </div> <div class="content__container content__container--overflow-initial"> <div class="custom-accordion-for-small-screen-link active"> <h2 class="no-padding-left">Latest Articles</h2> </div> <div class="custom-accordion-for-small-screen-content"> <div class="expanding-div collapsed"> <div class="generic-item article-item no-border"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 17 pages, 5124 KiB   </span> <a href="/2218-1997/10/12/437/pdf?version=1732517796" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Pulsation in Hot Main-Sequence Stars: Comparison of Observations with Models" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/12/437">Pulsation in Hot Main-Sequence Stars: Comparison of Observations with Models</a> <div class="authors"> by <span class="inlineblock "><strong>Luis A. Balona</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(12), 437; <a href="https://doi.org/10.3390/universe10120437">https://doi.org/10.3390/universe10120437</a> - 25 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> The locations of hot pulsating variables in the H–R diagram are found using the effective temperatures derived from spectroscopic analysis and luminosities from Gaia parallaxes. Frequency peaks extracted from TESS photometry were used to compare with model predictions. A large number of stars <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/12/437/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> The locations of hot pulsating variables in the H–R diagram are found using the effective temperatures derived from spectroscopic analysis and luminosities from Gaia parallaxes. Frequency peaks extracted from TESS photometry were used to compare with model predictions. A large number of stars with pulsation frequencies similar to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> Scuti variables were found between the predicted <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> Scuti and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> Cephei instability regions, contrary to the models. These Maia variables cannot be explained by rapid rotation. There is a serious mismatch between the observed and predicted frequencies for stars within the known <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> Scuti instability strip. In <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> Scuti and Maia stars, the frequency at the maximum amplitude as a function of the effective temperature was found to have a surprisingly well-defined upper envelope. The majority of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> Doradus stars were found within the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> Scuti instability strip. This is difficult to understand unless pulsational driving is non-linear. Non-linearity may also explain the huge variety in frequency patterns and the presence of low frequencies in hot <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> Scuti stars. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> Doradus stars were found all along the main sequence and into the B-star region, where they merged with SPB variables. There seemed to be no distinct instability regions in the H–R diagram. It was concluded that current models do not offer a satisfactory description of observations. <a href="/2218-1997/10/12/437">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/universe/special_issues/34SMK66L52 ">Variable Stars in the 21st Century: From Microvariability to Megavariability</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/12/437/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1528473"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1528473"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1528473" data-cycle-prev="#prev1528473" data-cycle-progressive="#images1528473" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1528473-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g001-550.jpg?1732517970" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1528473" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1528473-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g002-550.jpg?1732517972'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1528473-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g003-550.jpg?1732517973'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1528473-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g004-550.jpg?1732517975'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1528473-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g005-550.jpg?1732517978'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1528473-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g006-550.jpg?1732517980'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1528473-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g007-550.jpg?1732517983'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1528473-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g008-550.jpg?1732517984'><p>Figure 8</p></div></script></div></div><div id="article-1528473-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g001-550.jpg?1732517970" title=" <strong>Figure 1</strong><br/> <p>The location of various classes of pulsating stars in the H–R diagram (<b>left</b> panels) and location of Dziembowski models showing unstable p and g modes (<b>right</b> panels). Only stars with spectroscopic determinations of the effective temperature are shown. The dashed line is the zero-age main sequence. Also shown are the instability regions in BCEP and SPB stars for the solar abundance models from Miglio et al. [<a href="#B40-universe-10-00437" class="html-bibr">40</a>] (solid curve) and the hot and cool edges of the DSCT and GDOR stars from Dupret et al. [<a href="#B1-universe-10-00437" class="html-bibr">1</a>] (thick black lines) and Xiong et al. [<a href="#B2-universe-10-00437" class="html-bibr">2</a>] (orange lines).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/437'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g002-550.jpg?1732517972" title=" <strong>Figure 2</strong><br/> <p>The same as the left panel of <a href="#universe-10-00437-f001" class="html-fig">Figure 1</a> but with stars separated according to the way their effective temperatures were obtained. Stars with spectroscopic determinations of <math display="inline"><semantics> <msub> <mi>T</mi> <mi>eff</mi> </msub> </semantics></math> are shown in the left panel. The middle panel shows stars where <math display="inline"><semantics> <msub> <mi>T</mi> <mi>eff</mi> </msub> </semantics></math> was obtained from narrow-band photometry. Stars with less precise determinations of <math display="inline"><semantics> <msub> <mi>T</mi> <mi>eff</mi> </msub> </semantics></math> are shown in the right hand panel. Stars in the panels on the right, where for some stars, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>eff</mi> </msub> </semantics></math> was estimated from the spectral type, were dithered to eliminate vertical stripes corresponding to distinct subtypes.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/437'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g003-550.jpg?1732517973" title=" <strong>Figure 3</strong><br/> <p>The ratio <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>/</mo> <msub> <mi>N</mi> <mi>MS</mi> </msub> </mrow> </semantics></math> as a function of the effective temperature. <span class="html-italic">N</span> is the number of stars of the particular variability class and <math display="inline"><semantics> <msub> <mi>N</mi> <mi>MS</mi> </msub> </semantics></math> is the number of main-sequence stars within the temperature bin size. The vertical dashed lines indicate the minimum and maximum temperatures of the hot edges of the DSCT and GDOR stars predicted by various models. The cool edge of the BCEP instability region from Miglio et al. [<a href="#B39-universe-10-00437" class="html-bibr">39</a>] is also shown.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/437'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g004-550.jpg?1732517975" title=" <strong>Figure 4</strong><br/> <p>The top panel shows the frequency of the largest amplitude of various types of TESS pulsating stars as a function of the effective temperature. The bottom panel shows the frequencies of unstable modes with <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>≤</mo> <mn>2</mn> </mrow> </semantics></math> in non-rotating Dziembowski models.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/437'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g005-550.jpg?1732517978" title=" <strong>Figure 5</strong><br/> <p>The top panel shows the frequency of the maximum amplitude as a function of the effective temperature for the DSCT stars. The black outline is the envelope of the highest amplitude growth rate of low-degree p modes shown in Figure 9 of Xiong et al. [<a href="#B2-universe-10-00437" class="html-bibr">2</a>]. The blue outline is the envelope of the unstable modes from the Dziembowski models. The frequencies of the unstable modes in the Dziembowski models is shown in the bottom panel.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/437'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g006-550.jpg?1732517980" title=" <strong>Figure 6</strong><br/> <p>The top panel shows the locations of TESS DSCT stars in the H–R diagram enclosed by a schematic trapezium (magenta). The hot and cool edges were from Dupret et al. [<a href="#B1-universe-10-00437" class="html-bibr">1</a>] (black lines) and Xiong et al. [<a href="#B2-universe-10-00437" class="html-bibr">2</a>] (orange lines). The bottom panel shows the TESS GDOR stars enclosed by a schematic triangle (green) and corresponding hot and cool edges. The diagonal dashed line is the zero-age main sequence. In both panels, only stars with spectroscopic estimates of <math display="inline"><semantics> <msub> <mi>T</mi> <mi>eff</mi> </msub> </semantics></math> are shown.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/437'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g007-550.jpg?1732517983" title=" <strong>Figure 7</strong><br/> <p>The frequency of the maximum amplitude as a function of the effective temperature. The top-left panel shows all the DSCT and MAIA stars enclosed by a triangular envelope. The other panels on the left show the stars selected according to <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>L</mi> <mo>/</mo> <msub> <mi>L</mi> <mo>⊙</mo> </msub> </mrow> </semantics></math>, the luminosity above the zero-age main sequence. The panels on the right are the corresponding frequencies of the radial modes from the Dziembowski models.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/437'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00437/article_deploy/html/images/universe-10-00437-g008-550.jpg?1732517984" title=" <strong>Figure 8</strong><br/> <p>All observed frequencies in the BCEP, BCEP+SPB or pure SPB stars in the BCEP temperature range are shown in the top panel. The bottom panel shows unstable modes for <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>≤</mo> <mn>2</mn> </mrow> </semantics></math> from the Dziembowski models.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/437'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="extending-content content-ready"> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 9 pages, 312 KiB   </span> <a href="/2218-1997/10/12/436/pdf?version=1732270452" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="On the Hypothesis of Exact Conservation of Charged Weak Hadronic Vector Current in the Standard Model" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/12/436">On the Hypothesis of Exact Conservation of Charged Weak Hadronic Vector Current in the Standard Model</a> <div class="authors"> by <span class="inlineblock "><strong>Derar Altarawneh</strong>, </span><span class="inlineblock "><strong>Roman Höllwieser</strong> and </span><span class="inlineblock "><strong>Markus Wellenzohn</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(12), 436; <a href="https://doi.org/10.3390/universe10120436">https://doi.org/10.3390/universe10120436</a> - 22 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> We investigate the reliability of the conservation of the vector current (CVC) hypothesis in the neutron beta decay (<i>n</i> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>β</mi><mo>−</mo></msup></semantics></math></inline-formula> decay). We calculate the contribution of the phenomenological term, responsible for the CVC in the hadronic current of the <i>n</i> <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/12/436/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> We investigate the reliability of the conservation of the vector current (CVC) hypothesis in the neutron beta decay (<i>n</i> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>β</mi><mo>−</mo></msup></semantics></math></inline-formula> decay). We calculate the contribution of the phenomenological term, responsible for the CVC in the hadronic current of the <i>n</i> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>β</mi><mo>−</mo></msup></semantics></math></inline-formula> decay (or the CVC effect), to the neutron lifetime. We show that the CVC effect increases the neutron lifetime with a relative contribution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>8.684</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula>. This leads to the increase of the neutron lifetime by 76.4 s with respect to the world averaged value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>τ</mi><mi>n</mi></msub><mo>=</mo><mn>880.2</mn><mrow><mo>(</mo><mn>1.0</mn><mo>)</mo></mrow><mi mathvariant="normal">s</mi></mrow></semantics></math></inline-formula> from the Particle Data Group. We show that since in the Standard Model there are no interactions that are able to cancel such a huge increase in the neutron lifetime, we have to turn to the interactions beyond the Standard Model, the contribution of which to the neutron lifetime reduces to the Fierz interference term <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>b</mi><mi>F</mi></msub></semantics></math></inline-formula> only. Cancelling the CVC effect at the level of the experimental accuracy, we obtain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>b</mi><mi>F</mi></msub><mo>=</mo><mn>0.1219</mn><mrow><mo>(</mo><mn>12</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. If this value cannot be accepted for the Fierz interference term, the CVC effect induces irresistible problems for description and understanding of the <i>n</i> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>β</mi><mo>−</mo></msup></semantics></math></inline-formula> decay. <a href="/2218-1997/10/12/436">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/universe/sections/high_energy_nuclear_and_particle_physics">High Energy Nuclear and Particle Physics</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/12/436/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="absgraph cycle-slideshow"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1526996-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00436/article_deploy/html/images/universe-10-00436-g0A1-550.jpg?1732270557" alt="" style="border: 0;"><p>Figure A1</p></div></div></div><div id="article-1526996-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00436/article_deploy/html/images/universe-10-00436-g0A1-550.jpg?1732270557" title=" <strong>Figure A1</strong><br/> <p>The amplitude of the <span class="html-italic">n</span> radiative <math display="inline"><semantics> <msup> <mi>β</mi> <mo>−</mo> </msup> </semantics></math> decay in the tree approximation is defined using Feynman diagrams.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/436'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 28 pages, 10407 KiB   </span> <a href="/2218-1997/10/12/435/pdf?version=1732267142" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="On the Viscous Ringed Disk Evolution in the Kerr Black Hole Spacetime" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/12/435">On the Viscous Ringed Disk Evolution in the Kerr Black Hole Spacetime</a> <div class="authors"> by <span class="inlineblock "><strong>Daniela Pugliese</strong>, </span><span class="inlineblock "><strong>Zdenek Stuchlík</strong> and </span><span class="inlineblock "><strong>Vladimir Karas</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(12), 435; <a href="https://doi.org/10.3390/universe10120435">https://doi.org/10.3390/universe10120435</a> - 22 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Supermassive black holes <b>(SMBHs)</b> are observed in active galactic nuclei interacting with their environments, where chaotical, discontinuous accretion episodes may leave matter remnants orbiting the central attractor in the form of sequences of orbiting toroidal structures, with strongly different features as different rotation <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/12/435/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Supermassive black holes <b>(SMBHs)</b> are observed in active galactic nuclei interacting with their environments, where chaotical, discontinuous accretion episodes may leave matter remnants orbiting the central attractor in the form of sequences of orbiting toroidal structures, with strongly different features as different rotation orientations with respect to the central Kerr <b>BH</b>. Such ringed structures can be characterized by peculiar internal dynamics, where co-rotating and counter-rotating accretion stages can be mixed and distinguished by tori interaction, drying–feeding processes, screening effects, and inter-disk jet emission. A ringed accretion disk (<b>RAD</b>) is a full general relativistic model of a cluster of toroidal disks, an aggregate of axi-symmetric co-rotating and counter-rotating disks orbiting in the equatorial plane of a single central Kerr <b>SMBH</b>. In this work, we discuss the time evolution of a ringed disk. Our analysis is a detailed numerical study of the evolving <b>RAD</b> properties formed by relativistic thin disks, using a thin disk model and solving a diffusion-like evolution equation for an <b>RAD</b> in the Kerr spacetime, adopting an initial wavy (ringed) density profile. The <b>RAD</b> reaches a single-disk phase, building accretion to the inner edge regulated by the inner edge boundary conditions. The mass flux, the radial drift, and the disk mass of the ringed disk are evaluated and compared to each of its disk components. During early inter-disk interaction, the ring components spread, destroying the internal ringed structure and quickly forming a single disk with timescales governed by ring viscosity prescriptions. Different viscosities and boundary conditions have been tested. We propose that a system of viscously spreading accretion rings can originate as a product of tidal disruption of a multiple stellar system that comes too close to an <b>SMBH</b>. <a href="/2218-1997/10/12/435">Full article</a> </div> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/12/435/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1526860"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1526860"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1526860" data-cycle-prev="#prev1526860" data-cycle-progressive="#images1526860" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1526860-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g001-550.jpg?1732267216" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1526860" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g002-550.jpg?1732267217'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g003-550.jpg?1732267218'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g004-550.jpg?1732267219'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g005-550.jpg?1732267220'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g006-550.jpg?1732267221'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g007-550.jpg?1732267222'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g008-550.jpg?1732267224'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g009-550.jpg?1732267225'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g010-550.jpg?1732267226'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g011-550.jpg?1732267227'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g012-550.jpg?1732267228'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g013-550.jpg?1732267229'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g014-550.jpg?1732267230'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g015-550.jpg?1732267231'><p>Figure 15</p></div> --- <div class='openpopupgallery' data-imgindex='15' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g016-550.jpg?1732267232'><p>Figure 16</p></div> --- <div class='openpopupgallery' data-imgindex='16' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g017-550.jpg?1732267233'><p>Figure 17</p></div> --- <div class='openpopupgallery' data-imgindex='17' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g018-550.jpg?1732267234'><p>Figure 18</p></div> --- <div class='openpopupgallery' data-imgindex='18' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g019-550.jpg?1732267235'><p>Figure 19</p></div> --- <div class='openpopupgallery' data-imgindex='19' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g020-550.jpg?1732267236'><p>Figure 20</p></div> --- <div class='openpopupgallery' data-imgindex='20' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g021-550.jpg?1732267237'><p>Figure 21</p></div> --- <div class='openpopupgallery' data-imgindex='21' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g022-550.jpg?1732267237'><p>Figure 22</p></div> --- <div class='openpopupgallery' data-imgindex='22' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g023-550.jpg?1732267238'><p>Figure 23</p></div> --- <div class='openpopupgallery' data-imgindex='23' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g024-550.jpg?1732267239'><p>Figure 24</p></div> --- <div class='openpopupgallery' data-imgindex='24' data-target='article-1526860-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g0A1-550.jpg?1732267240'><p>Figure A1</p></div></script></div></div><div id="article-1526860-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g001-550.jpg?1732267216" title=" <strong>Figure 1</strong><br/> <p>Geodesic structure of the Kerr spacetime. Spin <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> </msub> <mo>≡</mo> <mn>0.37258</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi>a</mi> <mrow> <mi>γ</mi> </mrow> <mi>I</mi> </msubsup> <mo>≡</mo> <mn>0.3137</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi>a</mi> <mrow> <mi>γ</mi> </mrow> <mrow> <mi>I</mi> <mi>I</mi> </mrow> </msubsup> <mo>≡</mo> <mn>0.6383</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics></math> are defined in Section Constraints from <b>RAD</b> Systems. The black region is <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>&lt;</mo> <msub> <mi>r</mi> <mo>+</mo> </msub> </mrow> </semantics></math>, with <math display="inline"><semantics> <msub> <mi>r</mi> <mo>+</mo> </msub> </semantics></math> being the outer horizon of the Kerr geometry, the gray region is <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>&lt;</mo> <msubsup> <mi>r</mi> <mrow> <mi>ϵ</mi> </mrow> <mo>+</mo> </msubsup> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msubsup> <mi>r</mi> <mrow> <mi>ϵ</mi> </mrow> <mo>+</mo> </msubsup> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> is the outer ergosurface on the attractor equatorial plane. Radius <math display="inline"><semantics> <msubsup> <mi>r</mi> <mrow> <mi>m</mi> <mi>s</mi> <mi>o</mi> </mrow> <mo>±</mo> </msubsup> </semantics></math> is the marginally stable orbit, <math display="inline"><semantics> <msubsup> <mi>r</mi> <mrow> <mi>γ</mi> </mrow> <mo>±</mo> </msubsup> </semantics></math> is the marginally circular orbit, and <math display="inline"><semantics> <msubsup> <mi>r</mi> <mrow> <mi>m</mi> <mi>b</mi> <mi>o</mi> </mrow> <mo>±</mo> </msubsup> </semantics></math> is the marginally bounded orbit for counter-rotating and co-rotating particles, respectively. Radii <math display="inline"><semantics> <mrow> <msubsup> <mi>r</mi> <mrow> <mo>[</mo> <mi>m</mi> <mi>b</mi> <mi>o</mi> <mo>]</mo> </mrow> <mo>±</mo> </msubsup> <mo>,</mo> <msubsup> <mi>r</mi> <mrow> <mo>[</mo> <mi>γ</mi> <mo>]</mo> </mrow> <mo>±</mo> </msubsup> </mrow> </semantics></math> are in <a href="#universe-10-00435-t001" class="html-table">Table 1</a>. <b>The upper-left</b> (<b>center</b>) panel shows the situation for the co-rotating (counter-rotating) orbits. <b>The upper-right</b> panel shows the co-rotating and counter-rotating geodesic structures, and <b>the left-bottom</b> panel is a close-up view. Colored stripes in the panels are the regions locating the disk’s inner edges <math display="inline"><semantics> <mrow> <msubsup> <mi>r</mi> <mrow> <mo>×</mo> </mrow> <mo>±</mo> </msubsup> <mo>∈</mo> <mrow> <mo>]</mo> <msubsup> <mi>r</mi> <mrow> <mi>m</mi> <mi>b</mi> <mi>o</mi> </mrow> <mo>±</mo> </msubsup> <mo>,</mo> <msubsup> <mi>r</mi> <mrow> <mi>m</mi> <mi>s</mi> <mi>o</mi> </mrow> <mo>±</mo> </msubsup> <mo>]</mo> </mrow> </mrow> </semantics></math>. The bottom-center panel shows the co-rotating and counter-rotating geodesic structures where dotted stripes in the panels are the regions locating the disk’s inner edges <math display="inline"><semantics> <mrow> <msubsup> <mi>r</mi> <mrow> <mo>×</mo> </mrow> <mo>±</mo> </msubsup> <mo>∈</mo> <mrow> <mo>]</mo> <msubsup> <mi>r</mi> <mrow> <mi>m</mi> <mi>b</mi> <mi>o</mi> </mrow> <mo>±</mo> </msubsup> <mo>,</mo> <msubsup> <mi>r</mi> <mrow> <mi>m</mi> <mi>s</mi> <mi>o</mi> </mrow> <mo>±</mo> </msubsup> <mo>]</mo> </mrow> </mrow> </semantics></math>, and colored stripes locate the disk’s centers <math display="inline"><semantics> <mrow> <msubsup> <mi>r</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>n</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> <mo>±</mo> </msubsup> <mo>∈</mo> <mrow> <mo>[</mo> <msubsup> <mi>r</mi> <mrow> <mo>[</mo> <mi>m</mi> <mi>s</mi> <mi>o</mi> <mo>]</mo> </mrow> <mo>±</mo> </msubsup> <mo>,</mo> <msubsup> <mi>r</mi> <mrow> <mo>[</mo> <mi>m</mi> <mi>b</mi> <mi>o</mi> <mo>]</mo> </mrow> <mo>±</mo> </msubsup> <mo>[</mo> </mrow> </mrow> </semantics></math>. <b>The bottom-right</b> panel shows the co-rotating and counter-rotating geodesic structures for <b>BHs</b> spins <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>∈</mo> <mo>[</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> </semantics></math>. All quantities are dimensionless.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g002-550.jpg?1732267217" title=" <strong>Figure 2</strong><br/> <p>Evolution of the surface density <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> for the <span class="html-italic">ℓ</span>co-rotating rings orbiting in the Kerr spacetime with <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>∓</mo> <mn>0.9</mn> </mrow> </semantics></math> for counter-rotating <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>+</mo> <mo>)</mo> </mrow> </semantics></math> and co-rotating <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mo>)</mo> </mrow> </semantics></math> flows, respectively, at different times <span class="html-italic">t</span> signed on the panel (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">1</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Note, model <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </semantics></math> (<b>upper-right</b> panel) is composed of one counter-rotating ring). All the quantities are dimensionless.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g003-550.jpg?1732267218" title=" <strong>Figure 3</strong><br/> <p>Combined (independent) evolution of the surface densities <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> of <span class="html-italic">ℓ</span>counter-rotating rings couples composed by two sets of <span class="html-italic">ℓ</span>co-rotating rings from the integration in <a href="#universe-10-00435-f002" class="html-fig">Figure 2</a> for the Kerr spacetime with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>±</mo> <mn>0.9</mn> </mrow> </semantics></math> for co-rotating and counter-rotating fluids, respectively (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). Dimensionless time values for the different stages of evolution are signed on the panel. All the quantities are dimensionless. The initial density profiles are the combinations of models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> defined in <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">1</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Note, system <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>+</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </semantics></math> is an <span class="html-italic">ℓ</span>co-rotating triplet of counter-rotating tori <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. Notation <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>±</mo> <mo>)</mo> </mrow> </semantics></math> is for counter-rotating/co-rotating fluids, respectively. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>+</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>+</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>+</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating quadruplet of co-rotating rings: <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. The radial range has been adapted according to the combination of the independent integrations ranges. The viscosity coefficients <math display="inline"><semantics> <mi>ν</mi> </semantics></math> are fixed according to <a href="#universe-10-00435-f002" class="html-fig">Figure 2</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g004-550.jpg?1732267219" title=" <strong>Figure 4</strong><br/> <p>Evolution of the surface density <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> (<span class="html-italic">ℓ</span>co-rotating rings) in the Kerr metric with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>∓</mo> <mn>0.9</mn> </mrow> </semantics></math> at different times <span class="html-italic">t</span> for counter-rotating and co-rotating fluids, respectively (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). All the quantities are dimensionless. The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">E</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">H</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>), with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">2</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g005-550.jpg?1732267220" title=" <strong>Figure 5</strong><br/> <p>Combined (independent) evolution of the surface densities <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> of the <span class="html-italic">ℓ</span>counter-rotating rings couples composed by two clusters of <span class="html-italic">ℓ</span>co-rotating disks from the integration in <a href="#universe-10-00435-f004" class="html-fig">Figure 4</a>. The initial density profiles are the combinations of models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">E</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">H</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> defined in <a href="#universe-10-00435-t002" class="html-table">Table 2</a>), with boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">2</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">E</mi> <mo>+</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating quadruplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">E</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">E</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">H</mi> <mo>+</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating quadruplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">H</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">H</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>+</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating quadruplet of co-rotating rings <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. The radial range has been adapted according to the combination of the independent integrations ranges. The viscosity coefficients <math display="inline"><semantics> <mi>ν</mi> </semantics></math> are fixed according to <a href="#universe-10-00435-f004" class="html-fig">Figure 4</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g006-550.jpg?1732267221" title=" <strong>Figure 6</strong><br/> <p>Evolution of the surface density <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> (<span class="html-italic">ℓ</span>co-rotating rings) in the Kerr metric with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>±</mo> <mn>0.9</mn> </mrow> </semantics></math> for co-rotating and counter-rotating fluids, respectively, at different times <span class="html-italic">t</span> signed on the panels (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). All the quantities are dimensionless. The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">E</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">H</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>), with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">3</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g007-550.jpg?1732267222" title=" <strong>Figure 7</strong><br/> <p>Combined (independent) evolution of the surface densities <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> of the <span class="html-italic">ℓ</span>counter-rotating ring couples composed by two sets of <span class="html-italic">ℓ</span>co-rotating rings from the integration in <a href="#universe-10-00435-f006" class="html-fig">Figure 6</a>. The initial density profiles are the combinations of models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">E</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">H</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> defined in <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">3</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">E</mi> <mo>+</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating quadruplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">E</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">E</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">H</mi> <mo>+</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating quadruplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">H</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">H</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>+</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating quadruplet of co-rotating rings <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">F</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">G</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. The radial range has been adapted according to the combination of the independent integrations ranges. The viscosity coefficients <math display="inline"><semantics> <mi>ν</mi> </semantics></math> are fixed according to <a href="#universe-10-00435-f006" class="html-fig">Figure 6</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g008-550.jpg?1732267224" title=" <strong>Figure 8</strong><br/> <p>Evolution of the surface density <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> (<span class="html-italic">ℓ</span>co-rotating rings) at different times <span class="html-italic">t</span> signed on the panels in the Kerr metric with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>∓</mo> <mn>0.9</mn> </mrow> </semantics></math> (for counter-rotating and co-rotating fluids, respectively) (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">4</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Note, model <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </semantics></math> (<b>upper-right</b> panel) is composed of one counter-rotating ring).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g009-550.jpg?1732267225" title=" <strong>Figure 9</strong><br/> <p>Evolution of the surface density <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> (<span class="html-italic">ℓ</span>co-rotating rings) at different times <span class="html-italic">t</span> signed on the panels in the Kerr metric with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>±</mo> <mn>0.9</mn> </mrow> </semantics></math> for co-rotating and counter-rotating fluids, respectively (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">5</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Note, model <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </semantics></math> (<b>upper-right</b> panel) is composed of one counter-rotating ring).