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class="vector-toc-list"> <li id="toc-Status_in_physics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Status_in_physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Status in physics</span> </div> </a> <ul id="toc-Status_in_physics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Challenges_in_computational_physics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Challenges_in_computational_physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Challenges in computational physics</span> </div> </a> <ul id="toc-Challenges_in_computational_physics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Methods_and_algorithms" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Methods_and_algorithms"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Methods and algorithms</span> </div> </a> <ul id="toc-Methods_and_algorithms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Divisions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Divisions"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Divisions</span> </div> </a> <ul id="toc-Divisions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Applications</span> </div> </a> <ul id="toc-Applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon 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Available in 36 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-36" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">36 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%81%D9%8A%D8%B2%D9%8A%D8%A7%D8%A1_%D9%85%D8%AD%D9%88%D8%B3%D8%A8%D8%A9" title="فيزياء محوسبة – Arabic" lang="ar" hreflang="ar" data-title="فيزياء محوسبة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Hesablama_fizikas%C4%B1" title="Hesablama fizikası – Azerbaijani" lang="az" hreflang="az" data-title="Hesablama fizikası" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%97%E0%A6%A3%E0%A6%A8%E0%A6%BE%E0%A6%AE%E0%A7%82%E0%A6%B2%E0%A6%95_%E0%A6%AA%E0%A6%A6%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%A5%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="পরিগণনামূলক পদার্থবিজ্ঞান – Bangla" lang="bn" hreflang="bn" data-title="পরিগণনামূলক পদার্থবিজ্ঞান" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/F%C3%ADsica_computacional" title="Física computacional – Catalan" lang="ca" hreflang="ca" data-title="Física computacional" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A8%D1%83%D1%82%D0%BB%D0%B0%D0%B2%D0%BB%D0%B0_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Шутлавла физика – Chuvash" lang="cv" hreflang="cv" data-title="Шутлавла физика" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Computerfysik" title="Computerfysik – Danish" lang="da" hreflang="da" data-title="Computerfysik" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Computerphysik" title="Computerphysik – German" lang="de" hreflang="de" data-title="Computerphysik" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A5%CF%80%CE%BF%CE%BB%CE%BF%CE%B3%CE%B9%CF%83%CF%84%CE%B9%CE%BA%CE%AE_%CF%86%CF%85%CF%83%CE%B9%CE%BA%CE%AE" title="Υπολογιστική φυσική – Greek" lang="el" hreflang="el" data-title="Υπολογιστική φυσική" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/F%C3%ADsica_computacional" title="Física computacional – Spanish" lang="es" hreflang="es" data-title="Física computacional" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%DB%8C%D8%B2%DB%8C%DA%A9_%D9%85%D8%AD%D8%A7%D8%B3%D8%A8%D8%A7%D8%AA%DB%8C" title="فیزیک محاسباتی – Persian" lang="fa" hreflang="fa" data-title="فیزیک محاسباتی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Physique_num%C3%A9rique" title="Physique numérique – French" lang="fr" hreflang="fr" data-title="Physique numérique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B3%84%EC%82%B0%EB%AC%BC%EB%A6%AC%ED%95%99" title="계산물리학 – Korean" lang="ko" hreflang="ko" data-title="계산물리학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A1%D5%B7%D5%BE%D5%B8%D5%B2%D5%A1%D5%AF%D5%A1%D5%B6_%D6%86%D5%AB%D5%A6%D5%AB%D5%AF%D5%A1" title="Հաշվողական ֆիզիկա – Armenian" lang="hy" hreflang="hy" data-title="Հաշվողական ֆիզիկա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%AD%E0%A4%BF%E0%A4%95%E0%A4%B2%E0%A4%A8%E0%A4%BE%E0%A4%A4%E0%A5%8D%E0%A4%AE%E0%A4%95_%E0%A4%AD%E0%A5%8C%E0%A4%A4%E0%A4%BF%E0%A4%95%E0%A5%80" title="अभिकलनात्मक भौतिकी – Hindi" lang="hi" hreflang="hi" data-title="अभिकलनात्मक भौतिकी" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Fisika_komputasi" title="Fisika komputasi – Indonesian" lang="id" hreflang="id" data-title="Fisika komputasi" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Fisica_computazionale" title="Fisica computazionale – Italian" lang="it" hreflang="it" data-title="Fisica computazionale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%99%D7%96%D7%99%D7%A7%D7%94_%D7%97%D7%99%D7%A9%D7%95%D7%91%D7%99%D7%AA" title="פיזיקה חישובית – Hebrew" lang="he" hreflang="he" data-title="פיזיקה חישובית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B4%AE%E0%B5%8D%E0%B4%AA%E0%B5%8D%E0%B4%AF%E0%B5%82%E0%B4%9F%E0%B5%8D%E0%B4%9F%E0%B5%87%E0%B4%B7%E0%B4%A8%E0%B5%BD_%E0%B4%AB%E0%B4%BF%E0%B4%B8%E0%B4%BF%E0%B4%95%E0%B5%8D%E0%B4%B8%E0%B5%8D" title="കമ്പ്യൂട്ടേഷനൽ ഫിസിക്സ് – Malayalam" lang="ml" hreflang="ml" data-title="കമ്പ്യൂട്ടേഷനൽ ഫിസിക്സ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BE%D1%86%D0%BE%D0%BE%D0%BB%D0%BB%D1%8B%D0%BD_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA" title="Тооцооллын физик – Mongolian" lang="mn" hreflang="mn" data-title="Тооцооллын физик" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Numerieke_natuurkunde" title="Numerieke natuurkunde – Dutch" lang="nl" hreflang="nl" data-title="Numerieke natuurkunde" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%A8%88%E7%AE%97%E7%89%A9%E7%90%86%E5%AD%A6" title="計算物理学 – Japanese" lang="ja" hreflang="ja" data-title="計算物理学" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Hisoblash_fizikasi" title="Hisoblash fizikasi – Uzbek" lang="uz" hreflang="uz" data-title="Hisoblash fizikasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%85%D8%AD%D8%A7%D8%B3%D8%A8%D8%A7%D8%AA%D9%8A_%D9%81%D8%B2%DB%8C%DA%A9" title="محاسباتي فزیک – Pashto" lang="ps" hreflang="ps" data-title="محاسباتي فزیک" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Fizyka_komputerowa" title="Fizyka komputerowa – Polish" lang="pl" hreflang="pl" data-title="Fizyka komputerowa" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/F%C3%ADsica_computacional" title="Física computacional – Portuguese" lang="pt" hreflang="pt" data-title="Física computacional" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%92%D1%8B%D1%87%D0%B8%D1%81%D0%BB%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Вычислительная