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g010-550.jpg?1732267226" title=" <strong>Figure 10</strong><br/> <p>Combined (independent) evolution of the surface densities <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> of the <span class="html-italic">ℓ</span>counter-rotating ring couples composed by two sets of <span class="html-italic">ℓ</span>co-rotating rings from the integration in <a href="#universe-10-00435-f008" class="html-fig">Figure 8</a>. The initial density profiles are combinations of models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> defined in <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">4</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Note, system <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>+</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </semantics></math> is a <span class="html-italic">ℓ</span>co-rotating triplet of counter-rotating tori <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. Notation <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>±</mo> <mo>)</mo> </mrow> </semantics></math> is for counter-rotating/co-rotating fluids, respectively). System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>+</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>+</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>+</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating quadruplet of co-rotating rings: <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. The radial range has been adapted according to the combination of the independent integrations ranges. The viscosity coefficients <math display="inline"><semantics> <mi>ν</mi> </semantics></math> are fixed according to <a href="#universe-10-00435-f008" class="html-fig">Figure 8</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g011-550.jpg?1732267227" title=" <strong>Figure 11</strong><br/> <p>Combined (independent) evolution of the surface densities <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> of the <span class="html-italic">ℓ</span>counter-rotating rings couples composed of two sets of <span class="html-italic">ℓ</span>co-rotating rings from the integration in <a href="#universe-10-00435-f009" class="html-fig">Figure 9</a>. The initial density profiles are the combinations of models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> defined in <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">5</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Note, system <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>+</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </semantics></math> is an <span class="html-italic">ℓ</span>co-rotating triplet of counter-rotating tori <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">A</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. Notation <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>±</mo> <mo>)</mo> </mrow> </semantics></math> is for counter-rotating/co-rotating fluids, respectively). System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>+</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>+</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">B</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>+</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating quadruplet of co-rotating rings: <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">D</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">C</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. The radial range has been adapted according to the combination of the independent integrations ranges. The viscosity coefficients <math display="inline"><semantics> <mi>ν</mi> </semantics></math> are fixed according to <a href="#universe-10-00435-f009" class="html-fig">Figure 9</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g012-550.jpg?1732267228" title=" <strong>Figure 12</strong><br/> <p>Evolution of the surface density <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> (<span class="html-italic">ℓ</span>co-rotating rings) in the Kerr metric with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>±</mo> <mn>0.2</mn> </mrow> </semantics></math> for co-rotating and counter-rotating fluids, respectively (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). All the quantities are dimensionless. Dimensionless time values for the different stages of evolution are signed on the panel. The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">1</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Note, model <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> </semantics></math> (<b>upper-right</b> panel) is composed of one counter-rotating ring).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g013-550.jpg?1732267229" title=" <strong>Figure 13</strong><br/> <p>Combined (independent) evolution of the surface densities <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> of the <span class="html-italic">ℓ</span>counter-rotating rings couples composed by two sets of <span class="html-italic">ℓ</span>co-rotating rings from the integration in <a href="#universe-10-00435-f012" class="html-fig">Figure 12</a>. The initial density profiles are the combinations of models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> defined in <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">1</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>+</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating triplet of counter-rotating rings <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>+</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>+</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating quadruplet of co-rotating rings <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>+</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. The radial range has been adapted according to the combination of the independent integrations ranges. The viscosity coefficients <math display="inline"><semantics> <mi>ν</mi> </semantics></math> are fixed according to <a href="#universe-10-00435-f012" class="html-fig">Figure 12</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g014-550.jpg?1732267230" title=" <strong>Figure 14</strong><br/> <p>Evolution of the surface density <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> (<span class="html-italic">ℓ</span>co-rotating rings) in the Kerr metric with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>±</mo> <mn>0.2</mn> </mrow> </semantics></math> for co-rotating and counter-rotating fluids, respectively, at different times <span class="html-italic">r</span> signed on the panels (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">O</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">R</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">2</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g015-550.jpg?1732267231" title=" <strong>Figure 15</strong><br/> <p>Combined (independent) evolution of the surface densities <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> of the <span class="html-italic">ℓ</span>counter-rotating rings couples composed by two sets of <span class="html-italic">ℓ</span>co-rotating rings from the integration in <a href="#universe-10-00435-f014" class="html-fig">Figure 14</a>. The initial density profiles are the combinations of models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">O</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">R</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> defined in <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">1</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">O</mi> <mo>+</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating quadruplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>+</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating quadruplet of co-rotating rings <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">R</mi> <mo>+</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating quadruplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">R</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">R</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. The radial range has been adapted according to the combination of the independent integrations ranges. The viscosity coefficients <math display="inline"><semantics> <mi>ν</mi> </semantics></math> are fixed according to <a href="#universe-10-00435-f014" class="html-fig">Figure 14</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g016-550.jpg?1732267232" title=" <strong>Figure 16</strong><br/> <p>Evolution of the surface density <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> (<span class="html-italic">ℓ</span>co-rotating rings) in the Kerr metric with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>±</mo> <mn>0.2</mn> </mrow> </semantics></math> for co-rotating and counter-rotating fluids, respectively, at different times <span class="html-italic">t</span> signed on the panels (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">O</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">R</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">3</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g017-550.jpg?1732267233" title=" <strong>Figure 17</strong><br/> <p>Combined (independent) evolution of the surface densities <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> of the <span class="html-italic">ℓ</span>counter-rotating rings couples composed by two sets of <span class="html-italic">ℓ</span>co-rotating rings from the integration in <a href="#universe-10-00435-f016" class="html-fig">Figure 16</a>. The initial density profiles are the combinations of models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">O</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">R</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> defined in <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">3</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">O</mi> <mo>+</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating quadruplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>+</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating quadruplet of co-rotating rings <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">P</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">R</mi> <mo>+</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating quadruplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">R</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">Q</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">R</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. The radial range has been adapted according to the combination of the independent integrations ranges. The viscosity coefficients <math display="inline"><semantics> <mi>ν</mi> </semantics></math> are fixed according to <a href="#universe-10-00435-f016" class="html-fig">Figure 16</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g018-550.jpg?1732267234" title=" <strong>Figure 18</strong><br/> <p>Evolution of the surface density <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> (<span class="html-italic">ℓ</span>co-rotating rings) in the Kerr metric with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>±</mo> <mn>0.2</mn> </mrow> </semantics></math> for co-rotating and counter-rotating fluids, respectively (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). All the quantities are dimensionless. Dimensionless time values for the different stages of evolution are signed on the panel. The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">4</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Note, model <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> </semantics></math> (upper-right panel) is composed of one counter-rotating ring).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g019-550.jpg?1732267235" title=" <strong>Figure 19</strong><br/> <p>Combined (independent) evolution of the surface densities <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> of the <span class="html-italic">ℓ</span>counter-rotating rings couples composed by two sets of <span class="html-italic">ℓ</span>co-rotating rings from the integration in <a href="#universe-10-00435-f018" class="html-fig">Figure 18</a>. The initial density profiles are the combinations of models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> defined in <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">4</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>+</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating triplet of counter-rotating rings <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>+</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>+</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating quadruplet of co-rotating rings <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>+</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. The radial range has been adapted according to the combination of independent integrations ranges. The viscosity coefficients <math display="inline"><semantics> <mi>ν</mi> </semantics></math> are fixed according to <a href="#universe-10-00435-f018" class="html-fig">Figure 18</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g020-550.jpg?1732267236" title=" <strong>Figure 20</strong><br/> <p>The mass flux <math display="inline"><semantics> <mi mathvariant="script">F</mi> </semantics></math> of Equation (<a href="#FD11-universe-10-00435" class="html-disp-formula">11</a>) for the <span class="html-italic">ℓ</span>co-rotating rings couples in the Kerr metric with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>±</mo> <mn>0.2</mn> </mrow> </semantics></math> for co-rotating and counter-rotating fluids, respectively (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). All the quantities are dimensionless. The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">4</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Density evolution is shown in <a href="#universe-10-00435-f018" class="html-fig">Figure 18</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g021-550.jpg?1732267237" title=" <strong>Figure 21</strong><br/> <p>Radial drift of the fluid density <math display="inline"><semantics> <mo>Σ</mo> </semantics></math>. Solution <math display="inline"><semantics> <mrow> <msup> <mo>Σ</mo> <mo>′</mo> </msup> <mo>≡</mo> <msub> <mo>∂</mo> <mi>r</mi> </msub> <mo>Σ</mo> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> in the plane <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>−</mo> <mi>r</mi> </mrow> </semantics></math> for co-rotating and counter-rotating fluids orbiting the <b>BH</b> spacetime with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>±</mo> <mn>0.2</mn> </mrow> </semantics></math>, respectively (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). All quantities are dimensionless. The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">4</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Density evolution is shown in <a href="#universe-10-00435-f018" class="html-fig">Figure 18</a>. The integration ranges consider the <b>RAD</b> inner <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">i</mi> <mo>)</mo> </mrow> </semantics></math>, center <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">c</mi> <mo>)</mo> </mrow> </semantics></math>, and outer <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">o</mi> <mo>)</mo> </mrow> </semantics></math> tori. The radial ranges distinguishing the <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">i</mi> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">c</mi> <mo>)</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">o</mi> <mo>)</mo> </mrow> </semantics></math> components are defined by the radii <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>IN</mi> </msub> <mo>&lt;</mo> <msub> <mi>r</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msub> <mo>≤</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>&lt;</mo> <msub> <mi>r</mi> <mo>∞</mo> </msub> </mrow> </semantics></math>. For the <span class="html-italic">ℓ</span>co-rotating seeds <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> </semantics></math>, the inner torus <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">i</mi> <mo>)</mo> </mrow> </semantics></math> is defined in the range <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi>r</mi> <mi>IN</mi> </msub> <mo>,</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>]</mo> </mrow> </semantics></math> and the outer torus <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="normal">o</mi> <mo>)</mo> </mrow> </semantics></math> is defined in <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>,</mo> <msub> <mi>r</mi> <mo>∞</mo> </msub> <mo>]</mo> </mrow> </semantics></math>, where the <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> </mrow> </semantics></math> seed there is <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>=</mo> <mn>30</mn> </mrow> </semantics></math>, and the <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> </semantics></math> seed there is <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>=</mo> <mn>22</mn> </mrow> </semantics></math>. For the combined independent system <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>+</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> </semantics></math>, there is <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msub> <mo>=</mo> <mn>22</mn> <mo>,</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>=</mo> <mn>28</mn> <mo>)</mo> </mrow> </semantics></math>, where the inner torus <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">i</mi> <mo>)</mo> </mrow> </semantics></math> is defined in <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi>r</mi> <mi>IN</mi> </msub> <mo>,</mo> <msub> <mi>r</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msub> <mo>]</mo> </mrow> </semantics></math>; the center torus <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">c</mi> <mo>)</mo> </mrow> </semantics></math> is defined in <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi>r</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msub> <mo>,</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>]</mo> </mrow> </semantics></math>; the outer torus <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">o</mi> <mo>)</mo> </mrow> </semantics></math> is defined in <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>,</mo> <msub> <mi>r</mi> <mo>∞</mo> </msub> <mo>]</mo> </mrow> </semantics></math>. The systems <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">Q</mi> <mo>)</mo> <mo>+</mo> <mo>(</mo> <mi mathvariant="script">P</mi> <mo>)</mo> </mrow> </semantics></math> for two general models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="script">Q</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="script">P</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> consider the sums two evolutions apart, which is the solution of <math display="inline"><semantics> <mrow> <msup> <mo>Σ</mo> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi mathvariant="script">Q</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msup> <mo>Σ</mo> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi mathvariant="script">P</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, while <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">Q</mi> <mo>+</mo> <mi mathvariant="script">P</mi> <mo>)</mo> </mrow> </semantics></math> is the solution of <math display="inline"><semantics> <mrow> <msup> <mo>Σ</mo> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi mathvariant="script">Q</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mo>Σ</mo> <mo>′</mo> </msup> <mrow> <mo>(</mo> <mi mathvariant="script">P</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g022-550.jpg?1732267237" title=" <strong>Figure 22</strong><br/> <p>Evolution of the disk mass as a function of the dimensionless time. For large times, the curves decrease approximately with a power law of <math display="inline"><semantics> <msup> <mi>t</mi> <mi>s</mi> </msup> </semantics></math> for co-rotating and counter-rotating fluids orbiting the <b>BH</b> spacetime with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>±</mo> <mn>0.2</mn> </mrow> </semantics></math>, respectively (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). All quantities are dimensionless. The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">4</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Density evolution is shown in <a href="#universe-10-00435-f018" class="html-fig">Figure 18</a>. The integration ranges consider the <b>RAD</b> inner <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">i</mi> <mo>)</mo> </mrow> </semantics></math>, center <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">c</mi> <mo>)</mo> </mrow> </semantics></math>, and outer <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">o</mi> <mo>)</mo> </mrow> </semantics></math> tori. The radial ranges distinguishing the <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">i</mi> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">c</mi> <mo>)</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">o</mi> <mo>)</mo> </mrow> </semantics></math> components are defined by the radii <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>IN</mi> </msub> <mo>&lt;</mo> <msub> <mi>r</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msub> <mo>≤</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>&lt;</mo> <msub> <mi>r</mi> <mo>∞</mo> </msub> </mrow> </semantics></math>. For the <span class="html-italic">ℓ</span>co-rotating seeds <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> </semantics></math>, the inner torus <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">i</mi> <mo>)</mo> </mrow> </semantics></math> is defined in the range <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi>r</mi> <mi>IN</mi> </msub> <mo>,</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>]</mo> </mrow> </semantics></math>, and the outer torus <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">o</mi> <mo>)</mo> </mrow> </semantics></math> is defined as <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>,</mo> <msub> <mi>r</mi> <mo>∞</mo> </msub> <mo>]</mo> </mrow> </semantics></math>, where for the <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> </mrow> </semantics></math> seed, <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>=</mo> <mn>30</mn> </mrow> </semantics></math>, and for the <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> </semantics></math> seed, <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>=</mo> <mn>22</mn> </mrow> </semantics></math>. For the combined independent system <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>+</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msub> <mo>=</mo> <mn>22</mn> <mo>,</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>=</mo> <mn>28</mn> <mo>)</mo> </mrow> </semantics></math>, where the inner torus <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">i</mi> <mo>)</mo> </mrow> </semantics></math> is defined in <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi>r</mi> <mi>IN</mi> </msub> <mo>,</mo> <msub> <mi>r</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msub> <mo>]</mo> </mrow> </semantics></math>; the center torus <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">c</mi> <mo>)</mo> </mrow> </semantics></math> is defined in <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi>r</mi> <mrow> <mo>(</mo> <mi>c</mi> <mo>)</mo> </mrow> </msub> <mo>,</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>]</mo> </mrow> </semantics></math>; the outer torus <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">o</mi> <mo>)</mo> </mrow> </semantics></math> is defined in <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mi>r</mi> <mo>*</mo> </msub> <mo>,</mo> <msub> <mi>r</mi> <mo>∞</mo> </msub> <mo>]</mo> </mrow> </semantics></math>. The systems <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">Q</mi> <mo>)</mo> <mo>+</mo> <mo>(</mo> <mi mathvariant="script">P</mi> <mo>)</mo> </mrow> </semantics></math> for two general models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="script">Q</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="script">P</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> consider the sums of the two evolutions apart, which is the sum of <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi mathvariant="script">Q</mi> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mi>π</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi mathvariant="script">P</mi> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mi>π</mi> </mrow> </semantics></math>, while <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">Q</mi> <mo>+</mo> <mi mathvariant="script">P</mi> <mo>)</mo> </mrow> </semantics></math> is the mass of the composed system formed by <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">Q</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="script">P</mi> <mo>)</mo> </mrow> </semantics></math> (the two evaluations clearly are coincident).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g023-550.jpg?1732267238" title=" <strong>Figure 23</strong><br/> <p>Evolution of the surface density <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> (<span class="html-italic">ℓ</span>co-rotating rings) in the Kerr metric with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>∓</mo> <mn>0.2</mn> </mrow> </semantics></math> for counter-rotating and co-rotating fluids, respectively (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). All the quantities are dimensionless. Dimensionless time values for the different stages of evolution are signed on the panel. The initial density profiles are the models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> of <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with the boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">5</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. Note, model <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> </semantics></math> (<b>upper-right</b> panel) is composed of one counter-rotating ring).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g024-550.jpg?1732267239" title=" <strong>Figure 24</strong><br/> <p>Combined (independent) evolution of the surface densities <math display="inline"><semantics> <mo>Σ</mo> </semantics></math> of the <span class="html-italic">ℓ</span>counter-rotating rings couples composed by two sets of <span class="html-italic">ℓ</span>co-rotating rings from the integration in <a href="#universe-10-00435-f023" class="html-fig">Figure 23</a> for the Kerr spacetime with spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mo>±</mo> <mn>0.2</mn> </mrow> </semantics></math> for co-rotating and counter-rotating fluids, respectively (see <a href="#universe-10-00435-t003" class="html-table">Table 3</a>). Dimensionless time values for the different stages of evolution are signed on the panel. All the quantities are dimensionless. The initial density profiles are the combinations of models <math display="inline"><semantics> <mrow> <mo>{</mo> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> <mo>,</mo> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> <mo>}</mo> </mrow> </semantics></math> defined in <a href="#universe-10-00435-t002" class="html-table">Table 2</a>, with boundary condition <math display="inline"><semantics> <mrow> <mo>[</mo> <mn mathvariant="bold">5</mn> <mo>]</mo> </mrow> </semantics></math> of Equation (<a href="#FD16-universe-10-00435" class="html-disp-formula">16</a>). <math display="inline"><semantics> <mi>ν</mi> </semantics></math> is the viscosity coefficient. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>+</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating triplet of counter-rotating rings <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">I</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>+</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>+</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>co-rotating quadruplet of co-rotating rings <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">M</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. System <math display="inline"><semantics> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>+</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </semantics></math> is the <span class="html-italic">ℓ</span>counter-rotating triplet <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">L</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi mathvariant="normal">C</mi> <mo>−</mo> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold">N</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. The radial range has been adapted according to the combination of the independent integrations ranges. The viscosity coefficients <math display="inline"><semantics> <mi>ν</mi> </semantics></math> are fixed according to <a href="#universe-10-00435-f023" class="html-fig">Figure 23</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00435/article_deploy/html/images/universe-10-00435-g0A1-550.jpg?1732267240" title=" <strong>Figure A1</strong><br/> <p>On the null flux <math display="inline"><semantics> <mi mathvariant="script">F</mi> </semantics></math> condition: <a href="#app1-universe-10-00435" class="html-app">Appendix A</a>. Radii <math display="inline"><semantics> <msubsup> <mi>r</mi> <mrow> <mo>⊙</mo> </mrow> <mo>±</mo> </msubsup> </semantics></math> for counter-rotating and co-rotating fluids, respectively, are plotted as functions of the central Kerr <b>BH</b> spin <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>]</mo> </mrow> </semantics></math>. All quantities are dimensionless. On <math display="inline"><semantics> <msubsup> <mi>r</mi> <mrow> <mo>⊙</mo> </mrow> <mo>±</mo> </msubsup> </semantics></math>, there is <math display="inline"><semantics> <mrow> <mi mathvariant="script">F</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msup> <mo>Σ</mo> <mo>′</mo> </msup> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>. The black region is <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>&lt;</mo> <msub> <mi>r</mi> <mo>+</mo> </msub> </mrow> </semantics></math>, with <math display="inline"><semantics> <msub> <mi>r</mi> <mo>+</mo> </msub> </semantics></math> being the outer horizon of the Kerr geometry, and the gray region is <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>&lt;</mo> <msubsup> <mi>r</mi> <mrow> <mi>ϵ</mi> </mrow> <mo>+</mo> </msubsup> </mrow> </semantics></math>, where <math display="inline"><semantics> <mrow> <msubsup> <mi>r</mi> <mrow> <mi>ϵ</mi> </mrow> <mo>+</mo> </msubsup> <mo>=</mo> <mn>2</mn> <mi>M</mi> </mrow> </semantics></math> is the outer ergosurface on the attractor equatorial plane. The geodesic structure of the Kerr spacetime is also plotted: radius <math display="inline"><semantics> <msubsup> <mi>r</mi> <mrow> <mi>m</mi> <mi>s</mi> <mi>o</mi> </mrow> <mo>±</mo> </msubsup> </semantics></math> is the marginally stable orbit, <math display="inline"><semantics> <msubsup> <mi>r</mi> <mrow> <mi>γ</mi> </mrow> <mo>±</mo> </msubsup> </semantics></math> is the marginally circular orbit, and <math display="inline"><semantics> <msubsup> <mi>r</mi> <mrow> <mi>m</mi> <mi>b</mi> <mi>o</mi> </mrow> <mo>±</mo> </msubsup> </semantics></math> is the marginally bounded orbit for counter-rotating and co-rotating particles, respectively. At <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mo>∝</mo> </msub> <mo>=</mo> <mn>0.8117</mn> </mrow> </semantics></math>, there is <math display="inline"><semantics> <mrow> <msubsup> <mi>r</mi> <mo>⊙</mo> <mo>−</mo> </msubsup> <mo>=</mo> <msubsup> <mi>r</mi> <mrow> <mi>ϵ</mi> </mrow> <mo>+</mo> </msubsup> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/435'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 17 pages, 561 KiB   </span> <a href="/2218-1997/10/12/434/pdf?version=1732191802" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Studying Intra-Night Optical Variability of AGNs Using the TESS Survey Data" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/12/434">Studying Intra-Night Optical Variability of AGNs Using the TESS Survey Data</a> <div class="authors"> by <span class="inlineblock "><strong>Yujian Yang</strong>, </span><span class="inlineblock "><strong>Bo Ma</strong> and </span><span class="inlineblock "><strong>Chen Chen</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(12), 434; <a href="https://doi.org/10.3390/universe10120434">https://doi.org/10.3390/universe10120434</a> - 21 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Active galactic nuclei (AGNs) exhibit significant luminosity variations across the entire electromagnetic spectrum, with timescales ranging from hours to years. Studying the optical variability of AGNs provides crucial insights into their physical properties. In this study, we explore the intra-night optical variability (INOV) <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/12/434/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Active galactic nuclei (AGNs) exhibit significant luminosity variations across the entire electromagnetic spectrum, with timescales ranging from hours to years. Studying the optical variability of AGNs provides crucial insights into their physical properties. In this study, we explore the intra-night optical variability (INOV) of AGNs using data from the TESS satellite’s all-sky survey. We derive differential light curves for a sample of 56 AGNs from 30-min cadence TESS full-frame images. Our analysis confirms that BL Lac objects typically exhibit stronger INOV compared to quasars, which generally show weaker variability. The duty cycle for INOV with an amplitude greater than 3% is approximately <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><mo>±</mo><mn>0.7</mn><mo>%</mo></mrow></semantics></math></inline-formula> for quasars and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>22</mn><mo>±</mo><mn>5</mn><mo>%</mo></mrow></semantics></math></inline-formula> for BL Lac objects. For INOV with an amplitude exceeding 10%, the corresponding duty cycle decreases to about <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.5</mn><mo>±</mo><mn>0.3</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>±</mo><mn>2</mn><mo>%</mo></mrow></semantics></math></inline-formula>, respectively. Furthermore, we identify a potential linear-log relationship between the duty cycle and the INOV amplitude, based on results from this study and previous findings, particularly from the ARIES program. <a href="/2218-1997/10/12/434">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/universe/sections/galaxies_and_clusters">Galaxies and Clusters</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/12/434/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1526150"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1526150"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1526150" data-cycle-prev="#prev1526150" data-cycle-progressive="#images1526150" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1526150-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00434/article_deploy/html/images/universe-10-00434-g001-550.jpg?1732191992" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1526150" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1526150-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00434/article_deploy/html/images/universe-10-00434-g002-550.jpg?1732191995'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1526150-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00434/article_deploy/html/images/universe-10-00434-g003-550.jpg?1732191996'><p>Figure 3</p></div></script></div></div><div id="article-1526150-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00434/article_deploy/html/images/universe-10-00434-g001-550.jpg?1732191992" title=" <strong>Figure 1</strong><br/> <p>The distribution of <math display="inline"><semantics> <msub> <mi>f</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>f</mi> <mn>2</mn> </msub> </semantics></math> calculated from the TESS light curves for the initial sample of 428 AGNs. The distribution of <math display="inline"><semantics> <msub> <mi>f</mi> <mn>1</mn> </msub> </semantics></math> reflects that there are unknown systematic errors when deriving the TESS light curves. The distribution of <math display="inline"><semantics> <msub> <mi>f</mi> <mn>2</mn> </msub> </semantics></math> reflects the existence of INOV on the level of ∼1–3% for most of the AGNs in our sample.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/434'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00434/article_deploy/html/images/universe-10-00434-g002-550.jpg?1732191995" title=" <strong>Figure 2</strong><br/> <p>Example light curves for Quasar RXS J10547+4831 and BL Lac object RXS J10586+5628, obtained from the TESS full-frame image. The gap in the middle indicates the removal of noisy data, which are caused by contamination from scattered light.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/434'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00434/article_deploy/html/images/universe-10-00434-g003-550.jpg?1732191996" title=" <strong>Figure 3</strong><br/> <p>INOV duty cycle for quasar and blazer (BL Lac object). The DC data are taken from this study and the literature [<a href="#B6-universe-10-00434" class="html-bibr">6</a>,<a href="#B9-universe-10-00434" class="html-bibr">9</a>,<a href="#B10-universe-10-00434" class="html-bibr">10</a>,<a href="#B15-universe-10-00434" class="html-bibr">15</a>,<a href="#B17-universe-10-00434" class="html-bibr">17</a>,<a href="#B34-universe-10-00434" class="html-bibr">34</a>]. There seems to exist a logarithmic relation between DC and the INOV amplitude threshold, awaiting verification from future studies. The shaded area indicates an arbitrary 50% deviation of the DC values from the fitted linear-log relationship.