физика – Russian" lang="ru" hreflang="ru" data-title="Вычислительная физика" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Po%C4%8D%C3%ADta%C4%8Dov%C3%A1_fyzika" title="Počítačová fyzika – Slovak" lang="sk" hreflang="sk" data-title="Počítačová fyzika" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Laskennallinen_fysiikka" title="Laskennallinen fysiikka – Finnish" lang="fi" hreflang="fi" data-title="Laskennallinen fysiikka" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Ber%C3%A4kningsfysik" title="Beräkningsfysik – Swedish" lang="sv" hreflang="sv" data-title="Beräkningsfysik" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Pisikang_pangkomputasyon" title="Pisikang pangkomputasyon – Tagalog" lang="tl" hreflang="tl" data-title="Pisikang pangkomputasyon" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Hesaplamal%C4%B1_fizik" title="Hesaplamalı fizik – Turkish" lang="tr" hreflang="tr" data-title="Hesaplamalı fizik" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9E%D0%B1%D1%87%D0%B8%D1%81%D0%BB%D1%8E%D0%B2%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0_%D1%84%D1%96%D0%B7%D0%B8%D0%BA%D0%B0" title="Обчислювальна фізика – Ukrainian" lang="uk" hreflang="uk" data-title="Обчислювальна фізика" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/V%E1%BA%ADt_l%C3%BD_t%C3%ADnh_to%C3%A1n" title="Vật lý tính toán – Vietnamese" lang="vi" hreflang="vi" data-title="Vật lý tính toán" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Fisika_pankompyutasyon" title="Fisika pankompyutasyon – Waray" lang="war" hreflang="war" data-title="Fisika pankompyutasyon" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%81%8B%E7%AE%97%E7%89%A9%E7%90%86%E5%AD%B8" title="運算物理學 – Cantonese" lang="yue" hreflang="yue" data-title="運算物理學" data-language-autonym="粵語" data-language-local-name="Cantonese" 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selflink">Computational physics</a></th></tr><tr><td class="sidebar-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Rayleigh-Taylor_instability.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Rayleigh-Taylor_instability.jpg/220px-Rayleigh-Taylor_instability.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Rayleigh-Taylor_instability.jpg/330px-Rayleigh-Taylor_instability.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Rayleigh-Taylor_instability.jpg/440px-Rayleigh-Taylor_instability.jpg 2x" data-file-width="500" data-file-height="500" /></a></span></td></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Computational_mechanics" title="Computational mechanics">Mechanics</a></li> <li><a href="/wiki/Computational_electromagnetics" title="Computational electromagnetics">Electromagnetics</a></li> <li><a href="/wiki/Multiphysics_simulation" title="Multiphysics simulation">Multiphysics</a></li> <li><a href="/wiki/Computational_particle_physics" title="Computational particle physics">Particle physics</a></li> <li><a href="/wiki/Computational_thermodynamics" title="Computational thermodynamics">Thermodynamics</a></li> <li><a href="/wiki/Computer_simulation" title="Computer simulation">Simulation</a><br /></li></ul></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Potentials</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Morse/Long-range_potential" title="Morse/Long-range potential">Morse/Long-range potential</a></li> <li><a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones potential</a></li> <li><a href="/wiki/Yukawa_potential" title="Yukawa potential">Yukawa potential</a></li> <li><a href="/wiki/Morse_potential" title="Morse potential">Morse potential</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">Fluid dynamics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Finite_difference_method" title="Finite difference method">Finite difference</a></li> <li><a href="/wiki/Finite_volume_method" title="Finite volume method">Finite volume</a></li> <li><a href="/wiki/Finite_element_method" title="Finite element method">Finite element</a></li> <li><a href="/wiki/Boundary_element_method" title="Boundary element method">Boundary element</a></li> <li><a href="/wiki/Lattice_Boltzmann_methods" title="Lattice Boltzmann methods">Lattice Boltzmann</a></li> <li><a href="/wiki/Riemann_solver" title="Riemann solver">Riemann solver</a></li> <li><a href="/wiki/Dissipative_particle_dynamics" title="Dissipative particle dynamics">Dissipative particle dynamics</a></li> <li><a href="/wiki/Smoothed-particle_hydrodynamics" title="Smoothed-particle hydrodynamics">Smoothed particle hydrodynamics</a></li> <li><a href="/wiki/Turbulence_modeling" title="Turbulence modeling">Turbulence models</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo methods</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Monte_Carlo_integration" title="Monte Carlo integration">Integration</a></li> <li><a href="/wiki/Gibbs_sampling" title="Gibbs sampling">Gibbs sampling</a></li> <li><a href="/wiki/Metropolis%E2%80%93Hastings_algorithm" title="Metropolis–Hastings algorithm">Metropolis algorithm</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Particle</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/N-body_simulation" title="N-body simulation">N-body</a></li> <li><a href="/wiki/Particle-in-cell" title="Particle-in-cell">Particle-in-cell</a></li> <li><a href="/wiki/Molecular_dynamics" title="Molecular dynamics">Molecular dynamics</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Sergei_K._Godunov" class="mw-redirect" title="Sergei K. Godunov">Godunov</a></li> <li><a href="/wiki/Stanislaw_Ulam" class="mw-redirect" title="Stanislaw Ulam">Ulam</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a></li> <li><a href="/wiki/Boris_Galerkin" title="Boris Galerkin">Galerkin</a></li> <li><a href="/wiki/Edward_Norton_Lorenz" title="Edward Norton Lorenz">Lorenz</a></li> <li><a href="/wiki/Kenneth_G._Wilson" title="Kenneth G. Wilson">Wilson</a></li> <li><a href="/wiki/Berni_Alder" title="Berni Alder">Alder</a></li> <li><a href="/wiki/Robert_D._Richtmyer" title="Robert D. Richtmyer">Richtmyer</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Computational_physics" title="Template:Computational physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Computational_physics" title="Template talk:Computational physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Computational_physics" title="Special:EditPage/Template:Computational physics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Computational physics</b> is the study and implementation of <a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical analysis</a> to solve problems in <a href="/wiki/Physics" title="Physics">physics</a>.<sup id="cite_ref-ThijssenBook_1-0" class="reference"><a href="#cite_note-ThijssenBook-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Historically, computational physics was the first application of modern computers in science, and is now a subset of <a href="/wiki/Computational_science" title="Computational science">computational science</a>. It is sometimes regarded as a subdiscipline (or offshoot) of <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a>, but others consider it an intermediate branch between theoretical and <a href="/wiki/Experimental_physics" title="Experimental physics">experimental physics</a> — an area of study which supplements both theory and experiment.<sup id="cite_ref-ComPhysPy_2-0" class="reference"><a href="#cite_note-ComPhysPy-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_physics&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Computational_physics_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Computational_physics_diagram.svg/220px-Computational_physics_diagram.svg.png" decoding="async" width="220" height="206" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Computational_physics_diagram.svg/330px-Computational_physics_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Computational_physics_diagram.svg/440px-Computational_physics_diagram.svg.png 2x" data-file-width="957" data-file-height="894" /></a><figcaption>A representation of the multidisciplinary nature of computational physics both as an overlap of physics, applied mathematics, and computer science and as a bridge among them<sup id="cite_ref-SurveyCompSci_3-0" class="reference"><a href="#cite_note-SurveyCompSci-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>In physics, different <a href="/wiki/Theory" title="Theory">theories</a> based on mathematical models provide very precise predictions on how systems behave. Unfortunately, it is often the case that solving the mathematical model for a particular system in order to produce a useful prediction is not feasible. This can occur, for instance, when the solution does not have a <a href="/wiki/Closed-form_expression" title="Closed-form expression">closed-form expression</a>, or is too complicated. In such cases, numerical approximations are required. Computational physics is the subject that deals with these numerical approximations: the approximation of the solution is written as a finite (and typically large) number of simple mathematical operations (<a href="/wiki/Algorithm" title="Algorithm">algorithm</a>), and a computer is used to perform these operations and compute an approximated solution and respective <a href="/wiki/Approximation_error" title="Approximation error">error</a>.<sup id="cite_ref-ThijssenBook_1-1" class="reference"><a href="#cite_note-ThijssenBook-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Status_in_physics">Status in physics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_physics&action=edit&section=2" title="Edit section: Status in physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There is a debate about the status of computation within the scientific method.<sup id="cite_ref-ercolessi_4-0" class="reference"><a href="#cite_note-ercolessi-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Sometimes it is regarded as more akin to theoretical physics; some others regard computer simulation as "<a href="/wiki/Computer_experiment" title="Computer experiment">computer experiments</a>",<sup id="cite_ref-ercolessi_4-1" class="reference"><a href="#cite_note-ercolessi-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> yet still others consider it an intermediate or different branch between theoretical and <a href="/wiki/Experimental_physics" title="Experimental physics">experimental physics</a>, a third way that supplements theory and experiment. While computers can be used in experiments for the measurement and recording (and storage) of data, this clearly does not constitute a computational approach. </p> <div class="mw-heading mw-heading2"><h2 id="Challenges_in_computational_physics">Challenges in computational physics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_physics&action=edit&section=3" title="Edit section: Challenges in computational physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Computational physics problems are in general very difficult to solve exactly. This is due to several (mathematical) reasons: lack of algebraic and/or analytic solvability, <a href="/wiki/Complexity" title="Complexity">complexity</a>, and chaos. For example, even apparently simple problems, such as calculating the <a href="/wiki/Wavefunction" class="mw-redirect" title="Wavefunction">wavefunction</a> of an electron orbiting an atom in a strong <a href="/wiki/Electric_field" title="Electric field">electric field</a> (<a href="/wiki/Stark_effect" title="Stark effect">Stark effect</a>), may require great effort to formulate a practical algorithm (if one can be found); other cruder or brute-force techniques, such as <a href="/wiki/Graphical_method" class="mw-redirect" title="Graphical method">graphical methods</a> or <a href="/wiki/Root_finding" class="mw-redirect" title="Root finding">root finding</a>, may be required. On the more advanced side, mathematical <a href="/wiki/Perturbation_theory" title="Perturbation theory">perturbation theory</a> is also sometimes used (a working is shown for this particular example <a href="/wiki/Perturbation_theory#Example_of_degenerate_perturbation_theory_–_Stark_effect_in_resonant_rotating_wave" title="Perturbation theory">here</a>). In addition, the <a href="/wiki/Computational_cost" class="mw-redirect" title="Computational cost">computational cost</a> and <a href="/wiki/Computational_complexity_theory" title="Computational complexity theory">computational complexity</a> for <a href="/wiki/Many-body_problem" title="Many-body problem">many-body problems</a> (and their <a href="/wiki/N-body_problem" title="N-body problem">classical counterparts</a>) tend to grow quickly. A macroscopic system typically has a size of the order of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10^{23}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>23</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{23}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48d016cc8b369146c9bdca3ef8551b0c18acd6fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.201ex; height:2.676ex;" alt="{\displaystyle 10^{23}}"></span> constituent particles, so it is somewhat of a problem. Solving quantum mechanical problems is generally of <a href="/wiki/EXP" class="mw-redirect" title="EXP">exponential order</a> in the size of the system<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> and for classical N-body it is of order N-squared. Finally, many physical systems are inherently nonlinear at best, and at worst <a href="/wiki/Chaos_theory" title="Chaos theory">chaotic</a>: this means it can be difficult to ensure any <a href="/wiki/Numerical_error" title="Numerical error">numerical errors</a> do not grow to the point of rendering the 'solution' useless.