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/12/434'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 31 pages, 1408 KiB   </span> <a href="/2218-1997/10/11/433/pdf?version=1732177340" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/11/433">Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity</a> <div class="authors"> by <span class="inlineblock "><strong>Maria Margarida Lima</strong> and </span><span class="inlineblock "><strong>Cláudio Gomes</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 433; <a href="https://doi.org/10.3390/universe10110433">https://doi.org/10.3390/universe10110433</a> - 20 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Schwarzschild and Reissner–Nordstrøm black hole solutions are found in the context of a non-minimal matter–curvature coupling with Weyl connection both in vacuum and in the presence of a cosmological constant-like matter content. This model has the advantage of an extra force term which <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/433/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Schwarzschild and Reissner–Nordstrøm black hole solutions are found in the context of a non-minimal matter–curvature coupling with Weyl connection both in vacuum and in the presence of a cosmological constant-like matter content. This model has the advantage of an extra force term which can mimic dark matter and dark energy, and simultaneously following Weyl’s idea of unifying gravity and electromagnetism. In fact, vacuum Schwarzschild solutions differ from the ones in a constant curvature scenario in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> theories, with the appearance of a coefficient in the term that is linear in <i>r</i> and a corrected “cosmological constant”. Non-vacuum Schwarzschild solutions formally have the same solutions as in the previous case, with the exception being the physical interpretation of a cosmological constant as the source of the matter Lagrangian and not a simple reparameterization of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> description. Reissner–Nordstrøm solutions cannot be found in a vacuum, only in the presence of matter fields, with the result that the solutions also differ from the constant curvature scenario in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> theories by the term being linear in <i>r</i>, the corrected/dressed charge, and the cosmological constant. These results have bearings on future numerical simulations for black holes and gravitational waves in next-generation wavelet templates. <a href="/2218-1997/10/11/433">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/universe/sections/gravitation">Gravitation</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/433/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1525088"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1525088"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1525088" data-cycle-prev="#prev1525088" data-cycle-progressive="#images1525088" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1525088-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g001-550.jpg?1732177421" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1525088" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g002-550.jpg?1732177422'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g003-550.jpg?1732177423'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g004-550.jpg?1732177424'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g005-550.jpg?1732177425'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g006-550.jpg?1732177427'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g007-550.jpg?1732177428'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g008-550.jpg?1732177430'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g009-550.jpg?1732177431'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g010-550.jpg?1732177432'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g011-550.jpg?1732177432'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g012-550.jpg?1732177434'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g013-550.jpg?1732177435'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g014-550.jpg?1732177437'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g015-550.jpg?1732177438'><p>Figure 15</p></div> --- <div class='openpopupgallery' data-imgindex='15' data-target='article-1525088-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g016-550.jpg?1732177440'><p>Figure 16</p></div></script></div></div><div id="article-1525088-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g001-550.jpg?1732177421" title=" <strong>Figure 1</strong><br/> <p>Global behavior of the standard Ricci scalar (built from the Levi–Civita part of the connection) as function of the distance, assuming <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g002-550.jpg?1732177422" title=" <strong>Figure 2</strong><br/> <p>Geodesic representation of the Schwarzschild-like black hole (30), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g003-550.jpg?1732177423" title=" <strong>Figure 3</strong><br/> <p>Geodesic representation of the Schwarzschild-like black hole (30), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>≫</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>4</mn> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g004-550.jpg?1732177424" title=" <strong>Figure 4</strong><br/> <p>Geodesic representation of the Schwarzschild-like black hole (30), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>≪</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g005-550.jpg?1732177425" title=" <strong>Figure 5</strong><br/> <p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mi>H</mi> </msub> </semantics></math> compared to <math display="inline"><semantics> <mi>ω</mi> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g006-550.jpg?1732177427" title=" <strong>Figure 6</strong><br/> <p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>crit</mi> </mrow> </msub> </semantics></math> compared to <math display="inline"><semantics> <mi>ω</mi> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g007-550.jpg?1732177428" title=" <strong>Figure 7</strong><br/> <p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>crit</mi> </mrow> </msub> </semantics></math> compared to <math display="inline"><semantics> <msub> <mi>r</mi> <mi>H</mi> </msub> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g008-550.jpg?1732177430" title=" <strong>Figure 8</strong><br/> <p>Global behavior of the standard Ricci scalar (built from the Levi–Civita part of the connection) as function of the distance, assuming <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g009-550.jpg?1732177431" title=" <strong>Figure 9</strong><br/> <p>Geodesic representation of the Schwarzschild-like black hole (36), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g010-550.jpg?1732177432" title=" <strong>Figure 10</strong><br/> <p>Geodesic representation of the Schwarzschild-like black hole (36), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>≫</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g011-550.jpg?1732177432" title=" <strong>Figure 11</strong><br/> <p>Geodesic representation of the Schwarzschild-like black hole (36), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>≪</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g012-550.jpg?1732177434" title=" <strong>Figure 12</strong><br/> <p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mi>H</mi> <mo>,</mo> <mi>ext</mi> </mrow> </msub> </semantics></math> compared to <math display="inline"><semantics> <mi>ω</mi> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g013-550.jpg?1732177435" title=" <strong>Figure 13</strong><br/> <p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>crit</mi> </mrow> </msub> </semantics></math> compared to <math display="inline"><semantics> <mi>ω</mi> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g014-550.jpg?1732177437" title=" <strong>Figure 14</strong><br/> <p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mi>H</mi> <mo>,</mo> <mi>ext</mi> </mrow> </msub> </semantics></math> compared to <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>crit</mi> </mrow> </msub> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g015-550.jpg?1732177438" title=" <strong>Figure 15</strong><br/> <p>Global behavior of the scalar curvature <math display="inline"><semantics> <mover accent="true"> <mi>R</mi> <mo>¯</mo> </mover> </semantics></math> as a function of the distance, assuming <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>Q</mi> <mo stretchy="false">˜</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00433/article_deploy/html/images/universe-10-00433-g016-550.jpg?1732177440" title=" <strong>Figure 16</strong><br/> <p>Global behavior of the standard Ricci scalar (built from the Levi–Civita part of the connection) as a function of the distance, assuming <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>Q</mi> <mo stretchy="false">˜</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/433'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 17 pages, 584 KiB   </span> <a href="/2218-1997/10/11/432/pdf?version=1732504873" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="The Properties of an Edge-On Low Surface Brightness Galaxies Sample" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/11/432">The Properties of an Edge-On Low Surface Brightness Galaxies Sample</a> <div class="authors"> by <span class="inlineblock "><strong>Tian-Wen Cao</strong>, </span><span class="inlineblock "><strong>Zi-Jian Li</strong>, </span><span class="inlineblock "><strong>Pei-Bin Chen</strong>, </span><span class="inlineblock "><strong>Venu M. Kalari</strong>, </span><span class="inlineblock "><strong>Cheng Cheng</strong>, </span><span class="inlineblock "><strong>Gaspar Galaz</strong>, </span><span class="inlineblock "><strong>Hong Wu</strong> and </span><span class="inlineblock "><strong>Junfeng Wang</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 432; <a href="https://doi.org/10.3390/universe10110432">https://doi.org/10.3390/universe10110432</a> - 20 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> We analyzed the properties of a sample of edge-on low-surface brightness galaxies, which are referred to as Cao23 ELSBGs. Cao23 ELSBGs exhibit a wide range of luminosities (−22 < <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mi>r</mi></msub></semantics></math></inline-formula> < −13) with a mean scale length of 3.19 ± 1.48 kpc. <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/432/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> We analyzed the properties of a sample of edge-on low-surface brightness galaxies, which are referred to as Cao23 ELSBGs. Cao23 ELSBGs exhibit a wide range of luminosities (−22 < <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mi>r</mi></msub></semantics></math></inline-formula> < −13) with a mean scale length of 3.19 ± 1.48 kpc. Compared to HI-rich dwarf ELSBGs, Cao23 ELSBGs display more extended disk structures and redder (g-r) colors. They are also, on average, more massive than HI-rich dwarf ELSBGs. Star formation rates (SFRs) were calculated using WISE 12 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">μ</mi></semantics></math></inline-formula>m luminosity conversions and spectral energy distribution (SED) fitting methods, respectively. Cao23 ELSBGs fall below the main sequence with specific star formation rates (sSFRs) primarily in the range of 0.01–0.1 Gyr<sup>−1</sup>. More massive Cao23 LSBGs tend to have lower sSFRs. Additionally, we derived the non-parametric star formation histories (SFHs) of Cao23 ELSBGs by SED fitting, dividing the SFHs into seven look back time bins with constant SFRs assumed for each bin. Our analysis indicates that high-mass (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mo>&lowast;</mo></msub></semantics></math></inline-formula> > 10<sup>9.0</sup><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>⊙</mo></mrow></semantics></math></inline-formula>) Cao23 ELSBGs assembled their mass earlier than their lower-mass counterparts, supporting a downsizing trend for LSBGs. <a href="/2218-1997/10/11/432">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/universe/special_issues/Y3T2Z3J1HS ">New Insights into High-Energy Astrophysics, Galaxies, and Cosmology—Celebrating the 10th Anniversary of the Re-establishment of the Department of Astronomy at Xiamen University (2012–2022)</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/432/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1524863"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1524863"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1524863" data-cycle-prev="#prev1524863" data-cycle-progressive="#images1524863" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1524863-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g001-550.jpg?1732505007" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1524863" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1524863-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g002-550.jpg?1732505011'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1524863-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g003-550.jpg?1732505015'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1524863-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g004-550.jpg?1732505018'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1524863-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g005-550.jpg?1732505021'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1524863-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g006-550.jpg?1732505023'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1524863-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g007-550.jpg?1732505026'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1524863-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g008-550.jpg?1732505030'><p>Figure 8</p></div></script></div></div><div id="article-1524863-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g001-550.jpg?1732505007" title=" <strong>Figure 1</strong><br/> <p>The relationship between the mean value of the scale height to scale length ratio (−2.5<math display="inline"><semantics> <mrow> <mspace width="3.33333pt"/> <mo>×</mo> <mspace width="3.33333pt"/> </mrow> </semantics></math>log(<math display="inline"><semantics> <msub> <mi>h</mi> <mi>s</mi> </msub> </semantics></math>/r<math display="inline"><semantics> <msub> <mi>r</mi> <mi>s</mi> </msub> </semantics></math>)) and inclination. We note the −2.5<math display="inline"><semantics> <mrow> <mspace width="3.33333pt"/> <mo>×</mo> <mspace width="3.33333pt"/> </mrow> </semantics></math>log(<math display="inline"><semantics> <msub> <mi>h</mi> <mi>s</mi> </msub> </semantics></math>/<math display="inline"><semantics> <msub> <mi>r</mi> <mi>s</mi> </msub> </semantics></math>) is the correction factor from the observed center surface brightness to face-on center surface brightness for edge-on cases [<a href="#B70-universe-10-00432" class="html-bibr">70</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/432'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g002-550.jpg?1732505011" title=" <strong>Figure 2</strong><br/> <p>Panel (<b>a</b>): The distribution of <math display="inline"><semantics> <msub> <mi>μ</mi> <msub> <mn>0</mn> <mrow> <mi>f</mi> <mi>a</mi> <mi>c</mi> <mi>e</mi> </mrow> </msub> </msub> </semantics></math> in g-band. Panel (<b>b</b>): The distribution of axis ratio (b/a) in g-band. Panel (<b>c</b>): The distribution of g-band absolute magnitude. Panel (<b>d</b>): The distribution of scale length (<math display="inline"><semantics> <msub> <mi>r</mi> <mi>s</mi> </msub> </semantics></math>) of g-band in the unit of kpc. Panel (<b>e</b>): The distribution of (g-r) color. The blue and green line represents Cao23 ELSBGs and HI-rich dwarf ELSBGs from [<a href="#B70-universe-10-00432" class="html-bibr">70</a>] in all panels, respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/432'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g003-550.jpg?1732505015" title=" <strong>Figure 3</strong><br/> <p>Panel (<b>a</b>): The distribution of <math display="inline"><semantics> <msub> <mi>M</mi> <mi>r</mi> </msub> </semantics></math> of Cao23 ELSBGs (blue line), STs (black line) [<a href="#B73-universe-10-00432" class="html-bibr">73</a>], and LSBGs (red line) [<a href="#B73-universe-10-00432" class="html-bibr">73</a>]. Panel (<b>b</b>): The <math display="inline"><semantics> <msub> <mi>M</mi> <mo>∗</mo> </msub> </semantics></math>-SFR relation of Cao23 ELSBGs (open blue circles), STs (gray dots) [<a href="#B73-universe-10-00432" class="html-bibr">73</a>], and LSBGs (red dots) [<a href="#B73-universe-10-00432" class="html-bibr">73</a>]. The gray dashed lines, arranged from bottom to top, correspond to specific specific star formation rates (sSFRs) of 0.01 Gyr<sup>−1</sup>, 0.1 Gyr<sup>−1</sup>, and 1 Gyr<sup>−1</sup>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/432'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g004-550.jpg?1732505018" title=" <strong>Figure 4</strong><br/> <p>Panel (<b>a</b>): SFR<sub>W3</sub> versus <math display="inline"><semantics> <msub> <mi>M</mi> <mo>∗</mo> </msub> </semantics></math> of 131 Cao23 ELSBGs (open blue circles) and MaNGA 472 edge-on galaxies (gray stars) from [<a href="#B80-universe-10-00432" class="html-bibr">80</a>]. The typical error is the mean value of the SFR uncertainty derived from the W3 magnitude error. Panel (<b>b</b>): sSFR<sub>W3</sub> versus <math display="inline"><semantics> <msub> <mi>M</mi> <mo>∗</mo> </msub> </semantics></math> of 131 Cao23 ELSBGs (open blue circles) and MaNGA 472 edge-on galaxies (gray stars) from [<a href="#B80-universe-10-00432" class="html-bibr">80</a>]. The green line represents the main sequence line for star-forming nearby galaxies with SFR derived from W3 luminosity [<a href="#B79-universe-10-00432" class="html-bibr">79</a>,<a href="#B80-universe-10-00432" class="html-bibr">80</a>]. The dashed and dotted lines indicate 50% and 25% levels of the main sequence lines from [<a href="#B80-universe-10-00432" class="html-bibr">80</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/432'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g005-550.jpg?1732505021" title=" <strong>Figure 5</strong><br/> <p>The <math display="inline"><semantics> <msub> <mi>M</mi> <mo>∗</mo> </msub> </semantics></math>-SFR relation. Blue open circles denote Cao23 ELSBGs and blue open circles with filled cyan color are those Cao23 ELSBGs with W4 detecion. Gray triangles represent dwarf LSBGs from [<a href="#B10-universe-10-00432" class="html-bibr">10</a>], orange triangles distinguish UDGs from [<a href="#B86-universe-10-00432" class="html-bibr">86</a>], and purple triangles are HI-rich UDGs from [<a href="#B83-universe-10-00432" class="html-bibr">83</a>]. Green filled and unfilled triangles are GLSBGs from [<a href="#B35-universe-10-00432" class="html-bibr">35</a>] with dust extinction correction and none correction, respectively. The orange and open cyan squares are the Milky Way [<a href="#B35-universe-10-00432" class="html-bibr">35</a>] and Massive disk galaxies [<a href="#B87-universe-10-00432" class="html-bibr">87</a>], respectively. The purple line, black line, and red line represent the main sequence from [<a href="#B61-universe-10-00432" class="html-bibr">61</a>,<a href="#B88-universe-10-00432" class="html-bibr">88</a>,<a href="#B89-universe-10-00432" class="html-bibr">89</a>]. The green line represents the main sequence line for star-forming nearby galaxies with the SFR derived from W3 luminosity [<a href="#B79-universe-10-00432" class="html-bibr">79</a>,<a href="#B80-universe-10-00432" class="html-bibr">80</a>]. The gray dashed lines, arranged from bottom to top, correspond to specific star formation rates (sSFRs) of 0.01 Gyr<sup>−1</sup>, 0.1 Gyr<sup>−1</sup>, and 1 Gyr<sup>−1</sup>. The typical error is the mean value of the SFR error from CIGALE. The IMF has been corrected to Chabrier IMF for all data points.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/432'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g006-550.jpg?1732505023" title=" <strong>Figure 6</strong><br/> <p>Panel (<b>a</b>): The <math display="inline"><semantics> <msub> <mi>M</mi> <mrow> <mi>H</mi> <mi>I</mi> </mrow> </msub> </semantics></math>-<math display="inline"><semantics> <msub> <mi>M</mi> <mo>∗</mo> </msub> </semantics></math> relation for LSBGs. Blue filled circles denote Cao23 ELSBGs with HI detection, gray triangles represent dwarf LSBGs from [<a href="#B10-universe-10-00432" class="html-bibr">10</a>], and purple triangles distinguish UDGs from [<a href="#B83-universe-10-00432" class="html-bibr">83</a>]. Green filled triangles are GLSBGs from [<a href="#B35-universe-10-00432" class="html-bibr">35</a>]. The orange square represents the Milky Way. The red solid line represents the relation followed by the HI-selected sample of galaxies with a 1<math display="inline"><semantics> <mi>σ</mi> </semantics></math> scatter of 0.5 dex, and the red dashed line shows the relation followed by the spiral galaxies out of the <math display="inline"><semantics> <msub> <mi>M</mi> <mo>∗</mo> </msub> </semantics></math>-selected sample with a 1<math display="inline"><semantics> <mi>σ</mi> </semantics></math> scatter of 0.4 dex from [<a href="#B34-universe-10-00432" class="html-bibr">34</a>]. Panel (<b>b</b>): The <math display="inline"><semantics> <msub> <mi>t</mi> <mrow> <mi>d</mi> <mi>e</mi> <mi>p</mi> </mrow> </msub> </semantics></math> (HI) vs. sSFR diagram of LSBGs. Blue filled circles denote Cao23 ELSBGs with HI detection, gray triangles denote dwarf LSBGs from [<a href="#B10-universe-10-00432" class="html-bibr">10</a>], and cyan triangles indicate HI-rich dwarf LSBGs from [<a href="#B25-universe-10-00432" class="html-bibr">25</a>]. The red star symbol is the mean value of Cao23 ELSBGs, while the gray and cyan stars represent the mean values for dwarf LSBGs and HI-rich dwarf LSBGs, respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/432'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g007-550.jpg?1732505026" title=" <strong>Figure 7</strong><br/> <p>The sSFR-<math display="inline"><semantics> <msub> <mi>M</mi> <mo>∗</mo> </msub> </semantics></math> relation for LSBGs. Blue open circles denote Cao23 ELSBGs, gray triangles represent dwarf LSBGs from [<a href="#B10-universe-10-00432" class="html-bibr">10</a>], and orange triangles and plum triangles distinguish UDGs from [<a href="#B83-universe-10-00432" class="html-bibr">83</a>,<a href="#B86-universe-10-00432" class="html-bibr">86</a>], respectively. The blue dotted lines demarcate the boundaries of each stellar bin, with intervals of 0.5 dex in log(<math display="inline"><semantics> <msub> <mi>M</mi> <mo>∗</mo> </msub> </semantics></math>/<math display="inline"><semantics> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </semantics></math>) spanning from 8.5 to 10.5. Stellar masses falling below 8.5 and exceeding 10.5 are grouped into single bins, respectively. The red star symbols signify the mean values within each stellar bin. The black line is at log(sSFR/Gyr<sup>−1</sup>) = −1.0. Furthermore, a red dashed line at log(sSFR/Gyr<sup>−1</sup>) = −2.0 provides sSFR thresholds with passive galaxies typically falling below the red line. Purple and gray star symbols represent the mean values of HI-gas UDGs from [<a href="#B83-universe-10-00432" class="html-bibr">83</a>] and dwarf LSBGs from [<a href="#B10-universe-10-00432" class="html-bibr">10</a>] with log(<math display="inline"><semantics> <msub> <mi>M</mi> <mo>∗</mo> </msub> </semantics></math>/<math display="inline"><semantics> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </semantics></math>) &lt; 8.5. The IMF has been corrected to Chabrier IMF for all data points.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/432'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00432/article_deploy/html/images/universe-10-00432-g008-550.jpg?1732505030" title=" <strong>Figure 8</strong><br/> <p>The mass growth curve through the look back times. The red line represents the mean value for those Cao23 ELSBGs with <math display="inline"><semantics> <msub> <mi>M</mi> <mo>∗</mo> </msub> </semantics></math> &gt; 10<sup>9.0</sup> <math display="inline"><semantics> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </semantics></math>, and the blue line represents the mean value for those Cao23 ELSBGs with <math display="inline"><semantics> <msub> <mi>M</mi> <mo>∗</mo> </msub> </semantics></math> ≤ 10<sup>9.0</sup> <math display="inline"><semantics> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/432'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 22 pages, 3167 KiB   </span> <a href="/2218-1997/10/11/431/pdf?version=1732523505" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="The Composite Spectral Energy Distribution of Quasars Is Surprisingly Universal Since Cosmic Noon" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/11/431">The Composite Spectral Energy Distribution of Quasars Is Surprisingly Universal Since Cosmic Noon</a> <div class="authors"> by <span class="inlineblock "><strong>Zhenyi Cai</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 431; <a href="https://doi.org/10.3390/universe10110431">https://doi.org/10.3390/universe10110431</a> - 19 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Leveraging the photometric data of the Sloan Digital Sky Survey and the Galaxy Evolution Explorer (GALEX), we construct mean/median spectral energy distributions (SEDs) for unique bright quasars in redshift bins of 0.2 and up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>≃</mo><mn>3</mn></mrow></semantics></math></inline-formula>, after taking the GALEX <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/431/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Leveraging the photometric data of the Sloan Digital Sky Survey and the Galaxy Evolution Explorer (GALEX), we construct mean/median spectral energy distributions (SEDs) for unique bright quasars in redshift bins of 0.2 and up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>≃</mo><mn>3</mn></mrow></semantics></math></inline-formula>, after taking the GALEX non-detection into account. Further correcting for the absorption of the intergalactic medium, these mean/median quasar SEDs constitute a surprisingly redshift-independent mean/median composite SED from the rest-frame optical down to ≃<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>500</mn><mo> </mo><mover accent="true"><mi mathvariant="normal">A</mi><mo>˚</mo></mover></mrow></semantics></math></inline-formula> for quasars with bolometric luminosity brighter than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>10</mn><mrow><mn>45.5</mn></mrow></msup><mrow><mi>erg</mi><msup><mi mathvariant="normal">s</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></mrow></semantics></math></inline-formula>. Moreover, the mean/median composite quasar SED is plausibly also independent of black hole mass and Eddington ratio, and suggests similar properties of dust and gas in the quasar host galaxies since cosmic noon. Both the mean and median composite SEDs are nicely consistent with previous mean composite quasar spectra at wavelengths beyond ≃<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1000</mn><mo> </mo><mover accent="true"><mi mathvariant="normal">A</mi><mo>˚</mo></mover></mrow></semantics></math></inline-formula>, but at shorter wavelengths, are redder, indicating, on average, less ionizing radiation than previously expected. Through comparing the model-predicted to the observed composite quasar SEDs, we favor a simply truncated disk model, rather than a standard thin disk model, for the quasar central engine, though we request more sophisticated disk models. Future deep ultraviolet facilities, such as the China Space Station Telescope and the Ultraviolet Explorer, would prompt revolutions in many aspects, including the quasar central engine, production of the broad emission lines in quasars, and cosmic reionization. <a href="/2218-1997/10/11/431">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/universe/special_issues/Y3T2Z3J1HS ">New Insights into High-Energy Astrophysics, Galaxies, and Cosmology—Celebrating the 10th Anniversary of the Re-establishment of the Department of Astronomy at Xiamen University (2012–2022)</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/431/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1524553"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1524553"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1524553" data-cycle-prev="#prev1524553" data-cycle-progressive="#images1524553" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1524553-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g001-550.jpg?1732523601" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1524553" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g002-550.jpg?1732523603'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g003-550.jpg?1732523605'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g004-550.jpg?1732523608'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g005-550.jpg?1732523610'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g006-550.jpg?1732523612'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g007a-550.jpg?1732523615'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g007b-550.jpg?1732523617'><p>Figure 7 Cont.</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g008-550.jpg?1732523620'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g009-550.jpg?1732523623'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g010-550.jpg?1732523624'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g011-550.jpg?1732523626'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1524553-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g012-550.jpg?1732523628'><p>Figure 12</p></div></script></div></div><div id="article-1524553-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g001-550.jpg?1732523601" title=" <strong>Figure 1</strong><br/> <p>The (<b>main</b>) panel presents distributions of our parent quasars (101,745; contours surrounded by sparse dots) and unique bright quasars (23,256; brighter than the green solid stepwise curve) in the luminosity-redshift space, while the (<b>top</b>) panel shows their redshift distributions, i.e., the black dotted histogram and the green solid histogram, respectively. The red dashed stepwise curve in the (<b>main</b>) panel indicates the peak of the luminosity distribution of quasars as a function of redshift, e.g., the peak of the dotted histogram for quasars in <math display="inline"><semantics> <mrow> <mn>1.8</mn> <mo>&lt;</mo> <mi>z</mi> <mo>≤</mo> <mn>2.0</mn> </mrow> </semantics></math> in the (<b>right</b>) panel. The red dashed histogram in the (<b>top</b>) panel is the redshift distribution of quasars brighter than the red dashed stepwise curve. For comparison, the (<b>main</b>) panel includes the medians and 25–75th percentile ranges of redshift and UV luminosity of four representative quasar samples (i.e., a circle for Scott et al. [<a href="#B32-universe-10-00431" class="html-bibr">32</a>], a triangle for Stevans et al. [<a href="#B35-universe-10-00431" class="html-bibr">35</a>], a diamond for Telfer et al. [<a href="#B31-universe-10-00431" class="html-bibr">31</a>], and a square for Lusso et al. [<a href="#B36-universe-10-00431" class="html-bibr">36</a>]), while the (<b>top</b>) panel contains the corresponding quasar numbers.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g002-550.jpg?1732523603" title=" <strong>Figure 2</strong><br/> <p>The (<b>main</b>) panel is the same as that of <a href="#universe-10-00431-f001" class="html-fig">Figure 1</a>. The orange crosses linked by dotted lines (the blue stars linked by solid lines) in the (<b>top</b>) panel are the GALEX NUV (FUV) detection fractions, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>NUV</mi> </msub> </semantics></math> (<math display="inline"><semantics> <msub> <mi>f</mi> <mi>FUV</mi> </msub> </semantics></math>), for our unique bright quasars, while the orange dotted (blue solid) histogram in the (<b>right</b>) panel is the GALEX NUV (FUV) detection fraction as a function of luminosity for quasars brighter than a given minimal <math display="inline"><semantics> <mrow> <mn>2200</mn> <mo> </mo> <mover accent="true"> <mi mathvariant="normal">A</mi> <mo>˚</mo> </mover> </mrow> </semantics></math> luminosity and in <math display="inline"><semantics> <mrow> <mn>1.8</mn> <mo>&lt;</mo> <mi>z</mi> <mo>≤</mo> <mn>2.0</mn> </mrow> </semantics></math> as an example.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g003-550.jpg?1732523605" title=" <strong>Figure 3</strong><br/> <p>Changed factors of <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">q</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>NUV</mi> </msub> </semantics></math>, and <math display="inline"><semantics> <msub> <mi>f</mi> <mi>FUV</mi> </msub> </semantics></math> as a function of redshift for quasar samples selected with larger (circles linked by dotted lines) or smaller (triangles linked by dashed lines) <math display="inline"><semantics> <mrow> <mo form="prefix">log</mo> <msubsup> <mi>L</mi> <mrow> <mn>2200</mn> </mrow> <mi>min</mi> </msubsup> </mrow> </semantics></math>, i.e., by <math display="inline"><semantics> <mrow> <mo>±</mo> <mn>0.2</mn> </mrow> </semantics></math> dex in all redshift bins, than our reference values of <math display="inline"><semantics> <mrow> <mo form="prefix">log</mo> <msubsup> <mi>L</mi> <mn>2200</mn> <mi>min</mi> </msubsup> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. Please note that the smaller <math display="inline"><semantics> <mrow> <mo form="prefix">log</mo> <msubsup> <mi>L</mi> <mrow> <mn>2200</mn> </mrow> <mi>min</mi> </msubsup> </mrow> </semantics></math>, the larger the sample size but the lower the GALEX detection.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g004-550.jpg?1732523608" title=" <strong>Figure 4</strong><br/> <p>The (<b>top</b>) panel: the bias-free mean SED for <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">q</mi> </msub> </semantics></math> quasars brighter than <math display="inline"><semantics> <mrow> <mo form="prefix">log</mo> <msubsup> <mi>L</mi> <mn>2200</mn> <mi>min</mi> </msubsup> </mrow> </semantics></math> in each redshift bin. Each legend contains the GALEX NUV- and FUV-detected fractions, i.e., <math display="inline"><semantics> <msubsup> <mi>f</mi> <mi>NUV</mi> <mi>w</mi> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi>f</mi> <mi>FUV</mi> <mi>w</mi> </msubsup> </semantics></math>, where the superscript, <span class="html-italic">w</span>, is the de-redshifted wavelength corresponding to the effective wavelength of the GALEX NUV/FUV band. We also show the mean quasar SED constructed by ([<a href="#B42-universe-10-00431" class="html-bibr">42</a>], CW23) as well as the mean composite quasar spectra from ([<a href="#B29-universe-10-00431" class="html-bibr">29</a>], without correction for the IGM absorption; red dotted curve) and ([<a href="#B31-universe-10-00431" class="html-bibr">31</a>], with correction for the IGM absorption; blue solid curve) for comparison. The (<b>bottom</b>) panel: same as the (<b>top</b>) one, but for the bias-free median quasar SEDs.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g005-550.jpg?1732523610" title=" <strong>Figure 5</strong><br/> <p>The IGM transmission curves as a function of the rest-frame wavelength for <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> (<b>top-left</b> panel), <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>1.1</mn> </mrow> </semantics></math> (<b>top-right</b> panel), <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>2.1</mn> </mrow> </semantics></math> (<b>bottom-left</b> panel), and <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>2.9</mn> </mrow> </semantics></math> (<b>bottom-right</b> panel). Averaging transmissions in 1000 LOS (equivalent to 1000 quasars) randomly selected from <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math> simulated LOS gives rise to the mean transmission and three upper transmission quantiles (i.e., 25%, median, and 75%), <math display="inline"><semantics> <msubsup> <mrow> <mo>⟨</mo> <msub> <mi>T</mi> <mi>LOS</mi> </msub> <mo>⟩</mo> </mrow> <mrow> <mn>1000</mn> </mrow> <mi>type</mi> </msubsup> </semantics></math>. For each “type” of transmission, the solid and dashed curves are the mean and <math display="inline"><semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math> dispersion of 1000 different realizations of <math display="inline"><semantics> <msubsup> <mrow> <mo>⟨</mo> <msub> <mi>T</mi> <mi>LOS</mi> </msub> <mo>⟩</mo> </mrow> <mrow> <mn>1000</mn> </mrow> <mi>type</mi> </msubsup> </semantics></math> (cf. the gray and light-gray curves for 1000 realizations of <math display="inline"><semantics> <msubsup> <mrow> <mo>⟨</mo> <msub> <mi>T</mi> <mi>LOS</mi> </msub> <mo>⟩</mo> </mrow> <mrow> <mn>1000</mn> </mrow> <mi>median</mi> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mrow> <mo>⟨</mo> <msub> <mi>T</mi> <mi>LOS</mi> </msub> <mo>⟩</mo> </mrow> <mrow> <mn>1000</mn> </mrow> <mi>mean</mi> </msubsup> </semantics></math>, respectively). At the bottom of each panel, there are de-redshifted FUV-, NUV-, <span class="html-italic">u</span>-, and <span class="html-italic">g</span>-band transmission curves from left to right, respectively. In each panel and each band, the square and star, superimposed by <math display="inline"><semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math> uncertainties, indicate the filter-weighted broadband mean and median IGM transmissions, respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g006-550.jpg?1732523612" title=" <strong>Figure 6</strong><br/> <p>By averaging 1000 LOS, squares and stars show the filter-weighted broadband mean and median IGM transmission as a function of redshift for four bands, i.e., <math display="inline"><semantics> <msub> <mi>T</mi> <mi>FUV</mi> </msub> </semantics></math> (<b>top-left</b>), <math display="inline"><semantics> <msub> <mi>T</mi> <mi>NUV</mi> </msub> </semantics></math> (<b>top-right</b>), <math display="inline"><semantics> <msub> <mi>T</mi> <mi>u</mi> </msub> </semantics></math> (<b>bottom-left</b>), and <math display="inline"><semantics> <msub> <mi>T</mi> <mi>g</mi> </msub> </semantics></math> (<b>bottom-right</b>). The superimposed <math display="inline"><semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math> uncertainties are associated with 1000 LOS. Please note that averaging more (less) LOS gives smaller (larger) <math display="inline"><semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math> uncertainties.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g007a-550.jpg?1732523615" title=" <strong>Figure 7</strong><br/> <p>Same as <a href="#universe-10-00431-f004" class="html-fig">Figure 4</a>, but for the intrinsic mean (<b>top</b> panel) and median (<b>bottom</b> panel) SEDs, whose EUV portion has been corrected for the IGM absorption. For each redshift bin with a central redshift <span class="html-italic">z</span>, the legend includes the median <math display="inline"><semantics> <mrow> <mn>2200</mn> <mo> </mo> <mover accent="true"> <mi mathvariant="normal">A</mi> <mo>˚</mo> </mover> </mrow> </semantics></math> luminosity of quasars, <math display="inline"><semantics> <mrow> <mo form="prefix">log</mo> <msubsup> <mi>L</mi> <mn>2200</mn> <mi>med</mi> </msubsup> </mrow> </semantics></math>, and the filter-weighted broadband IGM transmissions, <math display="inline"><semantics> <msubsup> <mi>T</mi> <mi>b</mi> <mi>w</mi> </msubsup> </semantics></math>, where <span class="html-italic">b</span> indicates the band name. After correcting for the IGM absorption, the intrinsic mean/median SEDs of quasars at different redshifts become strikingly consistent in the EUV and together form a mean/median composite SED. A smoothly broken power law with optical-to-FUV (<math display="inline"><semantics> <msub> <mi>α</mi> <mrow> <mi>OPT</mi> <mo>−</mo> <mi>FUV</mi> </mrow> </msub> </semantics></math>) and EUV (<math display="inline"><semantics> <msub> <mi>α</mi> <mi>EUV</mi> </msub> </semantics></math>) spectral indices for <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi>ν</mi> </msub> <mo>∝</mo> <msup> <mi>ν</mi> <mi>α</mi> </msup> </mrow> </semantics></math> is fit to the mean/median composite SED in several line-free windows (thick gray bars).