<sup id="cite_ref-Sauer1997_6-0" class="reference"><a href="#cite_note-Sauer1997-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Methods_and_algorithms">Methods and algorithms</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_physics&action=edit&section=4" title="Edit section: Methods and algorithms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Because computational physics uses a broad class of problems, it is generally divided amongst the different mathematical problems it numerically solves, or the methods it applies. Between them, one can consider: </p> <ul><li><a href="/wiki/Root-finding_algorithm" title="Root-finding algorithm">root finding</a> (using e.g. <a href="/wiki/Newton%27s_method" title="Newton's method">Newton-Raphson method</a>)</li> <li><a href="/wiki/System_of_linear_equations" title="System of linear equations">system of linear equations</a> (using e.g. <a href="/wiki/LU_decomposition" title="LU decomposition">LU decomposition</a>)</li> <li><a href="/wiki/Ordinary_differential_equation" title="Ordinary differential equation">ordinary differential equations</a> (using e.g. <a href="/wiki/Runge%E2%80%93Kutta_methods" title="Runge–Kutta methods">Runge–Kutta methods</a>)</li> <li><a href="/wiki/Integral" title="Integral">integration</a> (using e.g. <a href="/wiki/Romberg%27s_method" title="Romberg's method">Romberg method</a> and <a href="/wiki/Monte_Carlo_integration" title="Monte Carlo integration">Monte Carlo integration</a>)</li> <li><a href="/wiki/Partial_differential_equation" title="Partial differential equation">partial differential equations</a> (using e.g. <a href="/wiki/Finite_difference" title="Finite difference">finite difference</a> method and <a href="/wiki/Relaxation_(iterative_method)" title="Relaxation (iterative method)">relaxation</a> method)</li> <li><a href="/wiki/Matrix_eigenvalue_problem" class="mw-redirect" title="Matrix eigenvalue problem">matrix eigenvalue problem</a> (using e.g. <a href="/wiki/Jacobi_eigenvalue_algorithm" title="Jacobi eigenvalue algorithm">Jacobi eigenvalue algorithm</a> and <a href="/wiki/Power_iteration" title="Power iteration">power iteration</a>)</li></ul> <p>All these methods (and several others) are used to calculate physical properties of the modeled systems. </p><p>Computational physics also borrows a number of ideas from <a href="/wiki/Computational_chemistry" title="Computational chemistry">computational chemistry</a> - for example, the <a href="/wiki/Density_functional_theory" title="Density functional theory">density functional theory</a> used by computational solid state physicists to calculate properties of solids is basically the same as that used by chemists to calculate the properties of molecules. </p><p>Furthermore, computational physics encompasses the <a href="/wiki/Performance_tuning" title="Performance tuning">tuning</a> of the <a href="/wiki/Self-tuning#Examples" title="Self-tuning">software</a>/<a href="/wiki/Category:Computer_hardware_tuning" title="Category:Computer hardware tuning">hardware structure</a> to solve the problems (as the problems usually can be very large, in <a href="/wiki/High_performance_computing" class="mw-redirect" title="High performance computing">processing power need</a> or in <a href="/wiki/High-throughput_computing" title="High-throughput computing">memory requests</a>). </p> <div class="mw-heading mw-heading2"><h2 id="Divisions">Divisions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_physics&action=edit&section=5" title="Edit section: Divisions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is possible to find a corresponding computational branch for every major field in physics: </p> <ul><li><a href="/wiki/Computational_mechanics" title="Computational mechanics">Computational mechanics</a> consists of <a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">computational fluid dynamics</a> (CFD), computational <a href="/wiki/Solid_mechanics" title="Solid mechanics">solid mechanics</a> and computational <a href="/wiki/Contact_mechanics" title="Contact mechanics">contact mechanics</a>.</li></ul> <ul><li><a href="/wiki/Computational_electrodynamics" class="mw-redirect" title="Computational electrodynamics">Computational electrodynamics</a> is the process of modeling the interaction of <a href="/wiki/Electromagnetic_fields" class="mw-redirect" title="Electromagnetic fields">electromagnetic fields</a> with physical objects and the environment. One subfield at the confluence between CFD and electromagnetic modelling is <a href="/wiki/Computational_magnetohydrodynamics" title="Computational magnetohydrodynamics">computational magnetohydrodynamics</a>.</li></ul> <ul><li><a href="/wiki/Computational_chemistry" title="Computational chemistry">Computational chemistry</a> is a rapidly growing field that was developed due to the <a href="/wiki/Quantum_many-body_problem" class="mw-redirect" title="Quantum many-body problem">quantum many-body problem</a>.</li></ul> <ul><li>Computational <a href="/wiki/Solid_state_physics" class="mw-redirect" title="Solid state physics">solid state physics</a> is a very important division of computational physics dealing directly with <a href="/wiki/Material_science" class="mw-redirect" title="Material science">material science</a>.</li></ul> <ul><li>Computational <a href="/wiki/Statistical_mechanics" title="Statistical mechanics">statistical mechanics</a> is a field related to computational <a href="/wiki/Condensed_matter" class="mw-redirect" title="Condensed matter">condensed matter</a> which deals with the simulation of models and theories (such as <a href="/wiki/Percolation" title="Percolation">percolation</a> and <a href="/wiki/Spin_model" title="Spin model">spin models</a>) that are difficult to solve otherwise.</li></ul> <ul><li>Computational <a href="/wiki/Statistical_physics" class="mw-redirect" title="Statistical physics">statistical physics</a> makes heavy use of Monte Carlo-like methods. More broadly, (particularly through the use of <a href="/wiki/Agent_based_modeling" class="mw-redirect" title="Agent based modeling">agent based modeling</a> and <a href="/wiki/Cellular_automata" class="mw-redirect" title="Cellular automata">cellular automata</a>) it also concerns itself with (and finds application in, through the use of its techniques) in the <a href="/wiki/Social_sciences" class="mw-redirect" title="Social sciences">social sciences</a>, <a href="/wiki/Network_theory" title="Network theory">network theory</a>, and mathematical models for the propagation of disease (most notably, the <a href="/wiki/Compartmental_models_in_epidemiology#SIR_Model_on_Networks" title="Compartmental models in epidemiology">SIR Model</a>) and the <a href="/wiki/Wildfire_modeling" title="Wildfire modeling">spread of forest fires</a>.</li></ul> <ul><li><a href="/wiki/Numerical_relativity" title="Numerical relativity">Numerical relativity</a> is a (relatively) new field interested in finding numerical solutions to the field equations of both <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> and <a href="/wiki/General_relativity" title="General relativity">general relativity</a>.</li></ul> <ul><li><a href="/wiki/Computational_particle_physics" title="Computational particle physics">Computational particle physics</a> deals with problems motivated by particle physics.</li></ul> <ul><li><a href="/wiki/Computational_astrophysics" title="Computational astrophysics">Computational astrophysics</a> is the application of these techniques and methods to astrophysical problems and phenomena.</li></ul> <ul><li><a href="/wiki/Computational_biophysics" class="mw-redirect" title="Computational biophysics">Computational biophysics</a> is a branch of biophysics and <a href="/wiki/Computational_biology" title="Computational biology">computational biology</a> itself, applying methods of computer science and physics to large complex biological problems.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_physics&action=edit&section=6" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Due to the broad class of problems computational physics deals, it is an essential component of modern research in different areas of physics, namely: <a href="/wiki/Accelerator_physics" title="Accelerator physics">accelerator physics</a>, <a href="/wiki/Astrophysics" title="Astrophysics">astrophysics</a>, <a href="/wiki/General_theory_of_relativity" class="mw-redirect" title="General theory of relativity">general theory of relativity</a> (through <a href="/wiki/Numerical_relativity" title="Numerical relativity">numerical relativity</a>), <a href="/wiki/Fluid_mechanics" title="Fluid mechanics">fluid mechanics</a> (<a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">computational fluid dynamics</a>), <a href="/wiki/Lattice_field_theory" title="Lattice field theory">lattice field theory</a>/<a href="/wiki/Lattice_gauge_theory" title="Lattice gauge theory">lattice gauge theory</a> (especially <a href="/wiki/Lattice_QCD" title="Lattice QCD">lattice quantum chromodynamics</a>), <a href="/wiki/Plasma_physics" class="mw-redirect" title="Plasma physics">plasma physics</a> (see <a href="/wiki/Plasma_modeling" title="Plasma modeling">plasma modeling</a>), simulating physical systems (using e.g. <a href="/wiki/Molecular_dynamics" title="Molecular dynamics">molecular dynamics</a>), <a href="/wiki/Nuclear_engineering_computer_codes" class="mw-redirect" title="Nuclear engineering computer codes">nuclear engineering computer codes</a>, <a href="/wiki/Protein_structure_prediction" title="Protein structure prediction">protein structure prediction</a>, <a href="/wiki/Weather_prediction" class="mw-redirect" title="Weather prediction">weather prediction</a>, <a href="/wiki/Solid_state_physics" class="mw-redirect" title="Solid state physics">solid state physics</a>, <a href="/wiki/Soft_condensed_matter" class="mw-redirect" title="Soft condensed matter">soft condensed matter</a> physics, hypervelocity impact physics etc. </p><p>Computational solid state physics, for example, uses <a href="/wiki/Density_functional_theory" title="Density functional theory">density functional theory</a> to calculate properties of solids, a method similar to that used by chemists to study molecules. Other quantities of interest in solid state physics, such as the electronic band structure, magnetic properties and charge densities can be calculated by this and several methods, including the <a href="/wiki/Luttinger-Kohn_model" class="mw-redirect" title="Luttinger-Kohn model">Luttinger-Kohn</a>/<a href="/wiki/K.p_method" class="mw-redirect" title="K.p method">k.p method</a> and <a href="/wiki/Ab-initio" class="mw-redirect" title="Ab-initio">ab-initio</a> methods. </p><p>On top of advanced physics software, there are also a myriad of tools of analytics available for beginning students of physics such as the PASCO Capstone software. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_physics&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Advanced_Simulation_Library" title="Advanced Simulation Library">Advanced Simulation Library</a></li> <li><a href="/wiki/CECAM" class="mw-redirect" title="CECAM">CECAM - Centre européen de calcul atomique et moléculaire</a></li> <li><a href="/wiki/DCOMP#DCOMP" class="mw-redirect" title="DCOMP">Division of Computational Physics (DCOMP)</a> of the <a href="/wiki/American_Physical_Society" title="American Physical Society">American Physical Society</a></li> <li><a href="/wiki/List_of_publications_in_physics#Computational_physics" class="mw-redirect" title="List of publications in physics">Important publications in computational physics</a></li> <li><a href="/wiki/Mathematical_physics" title="Mathematical physics">Mathematical</a> and <a href="/wiki/Theoretical_physics" title="Theoretical physics">theoretical physics</a></li> <li><a href="/wiki/Open_Source_Physics" title="Open Source Physics">Open Source Physics</a>, computational physics libraries and pedagogical tools</li> <li><a href="/wiki/Timeline_of_computational_physics" title="Timeline of computational physics">Timeline of computational physics</a></li> <li><a href="/wiki/Car%E2%80%93Parrinello_molecular_dynamics" title="Car–Parrinello molecular dynamics">Car–Parrinello molecular dynamics</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_physics&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-ThijssenBook-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-ThijssenBook_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ThijssenBook_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFThijssen2007" class="citation book cs1">Thijssen, Jos (2007). <i>Computational Physics</i>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0521833462" title="Special:BookSources/978-0521833462"><bdi>978-0521833462</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+Physics&rft.pub=Cambridge+University+Press&rft.date=2007&rft.isbn=978-0521833462&rft.aulast=Thijssen&rft.aufirst=Jos&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputational+physics" class="Z3988"></span></span> </li> <li id="cite_note-ComPhysPy-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-ComPhysPy_2-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLandauPáezBordeianu2015" class="citation book cs1">Landau, Rubin H.; Páez, Manuel J.; Bordeianu, Cristian C. (2015). <a rel="nofollow" class="external text" href="http://www.wiley.com/WileyCDA/WileyTitle/productCd-3527413154.html"><i>Computational Physics: Problem Solving with Python</i></a>. <a href="/wiki/John_Wiley_%26_Sons" class="mw-redirect" title="John Wiley & Sons">John Wiley & Sons</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+Physics%3A+Problem+Solving+with+Python&rft.pub=John+Wiley+%26+Sons&rft.date=2015&rft.aulast=Landau&rft.aufirst=Rubin+H.