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g007b-550.jpg?1732523617" title=" <strong>Figure 7 Cont.</strong><br/> <p>Same as <a href="#universe-10-00431-f004" class="html-fig">Figure 4</a>, but for the intrinsic mean (<b>top</b> panel) and median (<b>bottom</b> panel) SEDs, whose EUV portion has been corrected for the IGM absorption. For each redshift bin with a central redshift <span class="html-italic">z</span>, the legend includes the median <math display="inline"><semantics> <mrow> <mn>2200</mn> <mo> </mo> <mover accent="true"> <mi mathvariant="normal">A</mi> <mo>˚</mo> </mover> </mrow> </semantics></math> luminosity of quasars, <math display="inline"><semantics> <mrow> <mo form="prefix">log</mo> <msubsup> <mi>L</mi> <mn>2200</mn> <mi>med</mi> </msubsup> </mrow> </semantics></math>, and the filter-weighted broadband IGM transmissions, <math display="inline"><semantics> <msubsup> <mi>T</mi> <mi>b</mi> <mi>w</mi> </msubsup> </semantics></math>, where <span class="html-italic">b</span> indicates the band name. After correcting for the IGM absorption, the intrinsic mean/median SEDs of quasars at different redshifts become strikingly consistent in the EUV and together form a mean/median composite SED. A smoothly broken power law with optical-to-FUV (<math display="inline"><semantics> <msub> <mi>α</mi> <mrow> <mi>OPT</mi> <mo>−</mo> <mi>FUV</mi> </mrow> </msub> </semantics></math>) and EUV (<math display="inline"><semantics> <msub> <mi>α</mi> <mi>EUV</mi> </msub> </semantics></math>) spectral indices for <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi>ν</mi> </msub> <mo>∝</mo> <msup> <mi>ν</mi> <mi>α</mi> </msup> </mrow> </semantics></math> is fit to the mean/median composite SED in several line-free windows (thick gray bars).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g008-550.jpg?1732523620" title=" <strong>Figure 8</strong><br/> <p>Physical properties, i.e., bolometric luminosity (<math display="inline"><semantics> <msub> <mi>L</mi> <mi>bol</mi> </msub> </semantics></math>; <b>top-left</b> panel), BH mass (<math display="inline"><semantics> <msub> <mi>M</mi> <mi>BH</mi> </msub> </semantics></math>; <b>top-right</b> panel), Eddington ratio (<math display="inline"><semantics> <msub> <mi>λ</mi> <mi>Edd</mi> </msub> </semantics></math>; <b>bottom-left</b> panel), and <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>Edd</mi> </msub> <mo>/</mo> <msub> <mi>M</mi> <mi>BH</mi> </msub> </mrow> </semantics></math> (<b>bottom-right</b> panel; note <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mn>0.1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>λ</mi> <mi>Edd</mi> </msub> <mo>/</mo> <mn>0.1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mn>9</mn> </msub> <mo>=</mo> <msub> <mi>M</mi> <mi>BH</mi> </msub> <mo>/</mo> <msup> <mn>10</mn> <mn>9</mn> </msup> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </semantics></math>), as a function of redshift for our parent quasar sample (black open circles; <a href="#sec2dot1-universe-10-00431" class="html-sec">Section 2.1</a>) and our unique bright quasar sample (blue filled stars; <a href="#sec2dot2-universe-10-00431" class="html-sec">Section 2.2</a>). At each redshift, symbols are median values, while vertical bars are the 25–75th percentile ranges. Nearly all quasars have measurements on <math display="inline"><semantics> <msub> <mi>L</mi> <mi>bol</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>M</mi> <mi>BH</mi> </msub> </semantics></math>, and <math display="inline"><semantics> <msub> <mi>λ</mi> <mi>Edd</mi> </msub> </semantics></math>, provided by Rakshit et al. [<a href="#B47-universe-10-00431" class="html-bibr">47</a>], but the large uncertainties on, and even systematic offsets of, these measurements must be taken seriously (see discussion in Sun [<a href="#B48-universe-10-00431" class="html-bibr">48</a>] for example).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g009-550.jpg?1732523623" title=" <strong>Figure 9</strong><br/> <p>Panels in each row are the same as <a href="#universe-10-00431-f007" class="html-fig">Figure 7</a>, but for the intrinsic quasar SEDs constructed from another two quasar samples selected with larger (<b>top</b> panels) or smaller (<b>bottom</b> panels) <math display="inline"><semantics> <mrow> <mo form="prefix">log</mo> <msubsup> <mi>L</mi> <mrow> <mn>2200</mn> </mrow> <mi>min</mi> </msubsup> </mrow> </semantics></math>, i.e., by <math display="inline"><semantics> <mrow> <mo>±</mo> <mn>0.2</mn> </mrow> </semantics></math> dex in all redshift bins, than our reference values. In each panel, the green dashed curve is the best-fit smoothly broken power law taken from the corresponding panel of <a href="#universe-10-00431-f007" class="html-fig">Figure 7</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g010-550.jpg?1732523624" title=" <strong>Figure 10</strong><br/> <p>SEDs predicted by the thin disk (<b>left</b> panel) and truncated disk (<b>right</b> panel) models for <math display="inline"><semantics> <msub> <mi>N</mi> <mi>ME</mi> </msub> </semantics></math> quasars, with measurements on both <math display="inline"><semantics> <msub> <mi>M</mi> <mi>BH</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mi>Edd</mi> </msub> </semantics></math>, of <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">q</mi> </msub> </semantics></math> quasars in <math display="inline"><semantics> <mrow> <mn>1.8</mn> <mo>&lt;</mo> <mi>z</mi> <mo>≤</mo> <mn>2.0</mn> </mrow> </semantics></math> as an example. Each gray thin solid curve is an SED of a quasar, while the blue dotted and red dashed curves are the resultant model-predicted mean and median composite SEDs for quasars in that redshift bin, respectively. For comparison, a black solid curve superimposed on the red dashed curve represents a specific SED implied by the median <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>Edd</mi> </msub> <mo>/</mo> <msub> <mi>M</mi> <mi>BH</mi> </msub> </mrow> </semantics></math> of the <math display="inline"><semantics> <msub> <mi>N</mi> <mi>ME</mi> </msub> </semantics></math> quasars.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g011-550.jpg?1732523626" title=" <strong>Figure 11</strong><br/> <p>(The <b>top</b> panels): comparing the model-predicated mean composite SEDs for quasars in different redshift bins (colored thin curves) to the observed mean composite SED (black thick solid curve), the truncated disk model (<b>top-right</b> panel) performs better than the thin disk model (<b>top-left</b> panel). The median values of <span class="html-italic">z</span> and <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>Edd</mi> </msub> <mo>/</mo> <msub> <mi>M</mi> <mi>BH</mi> </msub> </mrow> </semantics></math> for quasars in each redshift bin are nominated in the legend. In the right panel for the truncated disk model, the legend contains a typical truncation radius, <math display="inline"><semantics> <msub> <mi>r</mi> <mi>tr</mi> </msub> </semantics></math> (in gravitational radius <math display="inline"><semantics> <msub> <mi>r</mi> <mi mathvariant="normal">g</mi> </msub> </semantics></math>), corresponding to a maximum disk temperature determined by the median <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>Edd</mi> </msub> <mo>/</mo> <msub> <mi>M</mi> <mi>BH</mi> </msub> </mrow> </semantics></math> of quasars. (The <b>bottom</b> panels): same as the top ones, but for comparing the median composite SEDs.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00431/article_deploy/html/images/universe-10-00431-g012-550.jpg?1732523628" title=" <strong>Figure 12</strong><br/> <p>The blue dashed (red solid) curve is our mean (median) composite quasar SED. The black dotted curve is the AD2 SED of Netzer [<a href="#B69-universe-10-00431" class="html-bibr">69</a>], whose ionizing continuum is weakest among the four SEDs adopted by Netzer [<a href="#B69-universe-10-00431" class="html-bibr">69</a>] and has difficulties in producing large enough line luminosities, including C<span class="html-small-caps">iv</span> 1549, He<span class="html-small-caps">ii</span> 1640, and H<math display="inline"><semantics> <mi>β</mi> </semantics></math>. On the top axis, there are marked specific wavelengths corresponding to the ionization potential energies of H<span class="html-small-caps">i</span> (<math display="inline"><semantics> <mrow> <mn>911.8</mn> <mo> </mo> <mover accent="true"> <mi mathvariant="normal">A</mi> <mo>˚</mo> </mover> </mrow> </semantics></math>), He<span class="html-small-caps">i</span> (<math display="inline"><semantics> <mrow> <mn>504.3</mn> <mo> </mo> <mover accent="true"> <mi mathvariant="normal">A</mi> <mo>˚</mo> </mover> </mrow> </semantics></math>), He<span class="html-small-caps">ii</span> (<math display="inline"><semantics> <mrow> <mn>227.8</mn> <mo> </mo> <mover accent="true"> <mi mathvariant="normal">A</mi> <mo>˚</mo> </mover> </mrow> </semantics></math>), and C<span class="html-small-caps">iv</span> (<math display="inline"><semantics> <mrow> <mn>192.2</mn> <mo> </mo> <mover accent="true"> <mi mathvariant="normal">A</mi> <mo>˚</mo> </mover> </mrow> </semantics></math>).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/431'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 19 pages, 1057 KiB   </span> <a href="/2218-1997/10/11/430/pdf?version=1731982256" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Black Holes with a Cloud of Strings and Quintessence in a Non-Linear Electrodynamics Scenario" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/11/430">Black Holes with a Cloud of Strings and Quintessence in a Non-Linear Electrodynamics Scenario</a> <div class="authors"> by <span class="inlineblock "><strong>Francinaldo Florencio do Nascimento</strong>, </span><span class="inlineblock "><strong>Valdir Barbosa Bezerra</strong> and </span><span class="inlineblock "><strong>Jefferson de Morais Toledo</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 430; <a href="https://doi.org/10.3390/universe10110430">https://doi.org/10.3390/universe10110430</a> - 19 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> We obtain exact black hole solutions to Einstein gravity coupled with a nonlinear electrodynamics field, in the presence of a cloud of strings and quintessence, as sources. The solutions have four parameters, namely <i>m</i>, <i>k</i>, <i>a</i>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, corresponding <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/430/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> We obtain exact black hole solutions to Einstein gravity coupled with a nonlinear electrodynamics field, in the presence of a cloud of strings and quintessence, as sources. The solutions have four parameters, namely <i>m</i>, <i>k</i>, <i>a</i>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, corresponding to the physical mass of the black hole, the nonlinear charge of a self-gravitating magnetic field, the cloud of strings, and the intensity of the quintessential fluid. The consequences of these sources on the regularity or singularity of the solutions, on their horizons, as well as on the energy conditions, are discussed. We study some aspects concerning the thermodynamics of the black hole, by taking into account the mass, Hawking temperature, and heat capacity and show how these quantities depend on the presence of the cloud of strings and quintessence, in the scenario considered. <a href="/2218-1997/10/11/430">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Collection <a href=" /journal/universe/topical_collections/OpenQuestionsBlack_Hole_Physics ">Open Questions in Black Hole Physics</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/430/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1523828"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1523828"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1523828" data-cycle-prev="#prev1523828" data-cycle-progressive="#images1523828" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1523828-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g001-550.jpg?1731982343" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1523828" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1523828-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g002-550.jpg?1731982347'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1523828-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g003-550.jpg?1731982350'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1523828-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g004-550.jpg?1731982353'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1523828-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g005-550.jpg?1731982354'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1523828-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g006-550.jpg?1731982355'><p>Figure 6</p></div></script></div></div><div id="article-1523828-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g001-550.jpg?1731982343" title=" <strong>Figure 1</strong><br/> <p>The function <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </semantics></math> for different values of <span class="html-italic">k</span>, <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <span class="html-italic">a</span>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/430'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g002-550.jpg?1731982347" title=" <strong>Figure 2</strong><br/> <p>Black hole mass as a function of the entropy <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>(</mo> <mi>S</mi> <mo>)</mo> </mrow> </semantics></math> for different values of <span class="html-italic">k</span>, <span class="html-italic">a</span>, and <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/430'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g003-550.jpg?1731982350" title=" <strong>Figure 3</strong><br/> <p>Black hole temperature as a function of the entropy <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>(</mo> <mi>S</mi> <mo>)</mo> </mrow> </semantics></math> for different values of <span class="html-italic">k</span>, <span class="html-italic">a</span> and <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/430'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g004-550.jpg?1731982353" title=" <strong>Figure 4</strong><br/> <p>Black hole heat capacity as a function of the entropy <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>(</mo> <mi>S</mi> <mo>)</mo> </mrow> </semantics></math> for different values of <span class="html-italic">k</span>, <span class="html-italic">a</span>, and <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/430'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g005-550.jpg?1731982354" title=" <strong>Figure 5</strong><br/> <p>Plot of Gibbs free energy as a function of horizon radius.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/430'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00430/article_deploy/html/images/universe-10-00430-g006-550.jpg?1731982355" title=" <strong>Figure 6</strong><br/> <p>The trace of Hessian matrix as a function of the horizon radius.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/430'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 28 pages, 2411 KiB   </span> <a href="/2218-1997/10/11/429/pdf?version=1732008645" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Cosmological Models in Lovelock Gravity: An Overview of Recent Progress" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Review</span></div> <a class="title-link" href="/2218-1997/10/11/429">Cosmological Models in Lovelock Gravity: An Overview of Recent Progress</a> <div class="authors"> by <span class="inlineblock "><strong>Sergey Pavluchenko</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 429; <a href="https://doi.org/10.3390/universe10110429">https://doi.org/10.3390/universe10110429</a> - 18 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> In the current review, we provide a summary of the recent progress made in the cosmological aspect of extra-dimensional Lovelock gravity. Our review covers a wide variety of particular model/matter source combinations: Einstein–Gauss–Bonnet as well as cubic Lovelock gravities with vacuum, cosmological constant, <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/429/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> In the current review, we provide a summary of the recent progress made in the cosmological aspect of extra-dimensional Lovelock gravity. Our review covers a wide variety of particular model/matter source combinations: Einstein–Gauss–Bonnet as well as cubic Lovelock gravities with vacuum, cosmological constant, perfect fluid, spatial curvature, and some of their combinations. Our analysis suggests that it is possible to set constraints on the parameters of the above-mentioned models from the simple requirement of the existence of a smooth transition from the initial singularity to a realistic low-energy regime. Initially, anisotropic space naturally evolves into a configuration with two isotropic subspaces, and if one of these subspaces is three-dimensional and is expanding while another is contracting, we call it realistic compactification. Of course, the process is not devoid of obstacles, and in our paper, we review the results of the compactification occurrence investigation for the above-mentioned models. In particular, for vacuum and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">Λ</mi></semantics></math></inline-formula>-term EGB models, compactification is not suppressed (but is not the only possible outcome either) if the number of extra dimensions is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mo>⩾</mo><mn>2</mn></mrow></semantics></math></inline-formula>; for vacuum cubic Lovelock gravities it is always present (however, cubic Lovelock gravity is defined only for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mo>⩾</mo><mn>3</mn></mrow></semantics></math></inline-formula> number of extra dimensions); for the EGB model with perfect fluid it is present for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> (we have not considered this model in higher dimensions yet), and in the presence of spatial curvature, the realistic stabilization of extra dimensions is always present (however, such a model is well-defined only in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mo>⩾</mo><mn>4</mn></mrow></semantics></math></inline-formula> number of extra dimensions). <a href="/2218-1997/10/11/429">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/universe/special_issues/T0P2T501H4 ">Cosmological Models of the Universe</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/429/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1523459"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1523459"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1523459" data-cycle-prev="#prev1523459" data-cycle-progressive="#images1523459" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1523459-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g001-550.jpg?1732008740" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1523459" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1523459-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g002-550.jpg?1732008744'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1523459-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g003-550.jpg?1732008746'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1523459-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g004-550.jpg?1732008748'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1523459-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g005-550.jpg?1732008751'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1523459-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g006-550.jpg?1732008752'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1523459-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g007-550.jpg?1732008752'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1523459-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g008-550.jpg?1732008753'><p>Figure 8</p></div></script></div></div><div id="article-1523459-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g001-550.jpg?1732008740" title=" <strong>Figure 1</strong><br/> <p>Resulting regimes for the <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> vacuum case: <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math> on (<b>a</b>) and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math> on (<b>b</b>) (see the text for more details).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/429'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g002-550.jpg?1732008744" title=" <strong>Figure 2</strong><br/> <p>Resulting regimes for EGB vacuum cases: <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> (panel (<b>a</b>) for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math> and panel (<b>b</b>) for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math>), <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> (panel (<b>c</b>) for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math> and panel (<b>d</b>) for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math>), and general <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>⩾</mo> <mn>4</mn> </mrow> </semantics></math> case (panel (<b>e</b>) for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, and panel (<b>f</b>) for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math>) (see the text for more details).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/429'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g003-550.jpg?1732008746" title=" <strong>Figure 3</strong><br/> <p>Viable regimes for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>⩾</mo> <mn>4</mn> </mrow> </semantics></math> EGB cosmology with <math display="inline"><semantics> <mi mathvariant="normal">Λ</mi> </semantics></math>-term: (<b>a</b>) panel: <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="normal">Λ</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math> featuring <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>→</mo> <msub> <mi>K</mi> <mn>3</mn> </msub> </mrow> </semantics></math> regime; (<b>b</b>) panel: <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="normal">Λ</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mi mathvariant="normal">Λ</mi> <mo>⩽</mo> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </mrow> </semantics></math> featuring <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>→</mo> <msubsup> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mi>D</mi> </mrow> <mn>1</mn> </msubsup> <mo>←</mo> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </msub> </mrow> </semantics></math> transitions; (<b>c</b>) panel: <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="normal">Λ</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math> featuring the same <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>→</mo> <msubsup> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mi>D</mi> </mrow> <mn>1</mn> </msubsup> <mo>←</mo> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </msub> </mrow> </semantics></math> transitions; (<b>d</b>) panel: <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="normal">Λ</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mi mathvariant="normal">Λ</mi> <mo>&lt;</mo> <msub> <mi>ζ</mi> <mn>2</mn> </msub> </mrow> </semantics></math> still featuring the same <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>→</mo> <msubsup> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mi>D</mi> </mrow> <mn>1</mn> </msubsup> <mo>←</mo> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </msub> </mrow> </semantics></math> transitions; (<b>e</b>) panel: <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="normal">Λ</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mi mathvariant="normal">Λ</mi> <mo>=</mo> <msub> <mi>ζ</mi> <mn>2</mn> </msub> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>→</mo> <msubsup> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mi>D</mi> </mrow> <mn>1</mn> </msubsup> <mo>←</mo> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </msub> </mrow> </semantics></math> transitions; (<b>f</b>) panel: <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="normal">Λ</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ζ</mi> <mn>2</mn> </msub> <mo>&lt;</mo> <mi>α</mi> <mi mathvariant="normal">Λ</mi> <mo>&lt;</mo> <msub> <mi>ζ</mi> <mn>3</mn> </msub> </mrow> </semantics></math> (see the text for more details).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/429'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g004-550.jpg?1732008748" title=" <strong>Figure 4</strong><br/> <p>Viable regimes for vacuum cubic Lovelock cosmology (all viable regimes are located in the second quadrant): (<b>a</b>) panel: <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </msub> <mo>→</mo> <msub> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mi>D</mi> </mrow> </msub> </mrow> </semantics></math> transition on the green branch for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>3</mn> <mo>÷</mo> <mn>7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>⩽</mo> <msub> <mi>μ</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>b</b>) panel: <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </msub> <mo>→</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> </mrow> </semantics></math> transition on the green-blue branch for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>3</mn> <mo>÷</mo> <mn>7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>&gt;</mo> <msub> <mi>μ</mi> <mn>1</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) panel: <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </msub> <mo>→</mo> <msub> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mi>D</mi> </mrow> </msub> </mrow> </semantics></math> transition on the green branch as well as <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mn>5</mn> </msub> <mo>→</mo> <msub> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mi>D</mi> </mrow> </msub> </mrow> </semantics></math> transition on the red branch for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>⩾</mo> <mn>8</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>⩽</mo> <msub> <mi>μ</mi> <mn>2</mn> </msub> </mrow> </semantics></math>; (<b>d</b>) panel: <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </msub> <mo>→</mo> <msub> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mi>D</mi> </mrow> </msub> <mo>←</mo> <msub> <mi>K</mi> <mn>5</mn> </msub> </mrow> </semantics></math> double transition on the green branch for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>⩾</mo> <mn>8</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>⩽</mo> <msub> <mi>μ</mi> <mn>3</mn> </msub> </mrow> </semantics></math>; (<b>e</b>) panel: <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </msub> <mo>→</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> </mrow> </semantics></math> transition on the right green-blue branch and <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mn>5</mn> </msub> <mo>→</mo> <msub> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mi>D</mi> </mrow> </msub> </mrow> </semantics></math> transition on the left green-blue branch for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>⩾</mo> <mn>8</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>&gt;</mo> <msub> <mi>μ</mi> <mn>3</mn> </msub> </mrow> </semantics></math> (see the text for more details).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/429'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g005-550.jpg?1732008751" title=" <strong>Figure 5</strong><br/> <p>Viable regimes for EGB model with a perfect fluid as a source: (<b>a</b>) panel: large-scale structure of the <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>h</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math> quadrant for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math>; (<b>b</b>) panel: vicinity of <math display="inline"><semantics> <msub> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mn>2</mn> </mrow> </msub> </semantics></math> stable point for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math>, initial conditions leading to <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>→</mo> <msub> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> transition are bounded by light-blue lines; (<b>c</b>) panel: large-scale structure of the <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>h</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math> quadrant for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>3</mn> <mo>&gt;</mo> <mi>ω</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>; (<b>d</b>) panel: vicinity of <math display="inline"><semantics> <msub> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mn>2</mn> </mrow> </msub> </semantics></math> stable point for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>3</mn> <mo>&gt;</mo> <mi>ω</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, initial conditions leading to <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>→</mo> <msub> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> transition are bounded by light-blue lines; (<b>e</b>) panel: large-scale structure of the <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>h</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math> quadrant for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>&gt;</mo> <mn>1</mn> <mo>/</mo> <mn>3</mn> </mrow> </semantics></math>, only <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>S</mi> <mo>→</mo> <msub> <mi>E</mi> <mrow> <mn>3</mn> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> transition remains; (<b>f</b>) vicinity of the exponential constant volume solution (<math display="inline"><semantics> <msub> <mi>E</mi> <mrow> <mi>C</mi> <mi>V</mi> <mi>S</mi> </mrow> </msub> </semantics></math>) (see the text for more details).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/429'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g006-550.jpg?1732008752" title=" <strong>Figure 6</strong><br/> <p>Illustrations for the dynamics of the EGB case with spatial curvature: regime with stabilization of extra dimensions (<math display="inline"><semantics> <mrow> <mi>H</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>h</mi> <mo>→</mo> <mn>0</mn> </mrow> </semantics></math>) on (<b>a</b>) panel, areas on the parameters space where stabilization of extra dimensions with positive spatial curvature is possible and stable, as a function of <span class="html-italic">D</span> (<b>b</b>,<b>c</b>) panels (see the text for more details).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/429'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g007-550.jpg?1732008752" title=" <strong>Figure 7</strong><br/> <p>Illustrations for the dynamics of the EGB case initial total anisotropy (Bianchi-I-type): different initial conditions for the model with 5 spatial dimensions could lead to either <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>3</mn> <mo>+</mo> <mn>2</mn> <mo>]</mo> </mrow> </semantics></math> spatial splitting ((<b>a</b>) panel) or isotropization ((<b>b</b>) panel); distribution of the initial conditions for the model with 6 spatial dimensions leading to either <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>4</mn> <mo>+</mo> <mn>2</mn> <mo>]</mo> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>3</mn> <mo>+</mo> <mn>3</mn> <mo>]</mo> </mrow> </semantics></math> spatial splittings ((<b>c</b>) panel) (see the text for more details).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/429'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00429/article_deploy/html/images/universe-10-00429-g008-550.jpg?1732008753" title=" <strong>Figure 8</strong><br/> <p>Summary of the bounds on <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>α</mi> <mo>,</mo> <mi mathvariant="normal">Λ</mi> <mo>)</mo> </mrow> </semantics></math> from this paper alone on (<b>a</b>) panel; from other considerations found in the literature on (<b>b</b>) panel; and the intersection between them on (<b>c</b>) panel (see the text for more details).