&rft.au=P%C3%A1ez%2C+Manuel+J.&rft.au=Bordeianu%2C+Cristian+C.&rft_id=http%3A%2F%2Fwww.wiley.com%2FWileyCDA%2FWileyTitle%2FproductCd-3527413154.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputational+physics" class="Z3988"></span></span> </li> <li id="cite_note-SurveyCompSci-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-SurveyCompSci_3-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLandauPaezBordeianu2011" class="citation book cs1">Landau, Rubin H.; Paez, Jose; Bordeianu, Cristian C. (2011). <a rel="nofollow" class="external text" href="http://press.princeton.edu/titles/8704.html"><i>A survey of computational physics: introductory computational science</i></a>. <a href="/wiki/Princeton_University_Press" title="Princeton University Press">Princeton University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780691131375" title="Special:BookSources/9780691131375"><bdi>9780691131375</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+survey+of+computational+physics%3A+introductory+computational+science&rft.pub=Princeton+University+Press&rft.date=2011&rft.isbn=9780691131375&rft.aulast=Landau&rft.aufirst=Rubin+H.&rft.au=Paez%2C+Jose&rft.au=Bordeianu%2C+Cristian+C.&rft_id=http%3A%2F%2Fpress.princeton.edu%2Ftitles%2F8704.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputational+physics" class="Z3988"></span></span> </li> <li id="cite_note-ercolessi-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-ercolessi_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ercolessi_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.fisica.uniud.it/~ercolessi/md/md/">A molecular dynamics primer</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150111014856/http://www.fisica.uniud.it/~ercolessi/md/md/">Archived</a> 2015-01-11 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, Furio Ercolessi, <a href="/wiki/University_of_Udine" title="University of Udine">University of Udine</a>, Italy. <a rel="nofollow" class="external text" href="http://www.fisica.uniud.it/~ercolessi/md/md.pdf">Article PDF</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150924013419/http://www.fisica.uniud.it/~ercolessi/md/md.pdf">Archived</a> 2015-09-24 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeynman1982" class="citation journal cs1"><a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman, Richard P.</a> (1982). "Simulating physics with computers". <i>International Journal of Theoretical Physics</i>. <b>21</b> (6–7): 467–488. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1982IJTP...21..467F">1982IJTP...21..467F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf02650179">10.1007/bf02650179</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0020-7748">0020-7748</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:124545445">124545445</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Theoretical+Physics&rft.atitle=Simulating+physics+with+computers&rft.volume=21&rft.issue=6%E2%80%937&rft.pages=467-488&rft.date=1982&rft_id=info%3Adoi%2F10.1007%2Fbf02650179&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A124545445%23id-name%3DS2CID&rft.issn=0020-7748&rft_id=info%3Abibcode%2F1982IJTP...21..467F&rft.aulast=Feynman&rft.aufirst=Richard+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputational+physics" class="Z3988"></span> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170812065758/http://www.mrtc.mdh.se/~gdc/work/ARTICLES/2014/3-CiE-journal/Background/SimulatingPhysicsWithComputers.pdf">Article PDF</a></span> </li> <li id="cite_note-Sauer1997-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Sauer1997_6-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSauerGrebogiYorke1997" class="citation journal cs1">Sauer, Tim; Grebogi, Celso; Yorke, James A (1997). "How Long Do Numerical Chaotic Solutions Remain Valid?". <i>Physical Review Letters</i>. <b>79</b> (1): 59–62. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1997PhRvL..79...59S">1997PhRvL..79...59S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.79.59">10.1103/PhysRevLett.79.59</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:102493915">102493915</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=How+Long+Do+Numerical+Chaotic+Solutions+Remain+Valid%3F&rft.volume=79&rft.issue=1&rft.pages=59-62&rft.date=1997&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A102493915%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.79.59&rft_id=info%3Abibcode%2F1997PhRvL..79...59S&rft.aulast=Sauer&rft.aufirst=Tim&rft.au=Grebogi%2C+Celso&rft.au=Yorke%2C+James+A&rfr_id=info%3Asid%2Fen.wikipedia.org%3AComputational+physics" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_physics&action=edit&section=9" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>A.K. Hartmann, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090211113048/http://worldscibooks.com/physics/6988.html">Practical Guide to Computer Simulations</a>, <a href="/wiki/World_Scientific" title="World Scientific">World Scientific</a> (2009)</li> <li><a rel="nofollow" class="external text" href="http://www.worldscinet.com/ijmpc/ijmpc.shtml">International Journal of Modern Physics C (IJMPC): Physics and Computers</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20041103090645/http://www.worldscinet.com/ijmpc/ijmpc.shtml">Archived</a> 2004-11-03 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <a href="/wiki/World_Scientific" title="World Scientific">World Scientific</a></li> <li><a href="/wiki/Steven_E._Koonin" title="Steven E. Koonin">Steven E. Koonin</a>, Computational Physics, <a href="/wiki/Addison-Wesley" title="Addison-Wesley">Addison-Wesley</a> (1986)</li> <li>T. Pang, An Introduction to Computational Physics, <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a> (2010)</li> <li>B. Stickler, E. Schachinger, Basic concepts in computational physics, <a href="/wiki/Springer_Verlag" class="mw-redirect" title="Springer Verlag">Springer Verlag</a> (2013). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783319024349" title="Special:BookSources/9783319024349">9783319024349</a>.</li> <li>E. Winsberg, <i>Science in the Age of Computer Simulation</i>. Chicago: <a href="/wiki/University_of_Chicago_Press" title="University of Chicago Press">University of Chicago Press</a>, 2010.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_physics&action=edit&section=10" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 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title="Branches of physics">branches of physics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Divisions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Basic_research" title="Basic research">Pure</a></li> <li><a href="/wiki/Applied_physics" title="Applied physics">Applied</a> <ul><li><a href="/wiki/Engineering_physics" title="Engineering physics">Engineering</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Approaches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Experimental_physics" title="Experimental physics">Experimental</a></li> <li><a href="/wiki/Theoretical_physics" title="Theoretical physics">Theoretical</a> <ul><li><a class="mw-selflink selflink">Computational</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Classical_physics" title="Classical physics">Classical</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a> <ul><li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newtonian</a></li> <li><a href="/wiki/Analytical_mechanics" title="Analytical mechanics">Analytical</a></li> <li><a href="/wiki/Celestial_mechanics" title="Celestial mechanics">Celestial</a></li> <li><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum</a></li></ul></li> <li><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a></li> <li><a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">Classical electromagnetism</a></li> <li><a href="/wiki/Classical_optics" class="mw-redirect" title="Classical optics">Classical optics</a> <ul><li><a href="/wiki/Geometrical_optics" title="Geometrical optics">Ray</a></li> <li><a href="/wiki/Physical_optics" title="Physical optics">Wave</a></li></ul></li> <li><a href="/wiki/Thermodynamics" title="Thermodynamics">Thermodynamics</a> <ul><li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical</a></li> <li><a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Modern_physics" title="Modern physics">Modern</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Relativistic_mechanics" title="Relativistic mechanics">Relativistic mechanics</a> <ul><li><a href="/wiki/Special_relativity" title="Special relativity">Special</a></li> <li><a href="/wiki/General_relativity" title="General relativity">General</a></li></ul></li> <li><a href="/wiki/Nuclear_physics" title="Nuclear physics">Nuclear physics</a></li> <li><a href="/wiki/Particle_physics" title="Particle physics">Particle physics</a></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li> <li><a href="/wiki/Atomic,_molecular,_and_optical_physics" title="Atomic, molecular, and optical physics">Atomic, molecular, and optical physics</a> <ul><li><a href="/wiki/Atomic_physics" title="Atomic physics">Atomic</a></li> <li><a href="/wiki/Molecular_physics" title="Molecular physics">Molecular</a></li> <li><a href="/wiki/Optics#Modern_optics" title="Optics">Modern optics</a></li></ul></li> <li><a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">Condensed matter physics</a> <ul><li><a href="/wiki/Solid-state_physics" title="Solid-state physics">Solid-state physics</a></li> <li><a href="/wiki/Crystallography" title="Crystallography">Crystallography</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Applied_and_interdisciplinary_physics" title="Category:Applied and interdisciplinary physics">Interdisciplinary</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Astrophysics" title="Astrophysics">Astrophysics</a></li> <li><a href="/wiki/Atmospheric_physics" title="Atmospheric physics">Atmospheric physics</a></li> <li><a href="/wiki/Biophysics" title="Biophysics">Biophysics</a></li> <li><a href="/wiki/Chemical_physics" title="Chemical physics">Chemical physics</a></li> <li><a href="/wiki/Geophysics" title="Geophysics">Geophysics</a></li> <li><a href="/wiki/Materials_science" title="Materials science">Materials science</a></li> <li><a href="/wiki/Mathematical_physics" title="Mathematical physics">Mathematical physics</a></li> <li><a href="/wiki/Medical_physics" title="Medical physics">Medical physics</a></li> <li><a href="/wiki/Physical_oceanography" title="Physical oceanography">Ocean physics</a></li> <li><a href="/wiki/Quantum_information_science" title="Quantum information science">Quantum information science</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_physics" title="History of physics">History of physics</a></li> <li><a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a></li> <li><a href="/wiki/Philosophy_of_physics" title="Philosophy of physics">Philosophy of physics</a></li> <li><a href="/wiki/Physics_education" title="Physics education">Physics education</a></li> <li><a href="/wiki/Timeline_of_fundamental_physics_discoveries" title="Timeline of fundamental physics discoveries">Timeline of physics discoveries</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Computational_science" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Computational_science" title="Template:Computational science"><abbr title="View this 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<li><a href="/wiki/Modelling_biological_systems" title="Modelling biological systems">Biological systems</a></li> <li><a href="/wiki/Computational_cognition" title="Computational cognition">Cognition</a></li> <li><a href="/wiki/Computational_genomics" title="Computational genomics">Genomics</a></li> <li><a href="/wiki/Computational_neuroscience" title="Computational neuroscience">Neuroscience</a></li> <li><a href="/wiki/Computational_phylogenetics" title="Computational phylogenetics">Phylogenetics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computational_chemistry" title="Computational chemistry">Chemistry</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Electronic_structure" class="mw-redirect" title="Electronic structure">Electronic structure</a></li> <li><a href="/wiki/Molecular_mechanics" title="Molecular mechanics">Molecular mechanics</a></li> <li><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Physics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computational_astrophysics" title="Computational astrophysics">Astrophysics</a></li> <li><a href="/wiki/Computational_electromagnetics" title="Computational