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/429'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 20 pages, 419 KiB   </span> <a href="/2218-1997/10/11/428/pdf?version=1731926211" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Current Density Induced by a Cosmic String in de Sitter Spacetime in the Presence of Two Flat Boundaries" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/11/428">Current Density Induced by a Cosmic String in de Sitter Spacetime in the Presence of Two Flat Boundaries</a> <div class="authors"> by <span class="inlineblock "><strong>Wagner Oliveira dos Santos</strong>, </span><span class="inlineblock "><strong>Herondy F. Santana Mota</strong> and </span><span class="inlineblock "><strong>Eugênio R. Bezerra de Mello</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 428; <a href="https://doi.org/10.3390/universe10110428">https://doi.org/10.3390/universe10110428</a> - 17 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> In this paper, we investigate the vacuum bosonic current density induced by a carrying-magnetic-flux cosmic string in a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>D</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-de Sitter spacetime considering the presence of two flat boundaries perpendicular to it. In this setup, the Robin boundary conditions <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/428/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> In this paper, we investigate the vacuum bosonic current density induced by a carrying-magnetic-flux cosmic string in a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>D</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-de Sitter spacetime considering the presence of two flat boundaries perpendicular to it. In this setup, the Robin boundary conditions are imposed on the scalar charged quantum field on the boundaries. The particular cases of Dirichlet and Neumann boundary conditions are studied separately. Due to the coupling of the quantum scalar field with the classical gauge field, corresponding to a magnetic flux running along the string’s core, a nonzero vacuum expectation value for the current density operator along the azimuthal direction is induced. The two boundaries divide the space in three regions with different properties of the vacuum states. In this way, our main objective is to calculate the induced currents in these three regions. In order to develop this analysis we calculate, for both regions, the positive frequency Wightman functions. Because the vacuum bosonic current in dS space has been investigated before, in this paper we consider only the contributions induced by the boundaries. We show that for each region the azimuthal current densities are odd functions of the magnetic flux along the string. To probe the correctness of our results, we take the particular cases and analyze some asymptotic limits of the parameters of the model. Also some graphs are presented exhibiting the behavior of the current with relevant physical parameter of the system. <a href="/2218-1997/10/11/428">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/universe/sections/field_theory">Field Theory</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/428/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1522866"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1522866"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1522866" data-cycle-prev="#prev1522866" data-cycle-progressive="#images1522866" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1522866-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00428/article_deploy/html/images/universe-10-00428-g001-550.jpg?1731926295" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1522866" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1522866-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00428/article_deploy/html/images/universe-10-00428-g002-550.jpg?1731926297'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1522866-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00428/article_deploy/html/images/universe-10-00428-g003-550.jpg?1731926298'><p>Figure 3</p></div></script></div></div><div id="article-1522866-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00428/article_deploy/html/images/universe-10-00428-g001-550.jpg?1731926295" title=" <strong>Figure 1</strong><br/> <p>The VEV of the azimuthal current density induced by a single plate, located at <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <msub> <mi>a</mi> <mi>j</mi> </msub> </mrow> </semantics></math>, is plotted as function of the proper distance from the string, <math display="inline"><semantics> <msub> <mi>r</mi> <mi>p</mi> </msub> </semantics></math>, (<b>top panel</b>) and the proper distance from the plate, <math display="inline"><semantics> <msub> <mi>z</mi> <mi>p</mi> </msub> </semantics></math>, (<b>bottom panel</b>), in units of <span class="html-italic">a</span>. In both plots, we consider Dirichlet and Neumann boundary conditions and various values of <span class="html-italic">q</span>. Both graphs are plotted for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>m</mi> <mi>a</mi> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>j</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>. Moreover, in the <b>top panel</b> we have fixed <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and in the <b>bottom</b> one, <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/428'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00428/article_deploy/html/images/universe-10-00428-g002-550.jpg?1731926297" title=" <strong>Figure 2</strong><br/> <p>The VEV of the azimuthal current density induced between the plates is plotted as function of the proper distance from the string, <math display="inline"><semantics> <msub> <mi>r</mi> <mi>p</mi> </msub> </semantics></math>. In the <b>top panel</b> we consider <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math> and in the <b>bottom panel</b>, <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>. In both plots we consider Dirichlet and Neumann boundary conditions and different values of <span class="html-italic">q</span>. Both graphs are plotted for <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>m</mi> <mi>a</mi> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math>. The positions of the plates are in both plots at <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/428'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00428/article_deploy/html/images/universe-10-00428-g003-550.jpg?1731926298" title=" <strong>Figure 3</strong><br/> <p>The VEV of the azimuthal current density induced between the plates is plotted as function of <math display="inline"><semantics> <msub> <mi>z</mi> <mi>p</mi> </msub> </semantics></math>. In the <b>top panel</b> we assume <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, and in the <b>bottom</b>, <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>. For both plots we also assume <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>m</mi> <mi>a</mi> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/428'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 16 pages, 823 KiB   </span> <a href="/2218-1997/10/11/427/pdf?version=1731916792" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian Approach" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/11/427">Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian Approach</a> <div class="authors"> by <span class="inlineblock "><strong>Diego Montalvo</strong>, </span><span class="inlineblock "><strong>Adam Smith-Orlik</strong>, </span><span class="inlineblock "><strong>Saeed Rastgoo</strong>, </span><span class="inlineblock "><strong>Laura Sagunski</strong>, </span><span class="inlineblock "><strong>Niklas Becker</strong> and </span><span class="inlineblock "><strong>Hazkeel Khan</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 427; <a href="https://doi.org/10.3390/universe10110427">https://doi.org/10.3390/universe10110427</a> - 17 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> We apply the Lagrangian method to study the post-Newtonian evolution of a compact binary system with environmental effects, including a dark matter spike, and obtain the resulting gravitational wave emission. This formalism allows one to incorporate post-Newtonian effects up to any desired known <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/427/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> We apply the Lagrangian method to study the post-Newtonian evolution of a compact binary system with environmental effects, including a dark matter spike, and obtain the resulting gravitational wave emission. This formalism allows one to incorporate post-Newtonian effects up to any desired known order, as well as any other environmental effect around the binary, as long as their dissipation power or force formulae are known. In particular, in this work, we employ this method to study a black hole–black hole binary system of mass ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mn>5</mn></msup></semantics></math></inline-formula> by including post-Newtonian effects of order 1PN and 2.5PN, as well as the effect of relativistic dynamical friction. We obtain the modified orbits and the corresponding modified gravitational waveform. Finally, we contrast these modifications against the LISA sensitivity curve in frequency space and show that this observatory can detect the associated signals. <a href="/2218-1997/10/11/427">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/universe/sections/compact_objects">Compact Objects</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/427/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1522748"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1522748"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1522748" data-cycle-prev="#prev1522748" data-cycle-progressive="#images1522748" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1522748-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g001-550.jpg?1731916884" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1522748" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1522748-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g002-550.jpg?1731916886'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1522748-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g003-550.jpg?1731916888'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1522748-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g004-550.jpg?1731916889'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1522748-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g005-550.jpg?1731916891'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1522748-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g006-550.jpg?1731916893'><p>Figure 6</p></div></script></div></div><div id="article-1522748-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g001-550.jpg?1731916884" title=" <strong>Figure 1</strong><br/> <p>Figure of the DM profile used under the relativistic corrections in [<a href="#B32-universe-10-00427" class="html-bibr">32</a>] for <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.3</mn> <mo>,</mo> <mn>0.5</mn> <mo>)</mo> </mrow> <mspace width="0.277778em"/> <mrow> <mi>GeV</mi> <mo>/</mo> <msup> <mi>cm</mi> <mn>3</mn> </msup> </mrow> </mrow> </semantics></math>. The dashed red lines represent the stages of the evolution. The right line is situated at the start of the evolution at <math display="inline"><semantics> <mrow> <mn>100</mn> <msub> <mi>r</mi> <mrow> <mi>I</mi> <mi>S</mi> <mi>C</mi> <mi>O</mi> </mrow> </msub> </mrow> </semantics></math>, and the left line is where we terminate the inspiral at <math display="inline"><semantics> <mrow> <mn>3</mn> <msub> <mi>r</mi> <mrow> <mi>S</mi> <mi>I</mi> <mi>C</mi> <mi>O</mi> </mrow> </msub> </mrow> </semantics></math>. These ranges correspond to observable GW frequency bands for LISA, as well as the range of validity of PN corrections and final stages of the inspiral.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/427'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g002-550.jpg?1731916886" title=" <strong>Figure 2</strong><br/> <p>Semi-major axis of the orbit as a function of time, where in all cases, evolution ranges from <math display="inline"><semantics> <mrow> <mn>100</mn> <mspace width="0.277778em"/> <msub> <mi>r</mi> <mi>ISCO</mi> </msub> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mn>3</mn> <mspace width="0.277778em"/> <msub> <mi>r</mi> <mi>ISCO</mi> </msub> </mrow> </semantics></math>. The dynamical friction term expedites energy dissipation and modifies the radial evolution of the binary. The no 1PN corrections curve refers to setting the <math display="inline"><semantics> <msub> <mi>L</mi> <mrow> <mn>1</mn> <mi>PN</mi> </mrow> </msub> </semantics></math> terms to zero, which has a noticeable effect, especially at the latter stages of the inspiral. All the curves above include the GW dissipative term.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/427'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g003-550.jpg?1731916888" title=" <strong>Figure 3</strong><br/> <p>Example of the time-domain “plus” polarization waveform, <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mo>+</mo> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, following the evolution of the <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> GeV/cm<sup>3</sup> DM halo vs. vacuum with all PN corrections. Assuming the system enters in-band at the early stages of the inspiral (<math display="inline"><semantics> <mrow> <mn>70</mn> <mspace width="0.277778em"/> <msub> <mi>r</mi> <mi>ISCO</mi> </msub> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) and at a point where the DM mini-spike is not at its densest, the timescale of this dephasing is set to start at about the four-year mark, which is within LISA’s lifetime.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/427'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g004-550.jpg?1731916889" title=" <strong>Figure 4</strong><br/> <p>Number of cycles comparison for different DM densities and vacuum as a function of GW frequency. Inset plots represent zoomed-in sections of the main plot at <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </semantics></math> Hz (left inset) and <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> Hz (right inset).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/427'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g005-550.jpg?1731916891" title=" <strong>Figure 5</strong><br/> <p>The strain and detectability for LISA’s sensitivity curve given for various DM densities parametrized by <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>0</mn> </msub> </semantics></math>. GW energy dissipation is dominant over DM friction during the later stages of the inspiral, which can be seen by the agreement of all strains at higher frequencies. Thus, searches for this DM friction would be the most sensitive during earlier parts of the inspiral but not earlier than the strain curves crossing LISA’s sensitivity. For our choice of parameters, this occurs near <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </semantics></math> Hz.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/427'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00427/article_deploy/html/images/universe-10-00427-g006-550.jpg?1731916893" title=" <strong>Figure 6</strong><br/> <p>Ratio between the characteristic strains between the case without dark matter, and the different values of <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>0</mn> </msub> </semantics></math>. As expected, the largest deviations occur during the early stages of the inspiral. Eventually, dissipation through gravitational wave radiation dominates dark matter friction and leads all waveforms to converge on the same frequency evolution. This stage, although the brightest on the LISA band, has the smallest contributions from dark matter signatures.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/427'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 11 pages, 255 KiB   </span> <a href="/2218-1997/10/11/426/pdf?version=1731665341" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Probing the Dark Universe with Gravitational Waves" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/11/426">Probing the Dark Universe with Gravitational Waves</a> <div class="authors"> by <span class="inlineblock "><strong>Antonio Enea Romano</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 426; <a href="https://doi.org/10.3390/universe10110426">https://doi.org/10.3390/universe10110426</a> - 15 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Gravitational waves (GWs) are expected to interact with dark energy and dark matter, affecting their propagation on cosmological scales. To model this interaction, we derive a gauge-invariant effective equation and action valid for all GW polarizations. This is achieved by encoding the effects <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/426/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Gravitational waves (GWs) are expected to interact with dark energy and dark matter, affecting their propagation on cosmological scales. To model this interaction, we derive a gauge-invariant effective equation and action valid for all GW polarizations. This is achieved by encoding the effects of GW interactions at different orders of perturbation into a polarization-, frequency-, and time-dependent effective speed. The invariance of perturbations under time-dependent conformal transformations and the gauge invariance of GWs allow us to derive the unitary gauge effective action in any conformally related frame, thereby clarifying the relationship between the Einstein and Jordan frames. Tests of the polarization and frequency dependencies in the propagation time and luminosity distance of different GW polarizations allow us to probe the dark Universe, which acts as an effective medium, modeled by the GW effective speed. <a href="/2218-1997/10/11/426">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Collection <a href=" /journal/universe/topical_collections/Gravitational_Waves_Astronomy ">Gravitational Waves as a New Probe for Astronomy and Fundamental Physics</a>)<br/> </div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 3 pages, 145 KiB   </span> <a href="/2218-1997/10/11/425/pdf?version=1731645204" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Editorial to the Special Issue “Space Missions to Small Bodies: Results and Future Activities”" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Editorial</span></div> <a class="title-link" href="/2218-1997/10/11/425">Editorial to the Special Issue “Space Missions to Small Bodies: Results and Future Activities”</a> <div class="authors"> by <span class="inlineblock "><strong>Andrea Longobardo</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 425; <a href="https://doi.org/10.3390/universe10110425">https://doi.org/10.3390/universe10110425</a> - 14 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-full inline"> Small bodies (asteroids, comets, and satellites) are the most primitive bodies of our solar system and, for this reason, represent the key to understanding its origin and early evolution [...] <a href="/2218-1997/10/11/425">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/universe/special_issues/Hi_small_bodies ">Space Missions to Small Bodies: Results and Future Activities</a>)<br/> </div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 30 pages, 11511 KiB   </span> <a href="/2218-1997/10/11/424/pdf?version=1732197779" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Sources and Radiations of the Fermi Bubbles" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/11/424">Sources and Radiations of the Fermi Bubbles</a> <div class="authors"> by <span class="inlineblock "><strong>Vladimir A. Dogiel</strong> and </span><span class="inlineblock "><strong>Chung-Ming Ko</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 424; <a href="https://doi.org/10.3390/universe10110424">https://doi.org/10.3390/universe10110424</a> - 12 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Two enigmatic gamma-ray features in the galactic central region, known as Fermi Bubbles (FBs), were found from Fermi-LAT data. An energy release, (e.g., by tidal disruption events in the Galactic Center, GC), generates a cavity with a shock that expands into the local <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/424/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Two enigmatic gamma-ray features in the galactic central region, known as Fermi Bubbles (FBs), were found from Fermi-LAT data. An energy release, (e.g., by tidal disruption events in the Galactic Center, GC), generates a cavity with a shock that expands into the local ambient medium of the galactic halo. A decade or so ago, a phenomenological model of the FBs was suggested as a result of routine star disruptions by the supermassive black hole in the GC which might provide enough energy for large-scale structures, like the FBs. In 2020, analytical and numerical models of the FBs as a process of routine tidal disruption of stars near the GC were developed; these disruption events can provide enough cumulative energy to form and maintain large-scale structures like the FBs. The disruption events are expected to be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo>&sim;</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><msup><mi>yr</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, providing an average power of energy release from the GC into the halo of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi mathvariant="script">E</mi><mo>˙</mo></mover><mo>&sim;</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>41</mn></msup></mrow></semantics></math></inline-formula> erg <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="normal">s</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, which is needed to support the FBs. Analysis of the evolution of superbubbles in exponentially stratified disks concluded that the FB envelope would be destroyed by the Rayleigh–Taylor (RT) instabilities at late stages. The shell is composed of swept-up gas of the bubble, whose thickness is much thinner in comparison to the size of the envelope. We assume that hydrodynamic turbulence is excited in the FB envelope by the RT instability. In this case, the universal energy spectrum of turbulence may be developed in the inertial range of wavenumbers of fluctuations (the Kolmogorov–Obukhov spectrum). From our model we suppose the power of the FBs is transformed partly into the energy of hydrodynamic turbulence in the envelope. If so, hydrodynamic turbulence may generate MHD fluctuations, which accelerate cosmic rays there and generate gamma-ray and radio emission from the FBs. We hope that this model may interpret the observed nonthermal emission from the bubbles. <a href="/2218-1997/10/11/424">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/universe/special_issues/7683EV6AD4 ">Studying Astrophysics with High-Energy Cosmic Particles</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/424/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1519436"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1519436"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1519436" data-cycle-prev="#prev1519436" data-cycle-progressive="#images1519436" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1519436-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g001-550.jpg?1732197878" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1519436" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g002-550.jpg?1732197879'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g003-550.jpg?1732197880'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g004-550.jpg?1732197881'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g005-550.jpg?1732197882'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g006-550.jpg?1732197883'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g007-550.jpg?1732197884'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g008-550.jpg?1732197886'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g009-550.jpg?1732197887'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g010-550.jpg?1732197888'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g011-550.jpg?1732197888'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g012-550.jpg?1732197889'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g013-550.jpg?1732197890'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g014-550.jpg?1732197891'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1519436-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g015-550.jpg?1732197891'><p>Figure 15</p></div></script></div></div><div id="article-1519436-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g001-550.jpg?1732197878" title=" <strong>Figure 1</strong><br/> <p>Comparison of the morphology of the gamma-ray bubbles (red) and the X-ray bubbles (cyan) in the direction of the Galactic Center. Figure reproduced from Predehl et al. [<a href="#B1-universe-10-00424" class="html-bibr">1</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g002-550.jpg?1732197879" title=" <strong>Figure 2</strong><br/> <p>X-ray superbubbles in the galaxy NGC 3079. Image from <a href="https://chandra.harvard.edu/photo/2019/ngc3079" target="_blank">https://chandra.harvard.edu/photo/2019/ngc3079</a> (accessed on 10 September 2024). Image credit: X-ray: NASA/CXC/University of Michigan. Optical: NASA/STScI.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g003-550.jpg?1732197880" title=" <strong>Figure 3</strong><br/> <p>The observed X-ray light curve of Swift J1644+57 from Swift, XMM-Newton, and Chandra. Figure reproduced from Cheng et al. [<a href="#B43-universe-10-00424" class="html-bibr">43</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g004-550.jpg?1732197881" title=" <strong>Figure 4</strong><br/> <p>A thermonuclear explosion in the terrestrial atmosphere. Image credit: United States Department of Energy. Image from <a href="https://commons.wikimedia.org/wiki/File:Castle_Bravo_nuclear_test_(cropped).jpg" target="_blank">https://commons.wikimedia.org/wiki/File:Castle_Bravo_nuclear_test_(cropped).jpg</a> (accessed on 10 September 2024).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g005-550.jpg?1732197882" title=" <strong>Figure 5</strong><br/> <p>Illustration of the double-bubble shock envelope in the halo evolving with time. The gas distribution in the halo in the left panel is exponential and in the right panel follows a power law. Figure adapted from Ko et al. [<a href="#B16-universe-10-00424" class="html-bibr">16</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g006-550.jpg?1732197883" title=" <strong>Figure 6</strong><br/> <p>Temporal variation in the shock velocity of the top of the bubble for the case of exponential halo with <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>=</mo> <mn>0.67</mn> </mrow> </semantics></math> kpc and <math display="inline"><semantics> <mrow> <msub> <mi>n</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.03</mn> <msup> <mi>cm</mi> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>. (<b>Left panel</b>): One single input of energy from the GC. (<b>Right panel</b>): Multiple TDEs with different values of power release at the GC. The horizontal dotted line indicates the velocity which is necessary for the shock in order not to stall in the halo, which is three times the sound speed in the halo <math display="inline"><semantics> <mrow> <mn>3</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>7</mn> </msup> </mrow> </semantics></math> cm <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>. Figure reproduced from Ko et al. [<a href="#B16-universe-10-00424" class="html-bibr">16</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g007-550.jpg?1732197884" title=" <strong>Figure 7</strong><br/> <p>Density distribution of numerical simulations of the FBs in an exponential halo. The two panels in the left column are results of multiple explosions (e.g., TDEs) and in the right column are results of a single huge explosion. In the upper left panel, “Me0.05-3e52erg 18.0 Myr” corresponds to multiple explosions with 0.05 Myr between successive explosions and the energy release by each explosion is <math display="inline"><semantics> <mrow> <mn>3</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>52</mn> </msup> </mrow> </semantics></math> erg, and the simulation ends at 18.0 Myr. In the upper right panel, “1e-1.08e55erg 10.0 Myr” corresponds to a single explosion with an energy release of <math display="inline"><semantics> <mrow> <mn>1.08</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>55</mn> </msup> </mrow> </semantics></math> erg, and the simulation ends at 10.0 Myr. Similar explanation for the lower panels. Lower panel figures reproduced from Ko et al. [<a href="#B16-universe-10-00424" class="html-bibr">16</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g008-550.jpg?1732197886" title=" <strong>Figure 8</strong><br/> <p>Coherent magnetic structure above and below the galactic plane [<a href="#B17-universe-10-00424" class="html-bibr">17</a>]. (<b>a</b>) Polarized synchrotron intensity map at <math display="inline"><semantics> <mrow> <mn>22.8</mn> </mrow> </semantics></math> GHz from WMAP. Green bars show the magnetic field direction. (<b>b</b>) Comparison between the polarized synchrotron emission at <math display="inline"><semantics> <mrow> <mn>22.8</mn> </mrow> </semantics></math> GHz (red) and the X-ray emission at <math display="inline"><semantics> <mrow> <mn>0.6</mn> </mrow> </semantics></math>∼<math display="inline"><semantics> <mrow> <mn>1.0</mn> </mrow> </semantics></math> keV from eROSITA (green). Magnetized ridges are shown in white. Figure reproduced from Zhang et al. [<a href="#B17-universe-10-00424" class="html-bibr">17</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g009-550.jpg?1732197887" title=" <strong>Figure 9</strong><br/> <p>The solid line shows the momentum diffusion coefficient derived for the bubble parameters when the CR absorption is taken into account. The dash-dotted line is the results ignoring the CR absorption. Figure reproduced from Cheng et al. [<a href="#B71-universe-10-00424" class="html-bibr">71</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g010-550.jpg?1732197888" title=" <strong>Figure 10</strong><br/> <p>Spectrum of radio (<b>left</b>) and gamma-ray (<b>right</b>) emission from the FBs (see [<a href="#B71-universe-10-00424" class="html-bibr">71</a>]). The microwave data were taken from Planck Collaboration [<a href="#B3-universe-10-00424" class="html-bibr">3</a>], and the gamma-ray data from Ackermann et al. [<a href="#B72-universe-10-00424" class="html-bibr">72</a>], Ackermann et al. [<a href="#B77-universe-10-00424" class="html-bibr">77</a>]. Figure adapted from Cheng et al. [<a href="#B71-universe-10-00424" class="html-bibr">71</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g011-550.jpg?1732197888" title=" <strong>Figure 11</strong><br/> <p>X-ray emission from the galactic plane whose excess emission is above the equilibrium Maxwellian spectrum. Dash-dotted line is a simple combination of thermal plus nonthermal spectrum. Solid line is the spectrum with the effect of runaway flux. Figure reproduced from Dogiel et al. [<a href="#B96-universe-10-00424" class="html-bibr">96</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g012-550.jpg?1732197889" title=" <strong>Figure 12</strong><br/> <p>The spectrum of electrons accelerated from background plasma (see [<a href="#B100-universe-10-00424" class="html-bibr">100</a>]). The solid line is the density of electrons, <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> </semantics></math>. The thick solid line is the pure thermal Maxwellian distribution. The dashed line is the power-law approximation of the nonthermal tail. For <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <msub> <mi>p</mi> <mi>inj</mi> </msub> </mrow> </semantics></math>, overheating is insignificant. Figure adapted from Chernyshov et al. [<a href="#B100-universe-10-00424" class="html-bibr">100</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g013-550.jpg?1732197890" title=" <strong>Figure 13</strong><br/> <p>The spectrum of SNR electrons from the galactic disk that have been re-accelerated in the FBs. The five spectra in the figure correspond to different cases of the model: (1) thick solid line: without re-acceleration, escape, and advection; (2) thick dash-dotted line: without re-acceleration and escape but with advection; (3) thin dash-dotted line: with re-acceleration but without escape from the region and advection; (4) thin dotted line: with re-acceleration and escape from the region but without advection; (5) thin dashed line: with re-acceleration and advection but without escape. The density of electrons needed for the observed gamma-ray flux from the bubbles is shown by the gray region. The electron spectrum of case (5) can reproduce the gamma-ray data from Fermi-LAT and the microwave data from Planck (<a href="#universe-10-00424-f010" class="html-fig">Figure 10</a>). The parameters of case (5) can be found in the main text. For parameters of other cases, the reader is referred to Cheng et al. [<a href="#B101-universe-10-00424" class="html-bibr">101</a>]. Figure reproduced from Cheng et al. [<a href="#B101-universe-10-00424" class="html-bibr">101</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g014-550.jpg?1732197891" title=" <strong>Figure 14</strong><br/> <p>CR spectrum at the Earth as a combination of the contributions from the SNRs in the galactic disk and the stochastic acceleration in the FBs. Figure reproduced from Cheng et al. [<a href="#B116-universe-10-00424" class="html-bibr">116</a>] with permission.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00424/article_deploy/html/images/universe-10-00424-g015-550.jpg?1732197891" title=" <strong>Figure 15</strong><br/> <p>A possible multiple-shock structure in the FBs resulting from multiple TDEs at the GC. The figure shows the pressure (<b>left panel</b>) and kinetic energy (<b>right panel</b>) distributions of a numerical simulation of the FBs in an exponential halo. In the panels, “Me0.05-1e53” corresponds to multiple TDEs with 0.05 Myr between successive TDEs and the energy release by each TDE is <math display="inline"><semantics> <msup> <mn>10</mn> <mn>53</mn> </msup> </semantics></math> erg. The simulation ends at 10.0 Myr. The units of the color bars in both panels are <math display="inline"><semantics> <mrow> <mn>1.178</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>8</mn> </mrow> </msup> </mrow> </semantics></math> erg <math display="inline"><semantics> <mrow> <msup> <mi>cm</mi> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/424'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 16 pages, 1992 KiB   </span> <a href="/2218-1997/10/11/423/pdf?version=1731376530" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Exploring γ-Ray Flares from High-Redshift Blazar B3 1343+451 at GeV Energies" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/11/423">Exploring <i>γ</i>-Ray Flares from High-Redshift Blazar B3 1343+451 at GeV Energies</a> <div class="authors"> by <span class="inlineblock "><strong>Xiongfei Geng</strong>, </span><span class="inlineblock "><strong>Yang Liu</strong>, </span><span class="inlineblock "><strong>Gang Cao</strong>, </span><span class="inlineblock "><strong>Jing Fan</strong>, </span><span class="inlineblock "><strong>Xiongbang Yang</strong>, </span><span class="inlineblock "><strong>Nan Ding</strong>, </span><span class="inlineblock "><strong>Minghu Gao</strong>, </span><span class="inlineblock "><strong>Yehui Yang</strong> and </span><span class="inlineblock "><strong>Zhijie Zhang</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 423; <a href="https://doi.org/10.3390/universe10110423">https://doi.org/10.3390/universe10110423</a> - 11 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> We study the temporal and spectral variability properties of the high-redshift blazar B3 1343+451 utilizing Fermi-LAT data from 2008 to 2022 in the energy range of 0.1–300 GeV. We identify six major flares with many substructures and analyze their temporal and spectral properties <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/423/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> We study the temporal and spectral variability properties of the high-redshift blazar B3 1343+451 utilizing Fermi-LAT data from 2008 to 2022 in the energy range of 0.1–300 GeV. We identify six major flares with many substructures and analyze their temporal and spectral properties in detail. The fastest rise and decay timescales are found to be 4.8 ± 0.48 h and 5.28 ± 0.72 h, respectively. The size of the emission region is constrained to be <i>R</i> &sim; 5.18 × <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mn>15</mn></msup></semantics></math></inline-formula>–1.56 × <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mn>16</mn></msup></semantics></math></inline-formula> cm with the typical Doppler factors of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> &sim; 10–30. Most of the peaks from the flares exhibit a symmetric temporal profile within the error bars, implying that the rise and decay timescales are dominated by the disturbances caused by dense plasma blobs passing through the standing shock front in the jet region. We also find that four flares are better fitted with a log-parabolic distribution, while two flares are better fitted with a power-law distribution. Our results indicate that the emission regions vary from one flare to another, which is consistent with earlier results. <a href="/2218-1997/10/11/423">Full article</a> </div> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/423/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1518696"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1518696"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1518696" data-cycle-prev="#prev1518696" data-cycle-progressive="#images1518696" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1518696-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g001-550.jpg?1731376629" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1518696" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1518696-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g002-550.jpg?1731376631'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1518696-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g003-550.jpg?1731376633'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1518696-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g004-550.jpg?1731376635'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1518696-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g005-550.jpg?1731376635'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1518696-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g006-550.jpg?1731376636'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1518696-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g0A1-550.jpg?1731376637'><p>Figure A1</p></div></script></div></div><div id="article-1518696-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g001-550.jpg?1731376629" title=" <strong>Figure 1</strong><br/> <p>Panel (<b>a</b>) presents the 7-day binned light curves of B3 1343+451 from 2008 to 2022 at <span class="html-italic">E</span> &gt; 100 MeV. The different patterns are divided by green vertical dashed lines. Panel (<b>b</b>) presents the <math display="inline"><semantics> <mi>γ</mi> </semantics></math>-ray photon index as a function of time. Panel (<b>c</b>) presents the TS values (&gt;9) as a function of time on a logarithmic scale. Panel (<b>d</b>) presents the arrival time and energy of <span class="html-italic">E</span> &gt; 10 GeV photons with the significance levels of 2<math display="inline"><semantics> <mi>σ</mi> </semantics></math> and 3<math display="inline"><semantics> <mi>σ</mi> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/423'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g002-550.jpg?1731376631" title=" <strong>Figure 2</strong><br/> <p>Panels (<b>a</b>,<b>b</b>,<b>d</b>–<b>f</b>) present the 2-day binned light curves of Flare-I, Flare-II, Flare-V, Flare-VI (A), and Flare-VI (B) that are identified in <a href="#universe-10-00423-f001" class="html-fig">Figure 1</a>, respectively. Panel (<b>c</b>) presents the 1-day binned light curves of Flare-III. The light curves are fitted with Equation (<a href="#FD1-universe-10-00423" class="html-disp-formula">1</a>). Here, the fitted residuals are shown in (<b>a</b>–<b>f</b>).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/423'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g003-550.jpg?1731376633" title=" <strong>Figure 3</strong><br/> <p>CCF calculated for the 2-day or 1-day light curves within the 0.1–1 GeV and 1–300 GeV energy bands. The top-left, top-middle, and top-right present the correlations of Flare-I (binned in 2-day periods), Flare-II (binned in 2-day periods), and Flare-III (binned in 1-day period), respectively. The bottom-left and bottom-right present the correlations of Flare-V (binned in 2-day periods) and Flare-VI (binned in 2-day periods). CCCD is the cross-correlation centroid distribution. CCPD is the cross-correlation peak distribution.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/423'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g004-550.jpg?1731376635" title=" <strong>Figure 4</strong><br/> <p><math display="inline"><semantics> <mi>γ</mi> </semantics></math>-ray SEDs of B3 1343+451 during the different states defined in <a href="#universe-10-00423-f001" class="html-fig">Figure 1</a>. These states are fitted by a PL (green lines) and LP (orange dashed curves). Their respective best-fitting parameters are given in <a href="#universe-10-00423-t003" class="html-table">Table 3</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/423'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g005-550.jpg?1731376635" title=" <strong>Figure 5</strong><br/> <p>(<b>a</b>) Histogram of all the 7-day binned flux data points. (<b>b</b>) Histogram of all the photon energy above 10 GeV. (<b>c</b>) Histogram of peak fluxes from <a href="#universe-10-00423-t001" class="html-table">Table 1</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/423'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g006-550.jpg?1731376636" title=" <strong>Figure 6</strong><br/> <p>(<b>a</b>) Histogram of rise and decay times from <a href="#universe-10-00423-t001" class="html-table">Table 1</a>. (<b>b</b>) Histogram of the symmetry factor (<math display="inline"><semantics> <mi>ξ</mi> </semantics></math>) from <a href="#universe-10-00423-t001" class="html-table">Table 1</a>. (<b>c</b>) Histogram of the rise and decay times from the fastest variability timescale from <a href="#universe-10-00423-t002" class="html-table">Table 2</a>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/423'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00423/article_deploy/html/images/universe-10-00423-g0A1-550.jpg?1731376637" title=" <strong>Figure A1</strong><br/> <p>The 2-day binned light curves of Flare-I, Flare-II, Flare-V, and Flare-VI and the 1-day binned light curves of Flare-III. The peaks are identified by the BB algorithm with the false alarm rate parameter <math display="inline"><semantics> <msub> <mi>p</mi> <mn>0</mn> </msub> </semantics></math> = 0.05.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/423'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 4 pages, 166 KiB   </span> <a href="/2218-1997/10/11/422/pdf?version=1731142039" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Solar Radio Emissions" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Editorial</span></div> <a class="title-link" href="/2218-1997/10/11/422">Solar Radio Emissions</a> <div class="authors"> by <span class="inlineblock "><strong>Baolin Tan</strong> and </span><span class="inlineblock "><strong>Jing Huang</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 422; <a href="https://doi.org/10.3390/universe10110422">https://doi.org/10.3390/universe10110422</a> - 9 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-full inline"> The radio emission from the Sun covers a very wide frequency band ranging from several hundreds of GHz (sub-millimeter wavelength) down to sub-MHz (kilometer wavelength) [...] <a href="/2218-1997/10/11/422">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/universe/special_issues/HQGD6L2JO3 ">Solar Radio Emissions</a>)<br/> </div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 14 pages, 616 KiB   </span> <a href="/2218-1997/10/11/421/pdf?version=1731479696" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Gravitational Lensing Effects from Models of Loop Quantum Gravity with Rigorous Quantum Parameters" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/11/421">Gravitational Lensing Effects from Models of Loop Quantum Gravity with Rigorous Quantum Parameters</a> <div class="authors"> by <span class="inlineblock "><strong>Haida Li</strong> and </span><span class="inlineblock "><strong>Xiangdong Zhang</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 421; <a href="https://doi.org/10.3390/universe10110421">https://doi.org/10.3390/universe10110421</a> - 8 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Many previous works have studied gravitational lensing effects from Loop Quantum Gravity. So far, gravitational lensing effects from Loop Quantum Gravity have only been studied by choosing large quantum parameters much larger than the Planck scale. However, by construction, the quantum parameters of <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/421/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Many previous works have studied gravitational lensing effects from Loop Quantum Gravity. So far, gravitational lensing effects from Loop Quantum Gravity have only been studied by choosing large quantum parameters much larger than the Planck scale. However, by construction, the quantum parameters of the effective models of Loop Quantum Gravity are usually related to the Planck length and, thus, are extremely small. In this work, by strictly imposing the quantum parameters as initially constructed, we study the true quantum corrections of gravitational lensing effects by five effective black hole models of Loop Quantum Gravity. Our study reveals several interesting results, including the different scales of quantum corrections displayed by each model and the connection between the quantum correction of deflection angles and the quantum correction of the metric. Observables related to the gravitational lensing effect are also obtained for all models in the case of SgrA* and M87*. <a href="/2218-1997/10/11/421">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/universe/special_issues/Z07Y02X3N1 ">Quantum Field Theory in Curved Spacetime and Its Implications for Cosmology, Blackholes and Quantum Gravity</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/421/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1516772"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1516772"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1516772" data-cycle-prev="#prev1516772" data-cycle-progressive="#images1516772" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1516772-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00421/article_deploy/html/images/universe-10-00421-g001-550.jpg?1731479829" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1516772" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1516772-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00421/article_deploy/html/images/universe-10-00421-g002-550.jpg?1731479832'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1516772-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00421/article_deploy/html/images/universe-10-00421-g003-550.jpg?1731479833'><p>Figure 3</p></div></script></div></div><div id="article-1516772-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00421/article_deploy/html/images/universe-10-00421-g001-550.jpg?1731479829" title=" <strong>Figure 1</strong><br/> <p>Deflection angle <math display="inline"><semantics> <mi>α</mi> </semantics></math> with respect to impact factor <span class="html-italic">b</span>. All of the models investigated in this paper share the same curve with Schwarzschild BH.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/421'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00421/article_deploy/html/images/universe-10-00421-g002-550.jpg?1731479832" title=" <strong>Figure 2</strong><br/> <p><math display="inline"><semantics> <msub> <mi>Log</mi> <mn>10</mn> </msub> </semantics></math>-<math display="inline"><semantics> <msub> <mi>Log</mi> <mn>10</mn> </msub> </semantics></math> graph of the exact difference <math display="inline"><semantics> <msub> <mi>D</mi> <mi>α</mi> </msub> </semantics></math> and relative difference <math display="inline"><semantics> <msub> <mi>R</mi> <mi>α</mi> </msub> </semantics></math> of the deflection angle <math display="inline"><semantics> <mi>α</mi> </semantics></math> between LQG BH models and Schwarzschild BH versus the relative distance <math display="inline"><semantics> <msub> <mi>R</mi> <mi>b</mi> </msub> </semantics></math> to Schwarzschild <math display="inline"><semantics> <msub> <mi>b</mi> <mi>m</mi> </msub> </semantics></math>. All results are obtained using input data from <math display="inline"><semantics> <msup> <mi>SgrA</mi> <mo>*</mo> </msup> </semantics></math>. (<b>a</b>,<b>d</b>) shows the results for all five models, where red dots instead of curves depict results corresponding to the MC1 model because of the overlap with the qOS model. In (<b>b</b>,<b>c</b>,<b>e</b>,<b>f</b>), the five models are further divided into two groups based on the values of their results.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/421'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00421/article_deploy/html/images/universe-10-00421-g003-550.jpg?1731479833" title=" <strong>Figure 3</strong><br/> <p>The relation between the quantum corrections of metric and the quantum corrections of deflection angle <math display="inline"><semantics> <mi>α</mi> </semantics></math>. (<b>a</b>): Relative difference in the metric for all five models. (<b>b</b>) The magnification rate <span class="html-italic">Z</span> for the AOS model, indicating the quantum effect is magnified significantly by the deflection angle compared to the metric’s quantum correction. (<b>c</b>) The magnification rate <span class="html-italic">Z</span> for the GOP model. No magnification is observed.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/421'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 41 pages, 549 KiB   </span> <a href="/2218-1997/10/11/420/pdf?version=1731661662" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Comparing a Gauge-Invariant Formulation and a “Conventional Complete Gauge-Fixing Approach” for l=0,1-Mode Perturbations on the Schwarzschild Background Spacetime" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2218-1997/10/11/420">Comparing a Gauge-Invariant Formulation and a “Conventional Complete Gauge-Fixing Approach” for <i>l</i>=0,1-Mode Perturbations on the Schwarzschild Background Spacetime</a> <div class="authors"> by <span class="inlineblock "><strong>Kouji Nakamura</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 420; <a href="https://doi.org/10.3390/universe10110420">https://doi.org/10.3390/universe10110420</a> - 7 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> This article provides a comparison of the gauge-invariant formulation for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn></mrow></semantics></math></inline-formula>-mode perturbations on the Schwarzschild background spacetime, proposed by the same author in 2021, and a “conventional complete gauge-fixing approach” where the spherical harmonic functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Y</mi><mrow><mi>l</mi><mi>m</mi></mrow></msub></semantics></math></inline-formula> <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/420/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> This article provides a comparison of the gauge-invariant formulation for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn></mrow></semantics></math></inline-formula>-mode perturbations on the Schwarzschild background spacetime, proposed by the same author in 2021, and a “conventional complete gauge-fixing approach” where the spherical harmonic functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Y</mi><mrow><mi>l</mi><mi>m</mi></mrow></msub></semantics></math></inline-formula> as the scalar harmonics are used from the starting point. Although it is often stated that “gauge-invariant formulations in general-relativistic perturbations are equivalent to complete gauge-fixing approaches”, we conclude that, as a result of this comparison, the derived solutions through the proposed gauge-invariant formulation and those through a “conventional complete gauge-fixing approach” are different. It is pointed out that there is a case where the boundary conditions and initial conditions are restricted in a conventional complete gauge-fixing approach. <a href="/2218-1997/10/11/420">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/universe/special_issues/99AG0SQD0B "><em>Universe</em>: Feature Papers 2024 – Compact Objects</a>)<br/> </div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 41 pages, 1918 KiB   </span> <a href="/2218-1997/10/11/419/pdf?version=1732602625" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Semi-Symmetric Metric Gravity: A Brief Overview" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Review</span></div> <a class="title-link" href="/2218-1997/10/11/419">Semi-Symmetric Metric Gravity: A Brief Overview</a> <div class="authors"> by <span class="inlineblock "><strong>Himanshu Chaudhary</strong>, </span><span class="inlineblock "><strong>Lehel Csillag</strong> and </span><span class="inlineblock "><strong>Tiberiu Harko</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 419; <a href="https://doi.org/10.3390/universe10110419">https://doi.org/10.3390/universe10110419</a> - 7 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> We present a review of the Semi-Symmetric Metric Gravity (SSMG) theory, representing a geometric extension of standard general relativity, based on a connection introduced by Friedmann and Schouten in 1924. The semi-symmetric connection is a connection that generalizes the Levi-Civita one by allowing <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/419/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> We present a review of the Semi-Symmetric Metric Gravity (SSMG) theory, representing a geometric extension of standard general relativity, based on a connection introduced by Friedmann and Schouten in 1924. The semi-symmetric connection is a connection that generalizes the Levi-Civita one by allowing for the presence of a simple form of the torsion, described in terms of a torsion vector. The Einstein field equations are postulated to have the same form as in standard general relativity, thus relating the Einstein tensor constructed with the help of the semi-symmetric connection, with the energy–momentum tensor. The inclusion of the torsion contributions in the field equations has intriguing cosmological implications, particularly during the late-time evolution of the Universe. Presumably, these effects also dominate under high-energy conditions, and thus SSMG could potentially address unresolved issues in general relativity and cosmology, such as the initial singularity, inflation, or the <sup>7</sup>Li problem of the Big-Bang Nucleosynthesis. The explicit presence of torsion in the field equations leads to the non-conservation of the energy–momentum tensor, which can be interpreted within the irreversible thermodynamics of open systems as describing particle creation processes. We also review in detail the cosmological applications of the theory, and investigate the statistical tests for several models, by constraining the model parameters via comparison with several observational datasets. <a href="/2218-1997/10/11/419">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/universe/special_issues/LH6E422750 ">Dark Energy and Dark Matter</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/419/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1516265"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1516265"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1516265" data-cycle-prev="#prev1516265" data-cycle-progressive="#images1516265" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1516265-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g001-550.jpg?1732602790" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1516265" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g002-550.jpg?1732602793'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g003-550.jpg?1732602793'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g004-550.jpg?1732602794'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g005-550.jpg?1732602795'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g006-550.jpg?1732602796'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g007-550.jpg?1732602797'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g008-550.jpg?1732602798'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g009-550.jpg?1732602799'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g010-550.jpg?1732602800'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g011-550.jpg?1732602801'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g012-550.jpg?1732602802'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1516265-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g013-550.jpg?1732602803'><p>Figure 13</p></div></script></div></div><div id="article-1516265-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g001-550.jpg?1732602790" title=" <strong>Figure 1</strong><br/> <p>The confidence contours at the 1<math display="inline"><semantics> <mi>σ</mi> </semantics></math> and 2<math display="inline"><semantics> <mi>σ</mi> </semantics></math> levels based on constraints for the Linear Model within the Semi-Symmetric Metric Gravity framework.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g002-550.jpg?1732602793" title=" <strong>Figure 2</strong><br/> <p>The confidence contours at the 1<math display="inline"><semantics> <mi>σ</mi> </semantics></math> and 2<math display="inline"><semantics> <mi>σ</mi> </semantics></math> levels for the polytropic model within the Semi-Symmetric Metric Gravity framework.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g003-550.jpg?1732602793" title=" <strong>Figure 3</strong><br/> <p>Evolution of the Hubble parameter <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> as a function of redshift <span class="html-italic">z</span>, using the joint data best-fit values, and compared with the CC dataset.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g004-550.jpg?1732602794" title=" <strong>Figure 4</strong><br/> <p>Evolution of the Hubble difference <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>H</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> as a function of redshift <span class="html-italic">z</span>, using the joint data best-fit values, and compared with the CC dataset.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g005-550.jpg?1732602795" title=" <strong>Figure 5</strong><br/> <p>Evolution of the distance modulus <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> as a function of redshift <span class="html-italic">z</span>, using the joint data best-fit values and compared with the SNe Ia dataset.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g006-550.jpg?1732602796" title=" <strong>Figure 6</strong><br/> <p>Evolution of the deceleration parameter <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> as a function of redshift <span class="html-italic">z</span>, using the joint data best-fit values.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g007-550.jpg?1732602797" title=" <strong>Figure 7</strong><br/> <p>Evolution of the jerk parameter <math display="inline"><semantics> <mrow> <mi>j</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> as a function of redshift <span class="html-italic">z</span>, using the joint data best-fit values.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g008-550.jpg?1732602798" title=" <strong>Figure 8</strong><br/> <p>Evolution of the snap parameter <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> as a function of redshift <span class="html-italic">z</span>, using the joint data best-fit values.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g009-550.jpg?1732602799" title=" <strong>Figure 9</strong><br/> <p>Evolution of the <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>m</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> diagnostic as a function of redshift <span class="html-italic">z</span>, using the joint data best-fit values.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g010-550.jpg?1732602800" title=" <strong>Figure 10</strong><br/> <p>Evolution of the dimensionless torsion vector <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> as a function of redshift <span class="html-italic">z</span>, using the joint data best-fit values.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g011-550.jpg?1732602801" title=" <strong>Figure 11</strong><br/> <p>Evolution of the dimensionless matter density <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> as a function of redshift <span class="html-italic">z</span>, using the joint data best-fit values.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g012-550.jpg?1732602802" title=" <strong>Figure 12</strong><br/> <p>Evolution of the dimensionless particle creation rate <math display="inline"><semantics> <mrow> <mo>Ψ</mo> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </semantics></math> as a function of redshift <span class="html-italic">z</span>, using the joint data best-fit values.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/universe/universe-10-00419/article_deploy/html/images/universe-10-00419-g013-550.jpg?1732602803" title=" <strong>Figure 13</strong><br/> <p>Evolution of the dimensionless particle creation pressure <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> as a function of redshift <span class="html-italic">z</span>, using the joint data best-fit values.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2218-1997/10/11/419'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 26 pages, 416 KiB   </span> <a href="/2218-1997/10/11/418/pdf?version=1730974612" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Foundational Issues in Dynamical Casimir Effect and Analogue Features in Cosmological Particle Creation" data-journal="universe"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Perspective</span></div> <a class="title-link" href="/2218-1997/10/11/418">Foundational Issues in Dynamical Casimir Effect and Analogue Features in Cosmological Particle Creation</a> <div class="authors"> by <span class="inlineblock "><strong>Jen-Tsung Hsiang</strong> and </span><span class="inlineblock "><strong>Bei-Lok Hu</strong></span> </div> <div class="color-grey-dark"> <em>Universe</em> <b>2024</b>, <em>10</em>(11), 418; <a href="https://doi.org/10.3390/universe10110418">https://doi.org/10.3390/universe10110418</a> - 7 Nov 2024 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Moving mirrors as analogue sources of Hawking radiation from black holes have been explored extensively but less so with cosmological particle creation (CPC), even though the analogy between the dynamical Casimir effect (DCE) and CPC based on the mechanism of the parametric amplification <a href="#" data-counterslink = "https://www.mdpi.com/2218-1997/10/11/418/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Moving mirrors as analogue sources of Hawking radiation from black holes have been explored extensively but less so with cosmological particle creation (CPC), even though the analogy between the dynamical Casimir effect (DCE) and CPC based on the mechanism of the parametric amplification of quantum field fluctuations has also been known for a long time. This ‘perspective’ essay intends to convey some of the rigor and thoroughness of quantum field theory in curved spacetime, which serves as the theoretical foundation of CPC, to DCE, which enjoys a variety of active experimental explorations. We have selected seven issues of relevance to address, starting from the naively simple ones, e.g., why one should be bothered with ‘curved’ spacetime when performing a laboratory experiment in ostensibly flat space, to foundational theoretical ones, such as the frequent appearance of nonlocal dissipation in the system dynamics induced by colored noises in its field environment, the existence of quantum Lenz law and fluctuation–dissipation relations in the backreaction effects of DCE emission on the moving atom/mirror or the source, and the construction of a microphysics model to account for the dynamical responses of a mirror or medium. The strengthening of the theoretical ground for DCE is not only useful for improving conceptual clarity but needed for the development of the proof-of-concept type of future experimental designs for DCE. The results from the DCE experiments in turn will enrich our understanding of quantum field effects in the early universe because they are, in the spirit of analogue gravity, our best hopes for the verification of these fundamental processes. <a href="/2218-1997/10/11/418">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/universe/special_issues/44645D0TKA ">Quantum Physics including Gravity: Highlights and Novelties</a>)<br/> </div> </div> </div> </div> </div> <div class="generic-item last-item"> <a class="bold" href="/search?q=&journal=universe&sort=pubdate&page_count=50">More Articles...</a> </div> </div> </div> </div> <div id="left-column" class="content__column large-3 large-pull-6 medium-3 medium-pull-6 small-12 columns"> <div id="js-large-main-top-container"> <div id="js-main-top-container" class="content__container"> <a href="/journal/universe"> <img src="https://pub.mdpi-res.com/img/journals/universe-logo.png?8600e93ff98dbf14" alt="universe-logo" title="Universe" style="max-height: 60px; margin: 0 0 0 0;"> </a> <div class="generic-item no-border" style="position: relative;"> <div class=""> <a class="button button--color button--color-journal button--full-width js-journal-active-only-link js-journal-active-only-submit-link UC_JournalSubmitButton" href="https://susy.mdpi.com/user/manuscripts/upload?form[journal_id]=133" data-disabledmessage="creating new submissions is not possible."> Submit to <i>Universe</i> </a> <a class="button button--color button--full-width js-journal-active-only-link UC_JournalReviewButton" href="https://susy.mdpi.com/volunteer/journals/review" data-disabledmessage="volunteering as journal reviewer is not possible."> Review for <em>Universe</em> </a> </div> <div class="journal-share-links"> <div class="journal-share-links-social"> <a class="button button--color UA_JournalShareButtons" target="_blank" rel="noopener noreferrer" href="https://twitter.com/Universe_MDPI"> <svg width="25" height="26" viewBox="0 0 1200 1227" fill="none" xmlns="http://www.w3.org/2000/svg" style="padding: 6px;"> <path d="M714.163 519.284L1160.89 0H1055.03L667.137 450.887L357.328 0H0L468.492 681.821L0 1226.37H105.866L515.491 750.218L842.672 1226.37H1200L714.137 519.284H714.163ZM569.165 687.828L521.697 619.934L144.011 79.6944H306.615L611.412 515.685L658.88 583.579L1055.08 1150.3H892.476L569.165 687.854V687.828Z" fill="black" /> </svg> </a> <a class="button button--color UA_JournalShareButtons" target="_blank" rel="noopener noreferrer" href="https://www.facebook.com/profile.php?id=61555838411472"> <svg width="26" height="26" viewBox="0 0 26 26" fill="none" xmlns="http://www.w3.org/2000/svg" style="margin-top: 1px; margin-bottom: -2px; margin-left: 1px;"> <path fill-rule="evenodd" clip-rule="evenodd" d="M14.1193 20.3917V13.0007H16.1262L16.3921 10.4537H14.1193L14.1228 9.17886C14.1228 8.51456 14.1848 8.15862 15.1233 8.15862H16.3779V5.61133H14.3708C11.96 5.61133 11.1114 6.8469 11.1114 8.92474V10.4539H9.60864V13.0009H11.1114V20.3917H14.1193Z" fill="black"/> </svg> </a> <a class="button button--color UA_JournalShareButtons" target="_blank" rel="noopener noreferrer" href="https://www.linkedin.com/company/universe-mdpi"> <svg width="26" height="26" viewBox="0 0 26 26" fill="none" xmlns="http://www.w3.org/2000/svg"> <path fill-rule="evenodd" clip-rule="evenodd" d="M9.43155 10.0654H6.26343V19.5981H9.43155V10.0654Z" fill="black"/> <path fill-rule="evenodd" clip-rule="evenodd" d="M9.64005 7.11532C9.61949 6.18065 8.95207 5.46875 7.86827 5.46875C6.78448 5.46875 6.07593 6.18065 6.07593 7.11532C6.07593 8.03064 6.76353 8.76304 7.82715 8.76304H7.84739C8.95207 8.76304 9.64005 8.03064 9.64005 7.11532Z" fill="black"/> <path fill-rule="evenodd" clip-rule="evenodd" d="M20.8571 14.1306C20.8571 11.2026 19.2942 9.83984 17.2094 9.83984C15.5274 9.83984 14.7743 10.7651 14.3538 11.4142V10.0639H11.1853C11.2271 10.9584 11.1853 19.5966 11.1853 19.5966H14.3538V14.2728C14.3538 13.9879 14.3744 13.7037 14.4581 13.4997C14.6871 12.9305 15.2084 12.3412 16.0837 12.3412C17.2306 12.3412 17.689 13.2154 17.689 14.4964V19.5964H20.857L20.8571 14.1306Z" fill="black"/> </svg> </a> </div> <div class="journal-share-links-generic"> <a class="button button--color button--full-width UA_JournalShareButtons" href="#" data-reveal-id="main-share-modal"> Share </a> </div> </div> </div> <div class="generic-item condensed-small UI_JournalMenu"> <h2 class="show-for-medium-up">Journal Menu</h2> <a href="#" class="bolded-text link-journal-menu show-for-small"> <span class="closed">►</span> <span class="open" style="display: none;">▼</span> Journal Menu </a> <ul class="accordion__dummy accordion__menu hide-small-down-initially" style="margin-top: 10px;"> <li class="accordion-navigation accordion-navigation__journal"> <ul> <li class="side-menu-li active "> <a href="/journal/universe"><em>Universe</em> Home </a> </li> <li class="side-menu-li "> <a href="/journal/universe/about">Aims & Scope</a> </li> <li class="side-menu-li "> <a href="/journal/universe/editors"> Editorial Board </a> </li> <li class="side-menu-li "> <a href="/journal/universe/submission_reviewers">Reviewer Board</a> </li> <li class="side-menu-li "> <a href="/journal/universe/topical_advisory_panel">Topical Advisory Panel</a> </li> <li class="side-menu-li "> <a href="/journal/universe/instructions">Instructions for Authors</a> </li> <li class="side-menu-li "> <a href="/journal/universe/special_issues">Special Issues</a> </li> <li class="side-menu-li"> <a href="/topics?journal=universe">Topics</a> </li> <li class="side-menu-li "> <a href="/journal/universe/sections">Sections & Collections</a> </li> <li class="side-menu-li "> <a href="/journal/universe/apc">Article Processing Charge</a> </li> <li class="side-menu-li "> <a href="/journal/universe/indexing">Indexing & Archiving</a> </li> <li class="side-menu-li "> <a href="/journal/universe/editors_choice">Editor’s Choice Articles</a> </li> <li class="side-menu-li "> <a href="/journal/universe/most_cited">Most Cited & Viewed</a> </li> <li class="side-menu-li "> <a href="/journal/universe/stats">Journal Statistics</a> </li> <li class="side-menu-li "> <a href="/journal/universe/history">Journal History</a> </li> <li class="side-menu-li "> <a href="/journal/universe/awards">Journal Awards</a> </li> <li class="side-menu-li "> <a href="/journal/universe/events">Conferences</a> </li> <li class="side-menu-li "> <a href="/journal/universe/editorial_office">Editorial Office</a> </li> </ul> </li> </ul> </div> <h2 class="show-for-medium-up">Journal Browser</h2> <a href="#" class="bolded-text link-journal-browser show-for-small" style="margin-bottom: 10px;"> <span class="closed">►</span> <span class="open" style="display: none;">▼</span> Journal Browser </a> <div class="show-for-medium-up"> <div class="generic-item last-item no-border"> <form method="post" action="/journal/universe" id="qckvi" onsubmit="return !$('#journal-browser-go').hasClass('button--grey');"> <div style="margin-bottom: 10px;" class="UI_JournalBrowser_Volume"> <select id="journal-browser-volume" name="volume" style="width: 100%; margin-bottom: 0;" class="chosen-select"> <option value='' data-id="0">volume</option> <option onclick="$('#journal-browser-namesystem').val($(this).data('namesystem'));" data-namesystem="universe" value="10"> 10 </option> <option onclick="$('#journal-browser-namesystem').val($(this).data('namesystem'));" data-namesystem="universe" value="9"> 9 </option> <option onclick="$('#journal-browser-namesystem').val($(this).data('namesystem'));" data-namesystem="universe" value="8"> 8 </option> <option onclick="$('#journal-browser-namesystem').val($(this).data('namesystem'));" data-namesystem="universe" value="7"> 7 </option> <option onclick="$('#journal-browser-namesystem').val($(this).data('namesystem'));" data-namesystem="universe" value="6"> 6 </option> <option onclick="$('#journal-browser-namesystem').val($(this).data('namesystem'));" data-namesystem="universe" value="5"> 5 </option> <option onclick="$('#journal-browser-namesystem').val($(this).data('namesystem'));" data-namesystem="universe" value="4"> 4 </option> <option onclick="$('#journal-browser-namesystem').val($(this).data('namesystem'));" data-namesystem="universe" value="3"> 3 </option> <option onclick="$('#journal-browser-namesystem').val($(this).data('namesystem'));" data-namesystem="universe" value="2"> 2 </option> <option onclick="$('#journal-browser-namesystem').val($(this).data('namesystem'));" data-namesystem="universe" value="1"> 1 </option> </select> </div> <div style="margin-bottom: 10px;" class="UI_JournalBrowser_Issue"> <select id="journal-browser-issue" name="issue" style="width: 100%; margin-bottom: 0;" class="chosen-select"> <option value='' class="volume-0">issue</option> <option value="1" class="volume-10" style="display: none;"> 1 </option> <option value="2" class="volume-10" style="display: none;"> 2 </option> <option value="3" class="volume-10" style="display: none;"> 3 </option> <option value="4" class="volume-10" style="display: none;"> 4 </option> <option value="5" class="volume-10" style="display: none;"> 5 </option> <option value="6" class="volume-10" style="display: none;"> 6 </option> <option value="7" class="volume-10" style="display: none;"> 7 </option> <option value="8" class="volume-10" style="display: none;"> 8 </option> <option value="9" class="volume-10" style="display: none;"> 9 </option> <option value="10" class="volume-10" style="display: none;"> 10 </option> <option value="11" class="volume-10" style="display: none;"> 11 </option> <option value="12" class="volume-10" style="display: none;"> 12 </option> <option value="1" class="volume-9" style="display: none;"> 1 </option> <option value="2" class="volume-9" style="display: none;"> 2 </option> <option value="3" class="volume-9" style="display: none;"> 3 </option> <option value="4" class="volume-9" style="display: none;"> 4 </option> <option value="5" class="volume-9" style="display: none;"> 5 </option> <option value="6" class="volume-9" style="display: none;"> 6 </option> <option value="7" class="volume-9" style="display: none;"> 7 </option> <option value="8" class="volume-9" style="display: none;"> 8 </option> <option value="9" class="volume-9" style="display: none;"> 9 </option> <option value="10" class="volume-9" style="display: none;"> 10 </option> <option value="11" class="volume-9" style="display: none;"> 11 </option> <option value="12" class="volume-9" style="display: none;"> 12 </option> <option value="1" class="volume-8" style="display: none;"> 1 </option> <option value="2" class="volume-8" style="display: none;"> 2 </option> <option value="3" class="volume-8" style="display: none;"> 3 </option> <option value="4" class="volume-8" style="display: none;"> 4 </option> <option value="5" class="volume-8" style="display: none;"> 5 </option> <option value="6" class="volume-8" style="display: none;"> 6 </option> <option value="7" class="volume-8" style="display: none;"> 7 </option> <option value="8" class="volume-8" style="display: none;"> 8 </option> <option value="9" class="volume-8" style="display: none;"> 9 </option> <option value="10" class="volume-8" style="display: none;"> 10 </option> <option value="11" class="volume-8" style="display: none;"> 11 </option> <option value="12" class="volume-8" style="display: none;"> 12 </option> <option value="1" class="volume-7" style="display: none;"> 1 </option> <option value="2" class="volume-7" style="display: none;"> 2 </option> <option value="3" class="volume-7" style="display: none;"> 3 </option> <option value="4" class="volume-7" style="display: none;"> 4 </option> <option value="5" class="volume-7" style="display: none;"> 5 </option> <option value="6" class="volume-7" style="display: none;"> 6 </option> <option value="7" class="volume-7" style="display: none;"> 7 </option> <option value="8" class="volume-7" style="display: none;"> 8 </option> <option value="9" class="volume-7" style="display: none;"> 9 </option> <option value="10" class="volume-7" style="display: none;"> 10 </option> <option value="11" class="volume-7" style="display: none;"> 11 </option> <option value="12" class="volume-7" style="display: none;"> 12 </option> <option value="1" class="volume-6" style="display: none;"> 1 </option> <option value="2" class="volume-6" style="display: none;"> 2 </option> <option value="3" class="volume-6" style="display: none;"> 3 </option> <option value="4" class="volume-6" style="display: none;"> 4 </option> <option value="5" class="volume-6" style="display: none;"> 5 </option> <option value="6" class="volume-6" style="display: none;"> 6 </option> <option value="7" class="volume-6" style="display: none;"> 7 </option> <option value="8" class="volume-6" style="display: none;"> 8 </option> <option value="9" class="volume-6" style="display: none;"> 9 </option> <option value="10" class="volume-6" style="display: none;"> 10 </option> <option value="11" class="volume-6" style="display: none;"> 11 </option> <option value="12" class="volume-6" style="display: none;"> 12 </option> <option value="1" class="volume-5" style="display: none;"> 1 </option> <option value="2" class="volume-5" style="display: none;"> 2 </option> <option value="3" class="volume-5" style="display: none;"> 3 </option> <option value="4" class="volume-5" style="display: none;"> 4 </option> <option value="5" class="volume-5" style="display: none;"> 5 </option> <option value="6" class="volume-5" style="display: none;"> 6 </option> <option value="7" class="volume-5" style="display: none;"> 7 </option> <option value="8" class="volume-5" style="display: none;"> 8 </option> <option value="9" class="volume-5" style="display: none;"> 9 </option> <option value="10" class="volume-5" style="display: none;"> 10 </option> <option value="11" class="volume-5" style="display: none;"> 11 </option> <option value="12" class="volume-5" style="display: none;"> 12 </option> <option value="1" class="volume-4" style="display: none;"> 1 </option> <option value="2" class="volume-4" style="display: none;"> 2 </option> <option value="3" class="volume-4" style="display: none;"> 3 </option> <option value="4" class="volume-4" style="display: none;"> 4 </option> <option value="5" class="volume-4" style="display: none;"> 5 </option> <option value="6" class="volume-4" style="display: none;"> 6 </option> <option value="7" class="volume-4" style="display: none;"> 7 </option> <option value="8" class="volume-4" style="display: none;"> 8 </option> <option value="9" class="volume-4" style="display: none;"> 9 </option> <option value="10" class="volume-4" style="display: none;"> 10 </option> <option value="11" class="volume-4" style="display: none;"> 11 </option> <option value="12" class="volume-4" style="display: none;"> 12 </option> <option value="1" class="volume-3" style="display: none;"> 1 </option> <option value="2" class="volume-3" style="display: none;"> 2 </option> <option value="3" class="volume-3" style="display: none;"> 3 </option> <option value="4" class="volume-3" style="display: none;"> 4 </option> <option value="1" class="volume-2" style="display: none;"> 1 </option> <option value="2" class="volume-2" style="display: none;"> 2 </option> <option value="3" class="volume-2" style="display: none;"> 3 </option> <option value="4" class="volume-2" style="display: none;"> 4 </option> <option value="1" class="volume-1" style="display: none;"> 1 </option> <option value="2" class="volume-1" style="display: none;"> 2 </option> <option value="3" class="volume-1" style="display: none;"> 3 </option> </select> </div> <input type="hidden" name="_token" value="Z1CXrbYaYjBZd5Vcmvab9lyn1VqKYsqH9H4o5b16bXY"> <input type="hidden" id="journal-browser-namesystem" name="namesystem" value="universe"> <input type="hidden" name="getIssueByVI" value="1"> <input type="submit" id="journal-browser-go" value="Go" style="" class="button button--grey button--full-width UI_JournalBrowser_GoButton"> </form> <div style="clear:both;"></div> </div> <div class="generic-item last-item first-item no-border"> <ul class="side-menu-ul"> <li class="side-menu-li side-menu-li__padded"> <a href="/2218-1997/10/12"> <i class="material-icons arrow" style="display: inline-block"> arrow_forward_ios </i> <strong>Forthcoming issue</strong> </a> <br/> <a href="/2218-1997/10/11"> <i class="material-icons arrow" style="display: inline-block"> arrow_forward_ios </i> <strong>Current issue</strong> </a> </li> <div class="show-for-medium-up"> <div class=""> <div class="journal-browser-volumes "> <li class="side-menu-li"> <a href="/2218-1997/10"> Vol. 10 (2024) </a> </li> <li class="side-menu-li"> <a href="/2218-1997/9"> Vol. 9 (2023) </a> </li> <li class="side-menu-li"> <a href="/2218-1997/8"> Vol. 8 (2022) </a> </li> <li class="side-menu-li"> <a href="/2218-1997/7"> Vol. 7 (2021) </a> </li> <li class="side-menu-li"> <a href="/2218-1997/6"> Vol. 6 (2020) </a> </li> <li class="side-menu-li"> <a href="/2218-1997/5"> Vol. 5 (2019) </a> </li> <li class="side-menu-li"> <a href="/2218-1997/4"> Vol. 4 (2018) </a> </li> <li class="side-menu-li"> <a href="/2218-1997/3"> Vol. 3 (2017) </a> </li> <li class="side-menu-li"> <a href="/2218-1997/2"> Vol. 2 (2016) </a> </li> <li class="side-menu-li"> <a href="/2218-1997/1"> Vol. 1 (2015) </a> </li> </div> </div> </div> </ul> </div> </div> </div> </div> <div class="show-for-medium-up"> <div class="content__container banner-container" style="padding:0px;"> <div> <div class="generic-item1"> <div id="bestAwardPaperAD" style="padding: 0px; width: 100%;"> <div id="banner1" class="adserver-banner" data-zone="4" data-repeat-interval="10" style="width: 100%; padding:0px;margin:0px;"></div> </div> </div> </div> </div> </div> <div class="content__container extending-content" data-url="/journal/ajax/most_accessed_articles/133"> <div class="custom-accordion-for-small-screen-link"> <h2>Highly Accessed Articles</h2> </div> <div class="target-item custom-accordion-for-small-screen-content show-for-medium-up"> <div class="last-item generic-item"> <a class="bold" href="/search?q=&journal=universe&sort=articles_stats_art_view_page&page_count=50">View More...</a> </div> </div> </div> <div class="content__container extending-content" data-url="/journal/ajax/latest_books/universe"> <div class="custom-accordion-for-small-screen-link"> <h2 class="show-for-small-only">Latest Books</h2> </div> <div class="target-item custom-accordion-for-small-screen-content show-for-medium-up"> <img src="https://pub.mdpi-res.com/img/design/books_logo_new.svg?76e680e5363e99ba?1732694169"> <div class="last-item generic-item"> <a class="bold" href="https://www.mdpi.com/books/search?type%5B%5D=Reprint&journal_facet%5B%5D=Universe" target="_blank" rel="noopener noreferrer">More Books and Reprints...</a> </div> </div> </div> </div> <div id="right-column" class="content__column large-25 medium-3 small-12 columns"> <div class="content__container"> <div class="custom-accordion-for-small-screen-link"> <h2>E-Mail Alert</h2> </div> <div class="target-item custom-accordion-for-small-screen-content show-for-medium-up"> <div id="journal-alerts" class="generic-item last-item no-border condensed-small"> <form method="post" action="/subscribe" id="subscribeForm" style="margin:0; padding:0;" onsubmit="return false;"> <div style="margin-bottom: 5px;">Add your e-mail address to receive forthcoming issues of this journal:</div> <input name="email" type="email" placeholder="Enter Your E-Mail Address..." required="required"> <input name="journals[]" type="hidden" value="universe"> <input type="hidden" name="_token" value="8slXxwTD3ekyDyy8M_Ua-e0DOmDaYBH1iRTp_AglF-E"> <input id="Email-Subscribe" class="button button--color button--full-width genericCaptcha UA_JournalSubscribeButton" name="email-button" value="Subscribe" type="submit"> </form> </div> </div> </div> <div class="content__container"> <div class="custom-accordion-for-small-screen-link"> <h2>News</h2> </div> <div class="target-item custom-accordion-for-small-screen-content show-for-medium-up"> <div class="generic-item news-item no-border"> <span class="text-information">25 November 2024</span> <br/> <a class="title-link" href="/journal/universe/announcements/9834">The 5<sup>th</sup> International Conference on Symmetry (Symmetry 2025)—Open for Submissions</a> <a href="/journal/universe/announcements/9834"><img style="margin: 5px 0; display: block; max-width: 100%; height: auto;" src="https://pub.mdpi-res.com/announcement/9834.jpg?1732694169" /></a> </div> <div class="generic-item news-item "> <span class="text-information">5 November 2024</span> <br/> <a class="title-link" href="/journal/universe/announcements/9690">MDPI INSIGHTS: The CEO's Letter #17 - OA Week, Basel Open Day, Beijing Graphene Forum</a> </div> <div class="generic-item news-item "> <span class="text-information">28 October 2024</span> <br/> <a class="title-link" href="/journal/universe/announcements/9641"><strong>Recruiting Early Career Editorial Board Members for <em>Universe</em></strong></a> </div> <div class="generic-item last-item UI_NewsAnnounce"> <a class="bold" href="/journal/universe/announcements">More News & Announcements...</a> </div> </div> </div> <div class="content__container selected-special-issues"> <div class="custom-accordion-for-small-screen-link"> <h2>Topics</h2> </div> <div class="custom-accordion-for-small-screen-content show-for-medium-up"> <div class="generic-item button-type no-border"> <a class="button button--color button--full-width submit-manuscript" href="/topics/proposal"> Propose a Topic </a> </div> <div class="generic-item"><div><span class="text-information times"> Topic in <span class="text-information italics times">IJMS</span>, <span class="text-information italics times">Pharmaceutics</span>, <span class="text-information italics times">Cells</span>, <span class="text-information italics times">Biomolecules</span>, <span class="text-information italics times">Plants</span>, <span class="text-information italics times">Universe</span>, <span class="text-information italics times">Cancers</span>, <span class="text-information italics times">Antioxidants</span></span></div><a class="title-link bold" href="/topics/T9B7L6S956"> Advances in Astrobiology </a><span class="text-information color-grey-dark">Topic Editors: Massimo Maffei, Barbara Cavalazzi, Marta del Bianco<br/></span><span class="text-information highlight">Deadline: 30 November 2024</span></div> <div class="generic-item"><div><span class="text-information times"> Topic in <span class="text-information italics times">Aerospace</span>, <span class="text-information italics times">Applied Sciences</span>, <span class="text-information italics times">Remote Sensing</span>, <span class="text-information italics times">Sensors</span>, <span class="text-information italics times">Universe</span>, <span class="text-information italics times">Data</span></span></div><a class="title-link bold" href="/topics/8E583WHY29"> Techniques and Science Exploitations for Earth Observation and Planetary Exploration </a><span class="text-information color-grey-dark">Topic Editors: Yu Tao, Siting Xiong, Rui Song<br/></span><span class="text-information highlight">Deadline: 31 March 2025</span></div> </div> </div> <div class="show-for-medium-up"> <div id="adBannerContent" class="content__container banner-container" style="text-align:center;"> <div id="banner2" class="adserver-banner" data-zone="2" data-repeat-interval="10" style="height: 600px; width: 160px; position: relative; margin: 0 auto;"> <img src="https://pub.mdpi-res.com/img/loading_circle.gif?9a82694213036313?1732694169" alt="loading..." style="position: absolute;top: 50%;left: 50%;"> </div> </div> </div> <div class="show-for-small"> <div class="content__container banner-container"> <div id="adBannerContentMobile" style="margin-bottom: 15px; padding: 0px; width: 100%;"> <div id="banner3" class="adserver-banner" data-zone="7" style="width: 100%;"></div> </div> </div> </div> <div class="content__container"> <div class="custom-accordion-for-small-screen-link"> <h2>Conferences</h2> </div> <div class="custom-accordion-for-small-screen-content show-for-medium-up"> <div class="generic-item button-type no-border"> <a class="button button--color button--full-width submit-manuscript" href="/events/add"> Announce Your Conference </a> </div> <div class="generic-item"><span class="text-information"> 16–19 May 2025 </span><a href="/journal/universe/events/17892" class="title-link bold">The 5th International Conference on Symmetry</a><a href="/journal/universe/events/17892"><img style="margin: 5px 0; max-width: 100%; height: auto;" src="https://pub.mdpi-res.com/img/misc/event_1733738244000.jpg?1732694169" border="0"></a></div> <div class="generic-item last-item"> <a href="/journal/universe/events" class="bold">More Conferences...</a><br/> </div> </div> </div> <div class="content__container selected-special-issues"> <div class="custom-accordion-for-small-screen-link"> <h2>Special Issues</h2> </div> <div class="custom-accordion-for-small-screen-content show-for-medium-up"> <div class="generic-item button-type no-border"> <a class="button button--color button--full-width submit-manuscript" href="/journalproposal/sendproposalspecialissue/universe" data-path="/journal/universe"> Propose a Special Issue </a> </div> <div class="generic-item"><div><span class="text-information times"> Special Issue in </span><span class="text-information italics times">Universe</span></div><a class="title-link bold" href="/journal/universe/special_issues/Q4Q103M8S7"> Universe: Feature Papers 2024—Space Science </a><span class="text-information color-grey-dark">Guest Editor: Ezio Caroli<br/></span><span class="text-information highlight">Deadline: 30 November 2024</span></div> <div class="generic-item"><div><span class="text-information times"> Special Issue in </span><span class="text-information italics times">Universe</span></div><a class="title-link bold" href="/journal/universe/special_issues/1C1KP05INH"> Multi-wavelength Properties of Active Galactic Nuclei </a><span class="text-information color-grey-dark">Guest Editor: Stefano Vercellone<br/></span><span class="text-information highlight">Deadline: 15 December 2024</span></div> <div class="generic-item"><div><span class="text-information times"> Special Issue in </span><span class="text-information italics times">Universe</span></div><a class="title-link bold" href="/journal/universe/special_issues/Y3T2Z3J1HS"> New Insights into High-Energy Astrophysics, Galaxies, and Cosmology—Celebrating the 10th Anniversary of the Re-establishment of the Department of Astronomy at Xiamen University (2012–2022) </a><span class="text-information color-grey-dark">Guest Editors: Taotao Fang, Weimin Gu, Tong Liu, Beibei Liu<br/></span><span class="text-information highlight">Deadline: 15 December 2024</span></div> <div class="generic-item"><div><span class="text-information times"> Special Issue in </span><span class="text-information italics times">Universe</span></div><a class="title-link bold" href="/journal/universe/special_issues/G95G88G98M"> Gravity and Cosmology: Exploring the Mysteries of f(T) Gravity </a><span class="text-information color-grey-dark">Guest Editors: Jose Carlos Neves De Araujo, Hemily Gomes Marciano Fortes, Emmanuel N. Saridakis<br/></span><span class="text-information highlight">Deadline: 20 December 2024</span></div> <div class="generic-item last-item"> <a href="/journal/universe/special_issues" class="bold">More Special Issues</a> </div> </div> </div> <div class="content__container selected-special-issues"> <div class="custom-accordion-for-small-screen-link"> <h2>Topical Collections</h2> </div> <div class="custom-accordion-for-small-screen-content show-for-medium-up"> <div class="generic-item"><div><span class="text-information times"> Topical Collection in </span><span class="text-information italics times">Universe</span></div><a class="title-link bold" href="/journal/universe/topical_collections/OpenQuestionsBlack_Hole_Physics"> Open Questions in Black Hole Physics </a><span class="text-information color-grey-dark">Collection Editors: Gonzalo Olmo, Diego Rubiera-Garcia<br/></span></div> <div class="generic-item"><div><span class="text-information times"> Topical Collection in </span><span class="text-information italics times">Universe</span></div><a class="title-link bold" href="/journal/universe/topical_collections/Gravitational_Waves_Astronomy"> Gravitational Waves as a New Probe for Astronomy and Fundamental Physics </a><span class="text-information color-grey-dark">Collection Editor: Houri Ziaeepour<br/></span></div> <div class="generic-item"><div><span class="text-information times"> Topical Collection in </span><span class="text-information italics times">Universe</span></div><a class="title-link bold" href="/journal/universe/topical_collections/JWST"> New Results on Galaxy Evolution from the James Webb Space Telescope </a><span class="text-information color-grey-dark">Collection Editor: Guinevere Kauffmann<br/></span></div> <div class="generic-item"><div><span class="text-information times"> Topical Collection in </span><span class="text-information italics times">Universe</span></div><a class="title-link bold" href="/journal/universe/topical_collections/MGCA"> Modified Theories of Gravity and Cosmological Applications </a><span class="text-information color-grey-dark">Collection Editors: Panayiotis Stavrinos, Emmanuel N. Saridakis<br/></span></div> <div class="generic-item last-item"> <a href="/journal/universe/topical_collections" class="bold">More Topical Collections</a> </div> </div> </div> <div class="column-padding"></div> </div> </div> </div> </section> <div id="footer"> <div class="journal-info"> <span> <em><a class="Var_JournalInfo" href="/journal/universe">Universe</a></em>, EISSN 2218-1997, Published by MDPI </span> <div class="large-right"> <span> <a href="/rss/journal/universe" class="rss-link">RSS</a> </span> <span> <a href="/journal/universe/toc-alert">Content Alert</a> </span> </div> </div> <div class="row full-width footer-links" data-equalizer="footer" data-equalizer-mq="small"> <div class="large-2 large-push-4 medium-3 small-6 columns" data-equalizer-watch="footer"> <h3> Further Information </h3> <a href="/apc"> Article Processing Charges </a> <a href="/about/payment"> Pay an Invoice </a> <a href="/openaccess"> Open Access Policy </a> <a href="/about/contact"> Contact MDPI </a> <a href="https://careers.mdpi.com" target="_blank" rel="noopener noreferrer"> Jobs at MDPI </a> </div> <div class="large-2 large-push-4 medium-3 small-6 columns" data-equalizer-watch="footer"> <h3> Guidelines </h3> <a href="/authors"> For Authors </a> <a href="/reviewers"> For Reviewers </a> <a href="/editors"> For Editors </a> <a href="/librarians"> For Librarians </a> <a href="/publishing_services"> For Publishers </a> <a href="/societies"> For Societies </a> <a href="/conference_organizers"> For Conference Organizers </a> </div> <div class="large-2 large-push-4 medium-3 small-6 columns"> <h3> MDPI Initiatives </h3> <a href="https://sciforum.net" target="_blank" rel="noopener noreferrer"> Sciforum </a> <a href="https://www.mdpi.com/books" target="_blank" rel="noopener noreferrer"> MDPI Books </a> <a href="https://www.preprints.org" target="_blank" rel="noopener noreferrer"> Preprints.org </a> <a href="https://www.scilit.net" target="_blank" rel="noopener noreferrer"> Scilit </a> <a href="https://sciprofiles.com?utm_source=mpdi.com&utm_medium=bottom_menu&utm_campaign=initiative" target="_blank" rel="noopener noreferrer"> SciProfiles </a> <a href="https://encyclopedia.pub" target="_blank" rel="noopener noreferrer"> Encyclopedia </a> <a href="https://jams.pub" target="_blank" rel="noopener noreferrer"> JAMS </a> <a href="/about/proceedings"> Proceedings Series </a> </div> <div class="large-2 large-push-4 medium-3 small-6 right-border-large-without columns UA_FooterFollowMDPI"> <h3> Follow MDPI </h3> <a href="https://www.linkedin.com/company/mdpi" target="_blank" rel="noopener noreferrer"> LinkedIn </a> <a href="https://www.facebook.com/MDPIOpenAccessPublishing" target="_blank" rel="noopener noreferrer"> Facebook </a> <a href="https://twitter.com/MDPIOpenAccess" target="_blank" rel="noopener noreferrer"> Twitter </a> </div> <div id="footer-subscribe" class="large-4 large-pull-8 medium-12 small-12 left-border-large columns"> <div class="footer-subscribe__container"> <img class="show-for-large-up" src="https://pub.mdpi-res.com/img/design/mdpi-pub-logo-white-small.png?71d18e5f805839ab?1732694169" alt="MDPI" title="MDPI Open Access Journals" style="height: 50px; margin-bottom: 10px;"> <form id="newsletter" method="POST" action="/subscribe"> <p> Subscribe to receive issue release notifications and newsletters from MDPI journals </p> <select multiple id="newsletter-journal" class="foundation-select" name="journals[]"> <option value="acoustics">Acoustics</option> <option value="amh">Acta Microbiologica Hellenica</option> <option value="actuators">Actuators</option> <option value="admsci">Administrative Sciences</option> <option value="adolescents">Adolescents</option> <option value="arm">Advances in Respiratory Medicine</option> <option value="aerobiology">Aerobiology</option> <option value="aerospace">Aerospace</option> <option value="agriculture">Agriculture</option> <option value="agriengineering">AgriEngineering</option> <option value="agrochemicals">Agrochemicals</option> <option value="agronomy">Agronomy</option> <option value="ai">AI</option> <option value="air">Air</option> <option value="algorithms">Algorithms</option> <option value="allergies">Allergies</option> <option value="alloys">Alloys</option> <option value="analytica">Analytica</option> <option value="analytics">Analytics</option> <option value="anatomia">Anatomia</option> <option value="anesthres">Anesthesia Research</option> <option value="animals">Animals</option> <option value="antibiotics">Antibiotics</option> <option value="antibodies">Antibodies</option> <option value="antioxidants">Antioxidants</option> <option value="applbiosci">Applied Biosciences</option> <option value="applmech">Applied Mechanics</option> <option value="applmicrobiol">Applied Microbiology</option> <option value="applnano">Applied Nano</option> <option value="applsci">Applied Sciences</option> <option value="asi">Applied System Innovation</option> <option value="appliedchem">AppliedChem</option> <option value="appliedmath">AppliedMath</option> <option value="aquacj">Aquaculture Journal</option> <option value="architecture">Architecture</option> <option value="arthropoda">Arthropoda</option> <option value="arts">Arts</option> <option value="astronomy">Astronomy</option> <option value="atmosphere">Atmosphere</option> <option value="atoms">Atoms</option> <option value="audiolres">Audiology Research</option> <option value="automation">Automation</option> <option value="axioms">Axioms</option> <option value="bacteria">Bacteria</option> <option value="batteries">Batteries</option> <option value="behavsci">Behavioral Sciences</option> <option value="beverages">Beverages</option> <option value="BDCC">Big Data and Cognitive Computing</option> <option value="biochem">BioChem</option> <option value="bioengineering">Bioengineering</option> <option value="biologics">Biologics</option> <option value="biology">Biology</option> <option value="blsf">Biology and Life Sciences Forum</option> <option value="biomass">Biomass</option> <option value="biomechanics">Biomechanics</option> <option value="biomed">BioMed</option> <option value="biomedicines">Biomedicines</option> <option value="biomedinformatics">BioMedInformatics</option> <option value="biomimetics">Biomimetics</option> <option value="biomolecules">Biomolecules</option> <option value="biophysica">Biophysica</option> <option value="biosensors">Biosensors</option> <option value="biotech">BioTech</option> <option value="birds">Birds</option> <option value="blockchains">Blockchains</option> <option value="brainsci">Brain Sciences</option> <option value="buildings">Buildings</option> <option value="businesses">Businesses</option> <option value="carbon">C</option> <option value="cancers">Cancers</option> <option value="cardiogenetics">Cardiogenetics</option> <option value="catalysts">Catalysts</option> <option value="cells">Cells</option> <option value="ceramics">Ceramics</option> <option value="challenges">Challenges</option> <option value="ChemEngineering">ChemEngineering</option> <option value="chemistry">Chemistry</option> <option value="chemproc">Chemistry Proceedings</option> <option value="chemosensors">Chemosensors</option> <option value="children">Children</option> <option value="chips">Chips</option> <option value="civileng">CivilEng</option> <option value="cleantechnol">Clean Technologies</option> <option value="climate">Climate</option> <option value="ctn">Clinical and Translational Neuroscience</option> <option value="clinbioenerg">Clinical Bioenergetics</option> <option value="clinpract">Clinics and Practice</option> <option value="clockssleep">Clocks & Sleep</option> <option value="coasts">Coasts</option> <option value="coatings">Coatings</option> <option value="colloids">Colloids and Interfaces</option> <option value="colorants">Colorants</option> <option value="commodities">Commodities</option> <option value="complications">Complications</option> <option value="compounds">Compounds</option> <option value="computation">Computation</option> <option value="csmf">Computer Sciences & Mathematics Forum</option> <option value="computers">Computers</option> <option value="condensedmatter">Condensed Matter</option> <option value="conservation">Conservation</option> <option value="constrmater">Construction Materials</option> <option value="cmd">Corrosion and Materials Degradation</option> <option value="cosmetics">Cosmetics</option> <option value="covid">COVID</option> <option value="crops">Crops</option> <option value="cryo">Cryo</option> <option value="cryptography">Cryptography</option> <option value="crystals">Crystals</option> <option value="cimb">Current Issues in Molecular Biology</option> <option value="curroncol">Current Oncology</option> <option value="dairy">Dairy</option> <option value="data">Data</option> <option value="dentistry">Dentistry Journal</option> <option value="dermato">Dermato</option> <option value="dermatopathology">Dermatopathology</option> <option value="designs">Designs</option> <option value="diabetology">Diabetology</option> <option value="diagnostics">Diagnostics</option> <option value="dietetics">Dietetics</option> <option value="digital">Digital</option> <option value="disabilities">Disabilities</option> <option value="diseases">Diseases</option> <option value="diversity">Diversity</option> <option value="dna">DNA</option> <option value="drones">Drones</option> <option value="ddc">Drugs and Drug Candidates</option> <option value="dynamics">Dynamics</option> <option value="earth">Earth</option> <option value="ecologies">Ecologies</option> <option value="econometrics">Econometrics</option> <option value="economies">Economies</option> <option value="education">Education Sciences</option> <option value="electricity">Electricity</option> <option value="electrochem">Electrochem</option> <option value="electronicmat">Electronic Materials</option> <option value="electronics">Electronics</option> <option value="ecm">Emergency Care and Medicine</option> <option value="encyclopedia">Encyclopedia</option> <option value="endocrines">Endocrines</option> <option value="energies">Energies</option> <option value="esa">Energy Storage and Applications</option> <option value="eng">Eng</option> <option value="engproc">Engineering Proceedings</option> <option value="entropy">Entropy</option> <option value="environsciproc">Environmental Sciences Proceedings</option> <option value="environments">Environments</option> <option value="epidemiologia">Epidemiologia</option> <option value="epigenomes">Epigenomes</option> <option value="ebj">European Burn Journal</option> <option value="ejihpe">European Journal of Investigation in Health, Psychology and Education</option> <option value="fermentation">Fermentation</option> <option value="fibers">Fibers</option> <option value="fintech">FinTech</option> <option value="fire">Fire</option> <option value="fishes">Fishes</option> <option value="fluids">Fluids</option> <option value="foods">Foods</option> <option value="forecasting">Forecasting</option> <option value="forensicsci">Forensic Sciences</option> <option value="forests">Forests</option> <option value="fossstud">Fossil Studies</option> <option value="foundations">Foundations</option> <option value="fractalfract">Fractal and Fractional</option> <option value="fuels">Fuels</option> <option value="future">Future</option> <option value="futureinternet">Future Internet</option> <option value="futurepharmacol">Future Pharmacology</option> <option value="futuretransp">Future Transportation</option> <option value="galaxies">Galaxies</option> <option value="games">Games</option> <option value="gases">Gases</option> <option value="gastroent">Gastroenterology Insights</option> <option value="gastrointestdisord">Gastrointestinal Disorders</option> <option value="gastronomy">Gastronomy</option> <option value="gels">Gels</option> <option value="genealogy">Genealogy</option> <option value="genes">Genes</option> <option value="geographies">Geographies</option> <option value="geohazards">GeoHazards</option> <option value="geomatics">Geomatics</option> <option value="geometry">Geometry</option> <option value="geosciences">Geosciences</option> <option value="geotechnics">Geotechnics</option> <option value="geriatrics">Geriatrics</option> <option value="glacies">Glacies</option> <option value="gucdd">Gout, Urate, and Crystal Deposition Disease</option> <option value="grasses">Grasses</option> <option value="hardware">Hardware</option> <option value="healthcare">Healthcare</option> <option value="hearts">Hearts</option> <option value="hemato">Hemato</option> <option value="hematolrep">Hematology Reports</option> <option value="heritage">Heritage</option> <option value="histories">Histories</option> <option value="horticulturae">Horticulturae</option> <option value="hospitals">Hospitals</option> <option value="humanities">Humanities</option> <option value="humans">Humans</option> <option value="hydrobiology">Hydrobiology</option> <option value="hydrogen">Hydrogen</option> <option value="hydrology">Hydrology</option> <option value="hygiene">Hygiene</option> <option value="immuno">Immuno</option> <option value="idr">Infectious Disease Reports</option> <option value="informatics">Informatics</option> <option value="information">Information</option> <option value="infrastructures">Infrastructures</option> <option value="inorganics">Inorganics</option> <option value="insects">Insects</option> <option value="instruments">Instruments</option> <option value="iic">Intelligent Infrastructure and Construction</option> <option value="ijerph">International Journal of Environmental Research and Public Health</option> <option value="ijfs">International Journal of Financial Studies</option> <option value="ijms">International Journal of Molecular Sciences</option> <option value="IJNS">International Journal of Neonatal Screening</option> <option value="ijpb">International Journal of Plant Biology</option> <option value="ijt">International Journal of Topology</option> <option value="ijtm">International Journal of Translational Medicine</option> <option value="ijtpp">International Journal of Turbomachinery, Propulsion and Power</option> <option value="ime">International Medical Education</option> <option value="inventions">Inventions</option> <option value="IoT">IoT</option> <option value="ijgi">ISPRS International Journal of Geo-Information</option> <option value="J">J</option> <option value="jal">Journal of Ageing and Longevity</option> <option value="jcdd">Journal of Cardiovascular Development and Disease</option> <option value="jcto">Journal of Clinical & Translational Ophthalmology</option> <option value="jcm">Journal of Clinical Medicine</option> <option value="jcs">Journal of Composites Science</option> <option value="jcp">Journal of Cybersecurity and Privacy</option> <option value="jdad">Journal of Dementia and Alzheimer's Disease</option> <option value="jdb">Journal of Developmental Biology</option> <option value="jeta">Journal of Experimental and Theoretical Analyses</option> <option value="jfb">Journal of Functional Biomaterials</option> <option value="jfmk">Journal of Functional Morphology and Kinesiology</option> <option value="jof">Journal of Fungi</option> <option value="jimaging">Journal of Imaging</option> <option value="jintelligence">Journal of Intelligence</option> <option value="jlpea">Journal of Low Power Electronics and Applications</option> <option value="jmmp">Journal of Manufacturing and Materials Processing</option> <option value="jmse">Journal of Marine Science and Engineering</option> <option value="jmahp">Journal of Market Access & Health Policy</option> <option value="jmp">Journal of Molecular Pathology</option> <option value="jnt">Journal of Nanotheranostics</option> <option value="jne">Journal of Nuclear Engineering</option> <option value="ohbm">Journal of Otorhinolaryngology, Hearing and Balance Medicine</option> <option value="jop">Journal of Parks</option> <option value="jpm">Journal of Personalized Medicine</option> <option value="jpbi">Journal of Pharmaceutical and BioTech Industry</option> <option value="jor">Journal of Respiration</option> <option value="jrfm">Journal of Risk and Financial Management</option> <option value="jsan">Journal of Sensor and Actuator Networks</option> <option value="joma">Journal of the Oman Medical Association</option> <option value="jtaer">Journal of Theoretical and Applied Electronic Commerce Research</option> <option value="jvd">Journal of Vascular Diseases</option> <option value="jox">Journal of Xenobiotics</option> <option value="jzbg">Journal of Zoological and Botanical Gardens</option> <option value="journalmedia">Journalism and Media</option> <option value="kidneydial">Kidney and Dialysis</option> <option value="kinasesphosphatases">Kinases and Phosphatases</option> <option value="knowledge">Knowledge</option> <option value="labmed">LabMed</option> <option value="laboratories">Laboratories</option> <option value="land">Land</option> <option value="languages">Languages</option> <option value="laws">Laws</option> <option value="life">Life</option> <option value="limnolrev">Limnological Review</option> <option value="lipidology">Lipidology</option> <option value="liquids">Liquids</option> <option value="literature">Literature</option> <option value="livers">Livers</option> <option value="logics">Logics</option> <option value="logistics">Logistics</option> <option value="lubricants">Lubricants</option> <option value="lymphatics">Lymphatics</option> <option value="make">Machine Learning and Knowledge Extraction</option> <option value="machines">Machines</option> <option value="macromol">Macromol</option> <option value="magnetism">Magnetism</option> <option value="magnetochemistry">Magnetochemistry</option> <option value="marinedrugs">Marine Drugs</option> <option value="materials">Materials</option> <option value="materproc">Materials Proceedings</option> <option value="mca">Mathematical and Computational Applications</option> <option value="mathematics">Mathematics</option> <option value="medsci">Medical Sciences</option> <option value="msf">Medical Sciences Forum</option> <option value="medicina">Medicina</option> <option value="medicines">Medicines</option> <option value="membranes">Membranes</option> <option value="merits">Merits</option> <option value="metabolites">Metabolites</option> <option value="metals">Metals</option> <option value="meteorology">Meteorology</option> <option value="methane">Methane</option> <option value="mps">Methods and Protocols</option> <option value="metrics">Metrics</option> <option value="metrology">Metrology</option> <option value="micro">Micro</option> <option value="microbiolres">Microbiology Research</option> <option value="micromachines">Micromachines</option> <option value="microorganisms">Microorganisms</option> <option value="microplastics">Microplastics</option> <option value="minerals">Minerals</option> <option value="mining">Mining</option> <option value="modelling">Modelling</option> <option value="mmphys">Modern Mathematical Physics</option> <option value="molbank">Molbank</option> <option value="molecules">Molecules</option> <option value="mti">Multimodal Technologies and Interaction</option> <option value="muscles">Muscles</option> <option value="nanoenergyadv">Nanoenergy Advances</option> <option value="nanomanufacturing">Nanomanufacturing</option> <option value="nanomaterials">Nanomaterials</option> <option value="ndt">NDT</option> <option value="network">Network</option> <option value="neuroglia">Neuroglia</option> <option value="neurolint">Neurology International</option> <option value="neurosci">NeuroSci</option> <option value="nitrogen">Nitrogen</option> <option value="ncrna">Non-Coding RNA</option> <option value="nursrep">Nursing Reports</option> <option value="nutraceuticals">Nutraceuticals</option> <option value="nutrients">Nutrients</option> <option value="obesities">Obesities</option> <option value="oceans">Oceans</option> <option value="onco">Onco</option> <option value="optics">Optics</option> <option value="oral">Oral</option> <option value="organics">Organics</option> <option value="organoids">Organoids</option> <option value="osteology">Osteology</option> <option value="oxygen">Oxygen</option> <option value="parasitologia">Parasitologia</option> <option value="particles">Particles</option> <option value="pathogens">Pathogens</option> <option value="pathophysiology">Pathophysiology</option> <option value="pediatrrep">Pediatric Reports</option> <option value="pets">Pets</option> <option value="pharmaceuticals">Pharmaceuticals</option> <option value="pharmaceutics">Pharmaceutics</option> <option value="pharmacoepidemiology">Pharmacoepidemiology</option> <option value="pharmacy">Pharmacy</option> <option value="philosophies">Philosophies</option> <option value="photochem">Photochem</option> <option value="photonics">Photonics</option> <option value="phycology">Phycology</option> <option value="physchem">Physchem</option> <option value="psf">Physical Sciences Forum</option> <option value="physics">Physics</option> <option value="physiologia">Physiologia</option> <option value="plants">Plants</option> <option value="plasma">Plasma</option> <option value="platforms">Platforms</option> <option value="pollutants">Pollutants</option> <option value="polymers">Polymers</option> <option value="polysaccharides">Polysaccharides</option> <option value="populations">Populations</option> <option value="poultry">Poultry</option> <option value="powders">Powders</option> <option value="proceedings">Proceedings</option> <option value="processes">Processes</option> <option value="prosthesis">Prosthesis</option> <option value="proteomes">Proteomes</option> <option value="psychiatryint">Psychiatry International</option> <option value="psychoactives">Psychoactives</option> <option value="psycholint">Psychology International</option> <option value="publications">Publications</option> <option value="qubs">Quantum Beam Science</option> <option value="quantumrep">Quantum Reports</option> <option value="quaternary">Quaternary</option> <option value="radiation">Radiation</option> <option value="reactions">Reactions</option> <option value="realestate">Real Estate</option> <option value="receptors">Receptors</option> <option value="recycling">Recycling</option> <option value="rsee">Regional Science and Environmental Economics</option> <option value="religions">Religions</option> <option value="remotesensing">Remote Sensing</option> <option value="reports">Reports</option> <option value="reprodmed">Reproductive Medicine</option> <option value="resources">Resources</option> <option value="rheumato">Rheumato</option> <option value="risks">Risks</option> <option value="robotics">Robotics</option> <option value="ruminants">Ruminants</option> <option value="safety">Safety</option> <option value="sci">Sci</option> <option value="scipharm">Scientia Pharmaceutica</option> <option value="sclerosis">Sclerosis</option> <option value="seeds">Seeds</option> <option value="sensors">Sensors</option> <option value="separations">Separations</option> <option value="sexes">Sexes</option> <option value="signals">Signals</option> <option value="sinusitis">Sinusitis</option> <option value="smartcities">Smart Cities</option> <option value="socsci">Social Sciences</option> <option value="siuj">Société Internationale d’Urologie Journal</option> <option value="societies">Societies</option> <option value="software">Software</option> <option value="soilsystems">Soil Systems</option> <option value="solar">Solar</option> <option value="solids">Solids</option> <option value="spectroscj">Spectroscopy Journal</option> <option value="sports">Sports</option> <option value="standards">Standards</option> <option value="stats">Stats</option> <option value="stresses">Stresses</option> <option value="surfaces">Surfaces</option> <option value="surgeries">Surgeries</option> <option value="std">Surgical Techniques Development</option> <option value="sustainability">Sustainability</option> <option value="suschem">Sustainable Chemistry</option> <option value="symmetry">Symmetry</option> <option value="synbio">SynBio</option> <option value="systems">Systems</option> <option value="targets">Targets</option> <option value="taxonomy">Taxonomy</option> <option value="technologies">Technologies</option> <option value="telecom">Telecom</option> <option value="textiles">Textiles</option> <option value="thalassrep">Thalassemia Reports</option> <option value="therapeutics">Therapeutics</option> <option value="thermo">Thermo</option> <option value="timespace">Time and Space</option> <option value="tomography">Tomography</option> <option value="tourismhosp">Tourism and Hospitality</option> <option value="toxics">Toxics</option> <option value="toxins">Toxins</option> <option value="transplantology">Transplantology</option> <option value="traumacare">Trauma Care</option> <option value="higheredu">Trends in Higher Education</option> <option value="tropicalmed">Tropical Medicine and Infectious Disease</option> <option value="universe">Universe</option> <option value="urbansci">Urban Science</option> <option value="uro">Uro</option> <option value="vaccines">Vaccines</option> <option value="vehicles">Vehicles</option> <option value="venereology">Venereology</option> <option value="vetsci">Veterinary Sciences</option> <option value="vibration">Vibration</option> <option value="virtualworlds">Virtual Worlds</option> <option value="viruses">Viruses</option> <option value="vision">Vision</option> <option value="waste">Waste</option> <option value="water">Water</option> <option value="wild">Wild</option> <option value="wind">Wind</option> <option value="women">Women</option> <option value="world">World</option> <option value="wevj">World Electric Vehicle Journal</option> <option value="youth">Youth</option> <option value="zoonoticdis">Zoonotic Diseases</option> </select> <input name="email" type="email" placeholder="Enter your email address..." required="required" /> <button class="genericCaptcha button button--dark UA_FooterNewsletterSubscribeButton" type="submit">Subscribe</button> </form> </div> </div> </div> <div id="footer-copyright"> <div class="row"> <div class="columns large-6 medium-6 small-12 text-left"> © 1996-2024 MDPI (Basel, Switzerland) unless otherwise stated </div> <div class="columns large-6 medium-6 small-12 small-text-left medium-text-right large-text-right"> <a data-dropdown="drop-view-disclaimer" aria-controls="drop-view-disclaimer" aria-expanded="false" data-options="align:top; is_hover:true; hover_timeout:2000;"> Disclaimer </a> <div id="drop-view-disclaimer" class="f-dropdown label__btn__dropdown label__btn__dropdown--wide text-left" data-dropdown-content aria-hidden="true" tabindex="-1"> Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. </div> <a href="/about/terms-and-conditions"> Terms and Conditions </a> <a href="/about/privacy"> Privacy Policy </a> </div> </div> </div> </div> <div id="cookie-notification" class="js-allow-cookies" style="display: none;"> <div class="columns large-10 medium-10 small-12"> We use cookies on our website to ensure you get the best experience.<br class="show-for-medium-up"/> Read more about our cookies <a href="/about/privacy">here</a>. </div> <div class="columns large-2 medium-2 small-12 small-only-text-left text-right"> <a class="button button--default" href="/accept_cookies">Accept</a> </div> </div> </div> <div id="main-share-modal" class="reveal-modal reveal-modal-new reveal-modal-new--small" data-reveal aria-labelledby="modalTitle" aria-hidden="true" role="dialog"> <div class="row"> <div class="small-12 columns"> <h2 style="margin: 0;">Share Link</h2> </div> <div class="small-12 columns"> <div class="social-media-links UA_ShareModalLinks" style="text-align: left;"> <a href="/cdn-cgi/l/email-protection#99a6bff8f4e9a2eaecfbf3fcfaeda4dfebf6f4bcaba9d4ddc9d0bcaad8bcaba9bcababbfe8ecf6eda2bff8f4e9a2fbf6fde0a4f1edede9eaa3b6b6eeeeeeb7f4fde9f0b7faf6f4b6f3f6ecebf7f8f5b6ecf7f0effcebeafcbcaad8bca9d8bca9d89393" title="Email"> <i class="fa fa-envelope-square" style="font-size: 30px;"></i> </a> <a href="https://twitter.com/intent/tweet?text=&hashtags=mdpiuniverse&url=https%3A%2F%2Fwww.mdpi.com%2Fjournal%2Funiverse&via=Universe_MDPI" onclick="windowOpen(this.href,600,800); return false" title="Twitter" target="_blank" rel="noopener noreferrer"> <i class="fa fa-twitter-x-square" style="font-size: 30px;"></i> </a> <a href=" http://www.linkedin.com/shareArticle?mini=true&url=https%3A%2F%2Fwww.mdpi.com%2Fjournal%2Funiverse&title=%26source%3Dhttps%3A%2F%2Fwww.mdpi.com" onclick="windowOpen(this.href,600,800); return false" title="LinkedIn" target="_blank" rel="noopener noreferrer"> <i class="fa fa-linkedin-square" style="font-size: 30px;"></i> </a> <a href="https://www.facebook.com/sharer.php?u=https://www.mdpi.com/journal/universe" title="facebook" target="_blank" rel="noopener noreferrer"> <i class="fa fa-facebook-square" style="font-size: 30px;"></i> </a> <a href="javascript:void(0);" title="Wechat" data-reveal-id="weixin-share-modal"> <i class="fa fa-weixin-square" style="font-size: 26px;"></i> </a> <a href="http://www.reddit.com/submit?url=https://www.mdpi.com/journal/universe" title="Reddit" target="_blank" rel="noopener noreferrer"> <i class="fa fa-reddit-square" style="font-size: 30px;"></i> </a> <a href="http://www.mendeley.com/import/?url=https://www.mdpi.com/journal/universe" title="Mendeley" target="_blank" rel="noopener noreferrer"> <i class="fa fa-mendeley-square" style="font-size: 30px;"></i> </a> <a href="http://www.citeulike.org/posturl?url=https://www.mdpi.com/journal/universe" title="CiteULike" target="_blank" rel="noopener noreferrer"> <i class="fa fa-citeulike-square" style="font-size: 30px;"></i> </a> </div> </div> <div class="small-9 columns"> <input id="js-clipboard-text" type="text" readonly value="https://www.mdpi.com/journal/universe" /> </div> <div class="small-3 columns text-left"> <a class="button button--color js-clipboard-copy" data-clipboard-target="#js-clipboard-text">Copy</a> </div> </div> <a class="close-reveal-modal" aria-label="Close"> <i class="material-icons">clear</i> </a> </div> <div id="weixin-share-modal" class="reveal-modal reveal-modal-new" data-reveal aria-labelledby="weixin-share-modal-title" aria-hidden="true" role="dialog"> <div class="row"> <div class="small-12 columns"> <h2 id="weixin-share-modal-title" style="margin: 0;">Share</h2> </div> <div class="small-12 columns"> <div class="weixin-qr-code-section"> <?xml version="1.0" standalone="no"?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"> <svg width="348" height="348" version="1.1" xmlns="http://www.w3.org/2000/svg"> <desc>https://www.mdpi.com/journal/universe</desc> <g id="elements" fill="black" stroke="none"> <rect x="0" y="0" width="12" height="12" /> <rect x="12" y="0" width="12" height="12" /> <rect x="24" y="0" width="12" height="12" /> <rect x="36" y="0" width="12" height="12" /> <rect x="48" y="0" width="12" height="12" /> <rect x="60" y="0" width="12" height="12" /> <rect x="72" y="0" width="12" height="12" /> <rect x="96" y="0" width="12" height="12" /> <rect x="108" y="0" width="12" height="12" /> <rect x="120" y="0" width="12" height="12" /> <rect x="132" y="0" width="12" height="12" /> <rect x="156" y="0" width="12" height="12" /> <rect x="168" y="0" width="12" height="12" /> <rect x="216" y="0" width="12" height="12" /> <rect x="264" y="0" width="12" height="12" /> <rect x="276" y="0" width="12" height="12" /> <rect x="288" y="0" width="12" height="12" /> <rect x="300" y="0" width="12" height="12" /> <rect x="312" y="0" width="12" height="12" /> <rect x="324" y="0" width="12" height="12" /> <rect x="336" y="0" width="12" height="12" /> <rect x="0" y="12" width="12" height="12" /> <rect x="72" y="12" width="12" height="12" /> <rect x="132" y="12" width="12" height="12" /> <rect x="144" y="12" width="12" height="12" /> <rect x="156" y="12" width="12" height="12" /> <rect x="192" y="12" width="12" height="12" /> <rect x="204" y="12" width="12" height="12" /> <rect x="228" y="12" width="12" height="12" /> <rect x="240" y="12" width="12" height="12" /> <rect x="264" y="12" width="12" height="12" /> <rect x="336" y="12" width="12" height="12" /> <rect x="0" y="24" width="12" height="12" /> <rect x="24" y="24" width="12" height="12" /> <rect x="36" y="24" width="12" height="12" /> <rect x="48" y="24" width="12" height="12" /> <rect x="72" y="24" width="12" height="12" /> <rect x="108" y="24" width="12" height="12" /> <rect x="132" y="24" width="12" height="12" /> <rect x="156" y="24" width="12" height="12" /> <rect x="168" y="24" width="12" height="12" /> <rect x="192" y="24" width="12" height="12" /> <rect x="264" y="24" width="12" height="12" /> <rect x="288" y="24" width="12" height="12" /> <rect x="300" y="24" width="12" height="12" /> <rect x="312" y="24" width="12" height="12" /> <rect x="336" y="24" width="12" height="12" /> <rect x="0" y="36" width="12" height="12" /> <rect x="24" y="36" width="12" height="12" /> <rect x="36" y="36" width="12" height="12" /> <rect x="48" y="36" width="12" height="12" /> <rect x="72" y="36" width="12" height="12" /> <rect x="120" y="36" width="12" height="12" /> <rect x="132" y="36" width="12" height="12" /> <rect x="168" y="36" width="12" height="12" /> <rect x="204" y="36" width="12" height="12" /> <rect x="228" y="36" width="12" height="12" /> <rect x="240" y="36" width="12" height="12" /> <rect x="264" y="36" width="12" height="12" /> <rect x="288" y="36" width="12" height="12" /> <rect x="300" y="36" width="12" height="12" /> <rect x="312" y="36" width="12" height="12" /> <rect x="336" y="36" width="12" height="12" /> <rect x="0" y="48" width="12" height="12" /> <rect x="24" y="48" width="12" height="12" /> <rect x="36" y="48" width="12" height="12" /> <rect x="48" y="48" width="12" height="12" /> <rect x="72" y="48" width="12" height="12" /> <rect x="120" y="48" width="12" height="12" /> <rect x="132" y="48" width="12" height="12" /> <rect x="144" y="48" width="12" height="12" /> <rect x="156" y="48" width="12" height="12" /> <rect x="168" y="48" width="12" height="12" /> <rect x="192" y="48" width="12" height="12" /> <rect x="204" y="48" width="12" height="12" /> <rect x="228" y="48" width="12" height="12" /> <rect x="264" y="48" width="12" height="12" /> <rect x="288" y="48" width="12" height="12" /> <rect x="300" y="48" width="12" height="12" /> <rect x="312" y="48" width="12" height="12" /> <rect x="336" y="48" width="12" height="12" /> <rect x="0" y="60" width="12" height="12" /> <rect x="72" y="60" width="12" height="12" /> <rect x="108" y="60" width="12" height="12" /> <rect x="132" y="60" width="12" height="12" /> <rect x="156" y="60" width="12" height="12" /> <rect x="168" y="60" width="12" height="12" /> <rect x="192" y="60" width="12" height="12" /> <rect x="204" y="60" width="12" height="12" /> <rect x="240" y="60" width="12" height="12" /> <rect x="264" y="60" width="12" height="12" /> <rect x="336" y="60" width="12" height="12" /> <rect x="0" y="72" width="12" height="12" /> <rect x="12" y="72" width="12" height="12" /> <rect x="24" y="72" width="12" height="12" /> <rect x="36" y="72" width="12" height="12" /> <rect x="48" y="72" width="12" height="12" /> <rect x="60" y="72" width="12" height="12" /> <rect x="72" y="72" width="12" height="12" /> <rect x="96" y="72" width="12" height="12" /> <rect x="120" y="72" width="12" height="12" /> <rect x="144" y="72" width="12" height="12" /> <rect x="168" y="72" width="12" height="12" /> <rect x="192" y="72" width="12" height="12" /> <rect x="216" y="72" width="12" height="12" /> <rect x="240" y="72" width="12" height="12" /> <rect x="264" y="72" width="12" height="12" /> <rect x="276" y="72" width="12" height="12" /> <rect x="288" y="72" width="12" height="12" /> <rect x="300" y="72" width="12" height="12" /> <rect x="312" y="72" width="12" height="12" /> <rect x="324" y="72" width="12" height="12" /> <rect x="336" y="72" width="12" height="12" /> <rect x="96" y="84" width="12" height="12" /> <rect x="108" y="84" width="12" height="12" /> <rect x="144" y="84" width="12" height="12" /> <rect x="168" y="84" width="12" height="12" /> <rect x="180" y="84" width="12" height="12" /> <rect x="0" y="96" width="12" height="12" /> <rect x="12" y="96" width="12" height="12" /> <rect x="36" y="96" width="12" height="12" /> <rect x="48" y="96" width="12" height="12" /> <rect x="72" y="96" width="12" height="12" /> <rect x="108" y="96" width="12" height="12" /> <rect x="144" y="96" width="12" height="12" /> <rect x="156" y="96" width="12" height="12" /> <rect x="168" y="96" width="12" height="12" /> <rect x="180" y="96" width="12" height="12" /> <rect x="204" y="96" width="12" height="12" /> <rect x="264" y="96" width="12" height="12" /> <rect x="336" y="96" width="12" height="12" /> <rect x="0" y="108" width="12" height="12" /> <rect x="36" y="108" width="12" height="12" /> <rect x="120" y="108" width="12" height="12" /> <rect x="168" y="108" width="12" height="12" /> <rect x="180" y="108" width="12" height="12" /> <rect x="228" y="108" width="12" height="12" /> <rect x="240" y="108" width="12" height="12" /> <rect x="276" y="108" width="12" height="12" /> <rect x="288" y="108" width="12" height="12" /> <rect x="312" y="108" width="12" height="12" /> <rect x="324" y="108" width="12" height="12" /> <rect x="12" y="120" width="12" height="12" /> <rect x="24" y="120" width="12" height="12" /> <rect x="48" y="120" width="12" height="12" /> <rect x="72" y="120" width="12" height="12" /> <rect x="108" y="120" width="12" height="12" /> <rect x="144" y="120" width="12" height="12" /> <rect x="168" y="120" width="12" height="12" /> <rect x="180" y="120" width="12" height="12" /> <rect x="192" y="120" width="12" height="12" /> <rect x="216" y="120" width="12" height="12" /> <rect x="264" y="120" width="12" height="12" /> <rect x="276" y="120" width="12" height="12" /> <rect x="312" y="120" width="12" height="12" /> <rect x="0" y="132" width="12" height="12" /> <rect x="12" y="132" width="12" height="12" /> <rect x="24" y="132" width="12" height="12" /> <rect x="48" y="132" width="12" height="12" /> <rect x="96" y="132" width="12" height="12" /> <rect x="168" y="132" width="12" height="12" /> <rect x="204" y="132" width="12" height="12" /> <rect x="216" y="132" width="12" height="12" /> <rect x="240" y="132" width="12" height="12" /> <rect x="252" y="132" width="12" height="12" /> <rect x="264" y="132" width="12" height="12" /> <rect x="300" y="132" width="12" height="12" /> <rect x="336" y="132" width="12" height="12" /> <rect x="24" y="144" width="12" height="12" /> <rect x="72" y="144" width="12" height="12" /> <rect x="84" y="144" width="12" height="12" /> <rect x="108" y="144" width="12" height="12" /> <rect x="120" y="144" width="12" height="12" /> <rect x="156" y="144" width="12" height="12" /> <rect x="168" y="144" width="12" height="12" /> <rect x="180" y="144" width="12" height="12" /> <rect x="192" y="144" width="12" height="12" /> <rect x="240" y="144" width="12" height="12" /> <rect x="264" y="144" width="12" height="12" /> <rect x="276" y="144" width="12" height="12" /> <rect x="336" y="144" width="12" height="12" /> <rect x="0" y="156" width="12" height="12" /> <rect x="12" y="156" width="12" height="12" /> <rect x="36" y="156" width="12" height="12" /> <rect x="48" y="156" width="12" height="12" /> <rect x="108" y="156" width="12" height="12" /> <rect x="120" y="156" width="12" height="12" /> <rect x="144" y="156" width="12" height="12" /> <rect x="180" y="156" width="12" height="12" /> <rect x="192" y="156" width="12" height="12" /> <rect x="204" y="156" width="12" height="12" /> <rect x="216" y="156" width="12" height="12" /> <rect x="264" y="156" width="12" height="12" /> <rect x="288" y="156" width="12" height="12" /> <rect x="300" y="156" width="12" height="12" /> <rect x="312" y="156" width="12" height="12" /> <rect x="324" y="156" width="12" height="12" /> <rect x="336" y="156" width="12" height="12" /> <rect x="0" y="168" width="12" height="12" /> <rect x="12" y="168" width="12" height="12" /> <rect x="48" y="168" width="12" height="12" /> <rect x="60" y="168" width="12" height="12" /> <rect x="72" y="168" width="12" height="12" /> <rect x="120" y="168" width="12" height="12" /> <rect x="168" y="168" width="12" height="12" /> <rect x="180" y="168" width="12" height="12" /> <rect x="192" y="168" width="12" height="12" /> <rect x="204" y="168" width="12" height="12" /> <rect x="228" y="168" width="12" height="12" /> <rect x="240" y="168" width="12" height="12" /> <rect x="264" y="168" width="12" height="12" /> <rect x="276" y="168" width="12" height="12" /> <rect x="312" y="168" width="12" height="12" /> <rect x="336" y="168" width="12" height="12" /> <rect x="0" y="180" width="12" height="12" /> <rect x="24" y="180" width="12" height="12" /> <rect x="48" y="180" width="12" height="12" /> <rect x="108" y="180" width="12" height="12" /> <rect x="120" y="180" width="12" height="12" /> <rect x="144" y="180" width="12" height="12" /> <rect x="156" y="180" width="12" height="12" /> <rect x="168" y="180" width="12" height="12" /> <rect x="180" y="180" width="12" height="12" /> <rect x="216" y="180" width="12" height="12" /> <rect x="228" y="180" width="12" height="12" /> <rect x="264" y="180" width="12" height="12" /> <rect x="276" y="180" width="12" height="12" /> <rect x="288" y="180" width="12" height="12" /> <rect x="312" y="180" width="12" height="12" /> <rect x="336" y="180" width="12" height="12" /> <rect x="36" y="192" width="12" height="12" /> <rect x="60" y="192" width="12" height="12" /> <rect x="72" y="192" width="12" height="12" /> <rect x="96" y="192" width="12" height="12" /> <rect x="108" y="192" width="12" height="12" /> <rect x="120" y="192" width="12" height="12" /> <rect x="132" y="192" width="12" height="12" /> <rect x="144" y="192" width="12" height="12" /> <rect x="180" y="192" width="12" height="12" /> <rect x="192" y="192" width="12" height="12" /> <rect x="228" y="192" width="12" height="12" /> <rect x="240" y="192" width="12" height="12" /> <rect x="300" y="192" width="12" height="12" /> <rect x="0" y="204" width="12" height="12" /> <rect x="24" y="204" width="12" height="12" /> <rect x="36" y="204" width="12" height="12" /> <rect x="60" y="204" width="12" height="12" /> <rect x="132" y="204" width="12" height="12" /> <rect x="180" y="204" width="12" height="12" /> <rect x="204" y="204" width="12" height="12" /> <rect x="216" y="204" width="12" height="12" /> <rect x="228" y="204" width="12" height="12" /> <rect x="240" y="204" width="12" height="12" /> <rect x="252" y="204" width="12" height="12" /> <rect x="288" y="204" width="12" height="12" /> <rect x="312" y="204" width="12" height="12" /> <rect x="324" y="204" width="12" height="12" /> <rect x="0" y="216" width="12" height="12" /> <rect x="12" y="216" width="12" height="12" /> <rect x="24" y="216" width="12" height="12" /> <rect x="60" y="216" width="12" height="12" /> <rect x="72" y="216" width="12" height="12" /> <rect x="120" y="216" width="12" height="12" /> <rect x="144" y="216" width="12" height="12" /> <rect x="156" y="216" width="12" height="12" /> <rect x="168" y="216" width="12" height="12" /> <rect x="180" y="216" width="12" height="12" /> <rect x="204" y="216" width="12" height="12" /> <rect x="216" y="216" width="12" height="12" /> <rect x="228" y="216" width="12" height="12" /> <rect x="252" y="216" width="12" height="12" /> <rect x="264" y="216" width="12" height="12" /> <rect x="300" y="216" width="12" height="12" /> <rect x="336" y="216" width="12" height="12" /> <rect x="0" y="228" width="12" height="12" /> <rect x="12" y="228" width="12" height="12" /> <rect x="132" y="228" width="12" height="12" /> <rect x="156" y="228" width="12" height="12" /> <rect x="240" y="228" width="12" height="12" /> <rect x="276" y="228" width="12" height="12" /> <rect x="288" y="228" width="12" height="12" /> <rect x="300" y="228" width="12" height="12" /> <rect x="312" y="228" width="12" height="12" /> <rect x="0" y="240" width="12" height="12" /> <rect x="12" y="240" width="12" height="12" /> <rect x="24" y="240" width="12" height="12" /> <rect x="48" y="240" width="12" height="12" /> <rect x="60" y="240" width="12" height="12" /> <rect x="72" y="240" width="12" height="12" /> <rect x="108" y="240" width="12" height="12" /> <rect x="132" y="240" width="12" height="12" /> <rect x="156" y="240" width="12" height="12" /> <rect x="192" y="240" width="12" height="12" /> <rect x="204" y="240" width="12" height="12" /> <rect x="228" y="240" width="12" height="12" /> <rect x="240" y="240" width="12" height="12" /> <rect x="252" y="240" width="12" height="12" /> <rect x="264" y="240" width="12" height="12" /> <rect x="276" y="240" width="12" height="12" /> <rect x="288" y="240" width="12" height="12" /> <rect x="300" y="240" width="12" height="12" /> <rect x="312" y="240" width="12" height="12" /> <rect x="324" y="240" width="12" height="12" /> <rect x="96" y="252" width="12" height="12" /> <rect x="144" y="252" width="12" height="12" /> <rect x="156" y="252" width="12" height="12" /> <rect x="180" y="252" width="12" height="12" /> <rect x="204" y="252" width="12" height="12" /> <rect x="216" y="252" width="12" height="12" /> <rect x="240" y="252" width="12" height="12" /> <rect x="288" y="252" width="12" height="12" /> <rect x="300" y="252" width="12" height="12" /> <rect x="0" y="264" width="12" height="12" /> <rect x="12" y="264" width="12" height="12" /> <rect x="24" y="264" width="12" height="12" /> <rect x="36" y="264" width="12" height="12" /> <rect x="48" y="264" width="12" height="12" /> <rect x="60" y="264" width="12" height="12" /> <rect x="72" y="264" width="12" height="12" /> <rect x="120" y="264" width="12" height="12" /> <rect x="132" y="264" width="12" height="12" /> <rect x="156" y="264" width="12" height="12" /> <rect x="180" y="264" width="12" height="12" /> <rect x="204" y="264" width="12" height="12" /> <rect x="228" y="264" width="12" height="12" /> <rect x="240" y="264" width="12" height="12" /> <rect x="264" y="264" width="12" height="12" /> <rect x="288" y="264" width="12" height="12" /> <rect x="300" y="264" width="12" height="12" /> <rect x="0" y="276" width="12" height="12" /> <rect x="72" y="276" width="12" height="12" /> <rect x="132" y="276" width="12" height="12" /> <rect x="144" y="276" width="12" height="12" /> <rect x="156" y="276" width="12" height="12" /> <rect x="180" y="276" width="12" height="12" /> <rect x="204" y="276" width="12" height="12" /> <rect x="216" y="276" width="12" height="12" /> <rect x="228" y="276" width="12" height="12" /> <rect x="240" y="276" width="12" height="12" /> <rect x="288" y="276" width="12" height="12" /> <rect x="324" y="276" width="12" height="12" /> <rect x="336" y="276" width="12" height="12" /> <rect x="0" y="288" width="12" height="12" /> <rect x="24" y="288" width="12" height="12" /> <rect x="36" y="288" width="12" height="12" /> <rect x="48" y="288" width="12" height="12" /> <rect x="72" y="288" width="12" height="12" /> <rect x="96" y="288" width="12" height="12" /> <rect x="108" y="288" width="12" height="12" /> <rect x="132" y="288" width="12" height="12" /> <rect x="144" y="288" width="12" height="12" /> <rect x="156" y="288" width="12" height="12" /> <rect x="192" y="288" width="12" height="12" /> <rect x="216" y="288" width="12" height="12" /> <rect x="228" y="288" width="12" height="12" /> <rect x="240" y="288" width="12" height="12" /> <rect x="252" y="288" width="12" height="12" /> <rect x="264" y="288" width="12" height="12" /> <rect x="276" y="288" width="12" height="12" /> <rect x="288" y="288" width="12" height="12" /> <rect x="300" y="288" width="12" height="12" /> <rect x="336" y="288" width="12" height="12" /> <rect x="0" y="300" width="12" height="12" /> <rect x="24" y="300" width="12" height="12" /> <rect x="36" y="300" width="12" height="12" /> <rect x="48" y="300" width="12" height="12" /> <rect x="72" y="300" width="12" height="12" /> <rect x="96" y="300" width="12" height="12" /> <rect x="108" y="300" width="12" height="12" /> <rect x="156" y="300" width="12" height="12" /> <rect x="168" y="300" width="12" height="12" /> <rect x="180" y="300" width="12" height="12" /> <rect x="192" y="300" width="12" height="12" /> <rect x="204" y="300" width="12" height="12" /> <rect x="216" y="300" width="12" height="12" /> <rect x="228" y="300" width="12" height="12" /> <rect x="252" y="300" width="12" height="12" /> <rect x="276" y="300" width="12" height="12" /> <rect x="336" y="300" width="12" height="12" /> <rect x="0" y="312" width="12" height="12" /> <rect x="24" y="312" width="12" height="12" /> <rect x="36" y="312" width="12" height="12" /> <rect x="48" y="312" width="12" height="12" /> <rect x="72" y="312" width="12" height="12" /> <rect x="108" y="312" width="12" height="12" /> <rect x="132" y="312" width="12" height="12" /> <rect x="144" y="312" width="12" height="12" /> <rect x="156" y="312" width="12" height="12" /> <rect x="180" y="312" width="12" height="12" /> <rect x="204" y="312" width="12" height="12" /> <rect x="240" y="312" width="12" height="12" /> <rect x="252" y="312" width="12" height="12" /> <rect x="276" y="312" width="12" height="12" /> <rect x="288" y="312" width="12" height="12" /> <rect x="312" y="312" width="12" height="12" /> <rect x="324" y="312" width="12" height="12" /> <rect x="336" y="312" width="12" height="12" /> <rect x="0" y="324" width="12" height="12" /> <rect x="72" y="324" width="12" height="12" /> <rect x="96" y="324" width="12" height="12" /> <rect x="108" y="324" width="12" height="12" /> <rect x="120" y="324" width="12" height="12" /> <rect x="132" y="324" width="12" height="12" /> <rect x="276" y="324" width="12" height="12" /> <rect x="300" y="324" width="12" height="12" /> <rect x="312" y="324" width="12" height="12" /> <rect x="336" y="324" width="12" height="12" /> <rect x="0" y="336" width="12" height="12" /> <rect x="12" y="336" width="12" height="12" /> <rect x="24" y="336" width="12" height="12" /> <rect x="36" y="336" width="12" height="12" /> <rect x="48" y="336" width="12" height="12" /> <rect x="60" y="336" width="12" height="12" /> <rect x="72" y="336" width="12" height="12" /> <rect x="96" y="336" width="12" height="12" /> <rect x="120" y="336" width="12" height="12" /> <rect x="168" y="336" width="12" height="12" /> <rect x="180" y="336" width="12" height="12" /> <rect x="192" y="336" width="12" height="12" /> <rect x="240" y="336" width="12" height="12" /> <rect x="288" y="336" width="12" height="12" /> <rect x="300" y="336" width="12" height="12" /> </g> </svg> </div> </div> </div> <a class="close-reveal-modal" aria-label="Close"> <i class="material-icons">clear</i> </a> </div> <a href="#" class="back-to-top"><span class="show-for-medium-up">Back to Top</span><span class="show-for-small">Top</span></a> <script data-cfasync="false" src="/cdn-cgi/scripts/5c5dd728/cloudflare-static/email-decode.min.js"></script><script src="https://pub.mdpi-res.com/assets/js/modernizr-2.8.3.min.js?5227e0738f7f421d?1732694169"></script> <script src="https://pub.mdpi-res.com/assets/js/jquery-1.12.4.min.js?4f252523d4af0b47?1732694169"></script> <script src="https://pub.mdpi-res.com/assets/js/foundation-5.5.3.min.js?6b2ec41c18b29054?1732694169"></script> <script src="https://pub.mdpi-res.com/assets/js/foundation-5.5.3.equalizer.min.js?0f6c549b75ec554c?1732694169"></script> <script src="https://pub.mdpi-res.com/assets/js/jquery.multiselect.js?0edd3998731d1091?1732694169"></script> <script src="https://pub.mdpi-res.com/assets/js/jquery.cycle2.min.js?63413052928f97ee?1732694169"></script> <script> // old browser fix - this way the console log rows won't throw (silent) errors in browsers not supporting console log if (!window.console) window.console = {}; if (!window.console.log) window.console.log = function () { }; var currentJournalNameSystem = "universe"; $(document).ready(function() { $('select.foundation-select').multiselect({ search: true, minHeight: 130, maxHeight: 130, }); $(document).foundation({ orbit: { timer_speed: 4000, }, reveal: { animation: 'fadeAndPop', animation_speed: 100, } }); $(".chosen-select").each(function(element) { var maxSelected = (undefined !== $(this).data('maxselectedoptions') ? $(this).data('maxselectedoptions') : 100); $(this).on('chosen:ready', function(event, data) { var select = $(data.chosen.form_field); if (select.attr('id') === 'journal-browser-volume') { $(data.chosen.dropdown).addClass('UI_JournalBrowser_Volume_Options'); } if (select.attr('id') === 'journal-browser-issue') { $(data.chosen.dropdown).addClass('UI_JournalBrowser_Issue_Options'); } }).chosen({ display_disabled_options: false, disable_search_threshold: 7, max_selected_options: maxSelected, width: "100%" }); }); $(".toEncode").each(function(e) { var oldHref = $(this).attr("href"); var newHref = oldHref.replace('.botdefense.please.enable.javascript.','@'); $(this).attr("href", newHref); if (!$(this).hasClass("emailCaptcha")) { $(this).html(newHref.replace('mailto:', '')); } $(this).removeClass("visibility-hidden"); }); $(document).on('opened.fndtn.reveal', '[data-reveal]', function() { $(document).foundation('equalizer', 'reflow'); }); // fix the images that have tag height / width defined // otherwise the default foundation styles overwrite the tag definitions $("img").each(function() { if ($(this).attr('width') != undefined || $(this).attr('height') != undefined) { $(this).addClass("img-fixed"); } }); $("#basic_search, #advanced_search").submit(function(e) { var searchArguments = false; $(this).find("input,select").not("#search,.search-button").each(function() { if (undefined === $(this).val() || "" === $(this).val()) { $(this).attr('name', null); } else { $(this).attr('name'); searchArguments = true; } }); if (!searchArguments) { window.location = $(this).attr('action'); return false; } }); $(".hide-show-desktop-option").click(function(e) { e.preventDefault(); var parentDiv = $(this).closest("div"); $.ajax({ url: $(this).attr('href'), success: function(msg) { parentDiv.removeClass().hide(); } }); }); $(".generic-toggleable-header").click(function(e) { $(this).toggleClass("active"); $(this).next(".generic-toggleable-content").toggleClass("active"); }); /* * handle whole row as a link if the row contains only one visible link */ $("table.new tr").hover(function() { if ($(this).find("td:visible a").length == 1) { $(this).addClass("single-link"); } }, function() { $(this).removeClass("single-link"); }); $("table.new:not(.table-of-tables)").on("click", "tr.single-link", function(e) { var target = $(e.target); if (!e.ctrlKey && !target.is("a")) { $(this).find("td:visible a")[0].click(); } }); $(document).on("click", ".custom-accordion-for-small-screen-link", function(e) { if ($(this).closest("#basic_search").length > 0) { if ($(".search-container__advanced").first().is(":visible")) { openAdvanced() } } if (Foundation.utils.is_small_only()) { if ($(this).hasClass("active")) { $(this).removeClass("active"); $(this).next(".custom-accordion-for-small-screen-content").addClass("show-for-medium-up"); } else { $(this).addClass("active"); $(this).next(".custom-accordion-for-small-screen-content").removeClass("show-for-medium-up"); $(document).foundation('orbit', 'reflow'); } } if (undefined !== $(this).data("callback")) { var customCallback = $(this).data("callback"); func = window[customCallback]; func(); } }); $(document).on("click", ".js-open-small-search", function(e) { e.preventDefault(); $(this).toggleClass("active").closest(".tab-bar").toggleClass("active"); $(".search-container").toggleClass("hide-for-small-down"); }); $(document).on("click", ".js-open-menu", function(e) { $(".search-container").addClass("hide-for-small-down"); }); $(window).on('resize', function() { recalculate_main_browser_position(); recalculate_responsive_moving_containers(); }); updateSearchLabelVisibilities(); recalculate_main_browser_position(); recalculate_responsive_moving_containers(); if (window.document.documentMode == 11) { $("<link/>", { rel: "stylesheet", type: "text/css", href: "https://fonts.googleapis.com/icon?family=Material+Icons"}).appendTo("head"); } }); function recalculate_main_browser_position() { if (Foundation.utils.is_small_only()) { if ($("#js-main-top-container").parent("#js-large-main-top-container").length > 0) { $("#js-main-top-container").appendTo($("#js-small-main-top-container")); } } else { if ($("#js-main-top-container").parent("#js-small-main-top-container").length > 0) { $("#js-main-top-container").appendTo($("#js-large-main-top-container")); } } } function recalculate_responsive_moving_containers() { $(".responsive-moving-container.large").each(function() { var previousParent = $(".responsive-moving-container.active[data-id='"+$(this).data("id")+"']"); var movingContent = previousParent.html(); if (Foundation.utils.is_small_only()) { var currentParent = $(".responsive-moving-container.small[data-id='"+$(this).data("id")+"']"); } else if (Foundation.utils.is_medium_only()) { var currentParent = $(".responsive-moving-container.medium[data-id='"+$(this).data("id")+"']"); } else { var currentParent = $(".responsive-moving-container.large[data-id='"+$(this).data("id")+"']"); } if (previousParent.attr("class") !== currentParent.attr("class")) { currentParent.html(movingContent); previousParent.html(); currentParent.addClass("active"); previousParent.removeClass("active"); } }); } // cookies allowed is checked from a) local storage and b) from server separately so that the footer bar doesn't // get included in the custom page caches function checkCookiesAllowed() { var cookiesEnabled = localStorage.getItem("mdpi_cookies_enabled"); if (null === cookiesEnabled) { $.ajax({ url: "/ajax_cookie_value/mdpi_cookies_accepted", success: function(data) { if (data.value) { localStorage.setItem("mdpi_cookies_enabled", true); checkDisplaySurvey(); } else { $(".js-allow-cookies").show(); } } }); } else { checkDisplaySurvey(); } } function checkDisplaySurvey() { } window.addEventListener('CookiebotOnAccept', function (e) { var CookieDate = new Date; if (Cookiebot.consent.preferences) { CookieDate.setFullYear(CookieDate.getFullYear() + 1); document.cookie = "mdpi_layout_type_v2=mobile; path=/; expires=" + CookieDate.toUTCString() + ";"; $(".js-toggle-desktop-layout-link").css("display", "inline-block"); } }, false); window.addEventListener('CookiebotOnDecline', function (e) { if (!Cookiebot.consent.preferences) { $(".js-toggle-desktop-layout-link").hide(); if ("" === "desktop") { window.location = "/toggle_desktop_layout_cookie"; } } }, false); var hash = $(location).attr('hash'); if ("#share" === hash) { if (1 === $("#main-share-modal").length) { $('#main-share-modal').foundation('reveal', 'open'); } } </script> <script src="https://pub.mdpi-res.com/assets/js/lib.js?f8d3d71b3a772f9d?1732694169"></script> <script src="https://pub.mdpi-res.com/assets/js/mdpi.js?c267ce58392b15da?1732694169"></script> <script>var banners_url = 'https://serve.mdpi.com';</script> <script type='text/javascript' src='https://pub.mdpi-res.com/assets/js/ifvisible.min.js?c621d19ecb761212?1732694169'></script> <script src="https://pub.mdpi-res.com/assets/js/xmltohtml/affix.js?ac4ea55275297c15?1732694169"></script> <script src="https://pub.mdpi-res.com/assets/js/clipboard.min.js?3f3688138a1b9fc4?1732694169"></script> <script type="text/javascript"> $(document).ready(function() { var helpFunctions = $(".middle-column__help__fixed"); var leftColumnAffix = $(".left-column__fixed"); var middleColumn = $("#middle-column"); var clone = null; helpFunctions.affix({ offset: { top: function() { return middleColumn.offset().top - 8 - (Foundation.utils.is_medium_only() ? 30 : 0); }, bottom: function() { return $("#footer").innerHeight() + 74 + (Foundation.utils.is_medium_only() ? 0 : 0); } } }); if (leftColumnAffix.length > 0) { clone = leftColumnAffix.clone(); clone.addClass("left-column__fixed__affix"); clone.insertBefore(leftColumnAffix); clone.css('width', leftColumnAffix.outerWidth() + 50); clone.affix({ offset: { top: function() { return leftColumnAffix.offset().top - 30 - (Foundation.utils.is_medium_only() ? 50 : 0); }, bottom: function() { return $("#footer").innerHeight() + 92 + (Foundation.utils.is_medium_only() ? 0 : 0); } } }); } $(window).on("resize", function() { if (clone !== null) { clone.css('width', leftColumnAffix.outerWidth() + 50); } }); new ClipboardJS('.js-clipboard-copy'); }); </script> <script type="text/javascript"> $(document).ready(function() { // create the left hand menu dynamically from the content var items = $("#middle-column h1, #middle-column h2"); if ($("#dynamic-menu").length == 1 && items.length > 1) { // menu container div var div = $("div#dynamic-menu"); div.addClass("generic-item"); // menu header var header = $("<h2></h2>"); header.text("Menu"); div.append(header); // menu list var ul = $("<ul></ul>"); ul.addClass("side-menu-ul"); div.append(ul); // menu list items (create additional anchors for page) items.each(function() { var header_title = $(this).text(); var link_title = header_title.replace(/ |-/gi, "_").toLowerCase(); var li = $("<li></li>"); li.addClass("side-menu-li"); ul.append(li); var a = $("<a></a>"); a.html(header_title); a.prop("href", "#" + link_title); li.append(a); var a = $("<a></a>"); a.prop("name", link_title); $(this).prepend(a); }); div.append(ul); div.show(); } }); </script> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/magnific-popup.min.css?04d343e036f8eecd?1732694169"> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/jquery-ui-1.10.4.custom.min.css?80647d88647bf347?1732694169"> <script src="https://pub.mdpi-res.com/assets/js/jquery-ui-1.13.2.min.js?1e2047978946a1d2?1732694169"></script> <script type="text/javascript" src="https://pub.mdpi-res.com/assets/js/magnific-popup.min.js?2be3d9e7dc569146?1732694169"></script> <script> var mainColumn1 = "#right-column"; var extendingReady = true; $(document).ready(function() { $("#journal-browser-go").toggleClass("button--grey", "" === $("#journal-browser-volume").val()); $("#journal-browser-go").toggleClass("button--color", "" !== $("#journal-browser-volume").val()); $("#journal-browser-volume").change(function(e) { $('#journal-browser-issue').find('option').not('.volume-0').hide(); $('#journal-browser-issue').find('.volume-' + $(this).val()).show(); $('#journal-browser-issue').find('option:first').prop('selected', 'selected'); $("#journal-browser-issue").trigger("chosen:updated"); $('#journal-browser-go').toggleClass('button--grey', '' === $(this).val()); $('#journal-browser-go').toggleClass('button--color', '' !== $(this).val()); }); // add resize event for the window (to recalculate side column elements) // TODO: is it better to use resize end or resize here? $(window).on('resize', function() { mdpi_column_height_module.calculateColumnHeights(false, mainColumn1); }); $(".link-journal-menu").click(function(e) { e.preventDefault(); $(this).find('span').toggle(); $(this).next("ul").toggleClass("active"); $("#social-media-links").toggle(); $("#journal-alerts").toggle(); }); $(".link-journal-browser").click(function(e) { e.preventDefault(); $(this).find('span').toggle(); $(this).next("div").toggleClass('show-for-medium-up'); }); }); </script>   <script type="text/plain" data-cookieconsent="marketing"> !function(e,t,n,s,u,a){e.twq||(s=e.twq=function(){s.exe?s.exe.apply(s,arguments):s.queue.push(arguments); },s.version='1.1',s.queue=[],u=t.createElement(n),u.async=!0,u.src='//static.ads-twitter.com/uwt.js', a=t.getElementsByTagName(n)[0],a.parentNode.insertBefore(u,a))}(window,document,'script'); // Insert Twitter Pixel ID and Standard Event data below twq('init','o2pip'); twq('track','PageView'); </script>  <script>(function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'8e910e89fe419c5d',t:'MTczMjY5OTM3OS4wMDAwMDA='};var a=document.createElement('script');a.nonce='';a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();</script></body> </html>

CINXE.COM

Universe | An Open Access Journal from MDPI