electromagnetics">Electromagnetics</a></li> <li><a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">Fluid dynamics</a></li> <li><a href="/wiki/Computational_geophysics" title="Computational geophysics">Geophysics</a></li> <li><a href="/wiki/Computational_mechanics" title="Computational mechanics">Mechanics</a></li> <li><a href="/wiki/Computational_particle_physics" title="Computational particle physics">Particle physics</a></li> <li><a href="/wiki/Computational_thermodynamics" title="Computational thermodynamics">Thermodynamics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computational_linguistics" title="Computational linguistics">Linguistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computational_semantics" title="Computational semantics">Semantics</a></li> <li><a href="/wiki/Computational_lexicology" title="Computational lexicology">Lexicology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computational_social_science" title="Computational social science">Social science</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computational_politics" title="Computational politics">Politics</a></li> <li><a href="/wiki/Computational_sociology" title="Computational sociology">Sociology</a></li> <li><a href="/wiki/Computational_economics" title="Computational economics">Economics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computational_finance" title="Computational finance">Finance</a></li> <li><a href="/wiki/Computational_materials_science" title="Computational materials science">Materials science</a></li> <li><a href="/wiki/Computational_mathematics" title="Computational mathematics">Mathematics</a></li> <li><a href="/wiki/Computational_statistics" title="Computational statistics">Statistics</a></li> <li><a href="/wiki/Computational_engineering" title="Computational engineering">Engineering</a></li> <li><a href="/wiki/Computational_semiotics" title="Computational semiotics">Semiotics</a></li> <li><a href="/wiki/Computational_transportation_science" title="Computational transportation science">Transportation science</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Computer_science" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Computer_science" title="Template:Computer science"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Computer_science" title="Template talk:Computer science"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Computer_science" title="Special:EditPage/Template:Computer science"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Computer_science" style="font-size:114%;margin:0 4em"><a href="/wiki/Computer_science" title="Computer science">Computer science</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>Note: This template roughly follows the 2012 <a href="/wiki/ACM_Computing_Classification_System" title="ACM Computing Classification System">ACM Computing Classification System</a>.</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_hardware" title="Computer hardware">Hardware</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Printed_circuit_board" title="Printed circuit board">Printed circuit board</a></li> <li><a href="/wiki/Peripheral" title="Peripheral">Peripheral</a></li> <li><a href="/wiki/Integrated_circuit" title="Integrated circuit">Integrated circuit</a></li> <li><a href="/wiki/Very_Large_Scale_Integration" class="mw-redirect" title="Very Large Scale Integration">Very Large Scale Integration</a></li> <li><a href="/wiki/System_on_a_chip" title="System on a chip">Systems on Chip (SoCs)</a></li> <li><a href="/wiki/Green_computing" title="Green computing">Energy consumption (Green computing)</a></li> <li><a href="/wiki/Electronic_design_automation" title="Electronic design automation">Electronic design automation</a></li> <li><a href="/wiki/Hardware_acceleration" title="Hardware acceleration">Hardware acceleration</a></li> <li><a href="/wiki/Processor_(computing)" title="Processor (computing)">Processor</a></li> <li><a href="/wiki/List_of_computer_size_categories" title="List of computer size categories">Size</a> / <a href="/wiki/Form_factor_(design)" title="Form factor (design)">Form</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Computer systems organization</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computer_architecture" title="Computer architecture">Computer architecture</a></li> <li><a href="/wiki/Computational_complexity" title="Computational complexity">Computational complexity</a></li> <li><a href="/wiki/Dependability" title="Dependability">Dependability</a></li> <li><a href="/wiki/Embedded_system" title="Embedded system">Embedded system</a></li> <li><a href="/wiki/Real-time_computing" title="Real-time computing">Real-time computing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_network" title="Computer network">Networks</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Network_architecture" title="Network architecture">Network architecture</a></li> <li><a href="/wiki/Network_protocol" class="mw-redirect" title="Network protocol">Network protocol</a></li> <li><a href="/wiki/Networking_hardware" title="Networking hardware">Network components</a></li> <li><a href="/wiki/Network_scheduler" title="Network scheduler">Network scheduler</a></li> <li><a href="/wiki/Network_performance" title="Network performance">Network performance evaluation</a></li> <li><a href="/wiki/Network_service" title="Network service">Network service</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Software organization</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Interpreter_(computing)" title="Interpreter (computing)">Interpreter</a></li> <li><a href="/wiki/Middleware" title="Middleware">Middleware</a></li> <li><a href="/wiki/Virtual_machine" title="Virtual machine">Virtual machine</a></li> <li><a href="/wiki/Operating_system" title="Operating system">Operating system</a></li> <li><a href="/wiki/Software_quality" title="Software quality">Software quality</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Programming_language_theory" title="Programming language theory">Software notations</a> and <a href="/wiki/Programming_tool" title="Programming tool">tools</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Programming_paradigm" title="Programming paradigm">Programming paradigm</a></li> <li><a href="/wiki/Programming_language" title="Programming language">Programming language</a></li> <li><a href="/wiki/Compiler_construction" class="mw-redirect" title="Compiler construction">Compiler</a></li> <li><a href="/wiki/Domain-specific_language" title="Domain-specific language">Domain-specific language</a></li> <li><a href="/wiki/Modeling_language" title="Modeling language">Modeling language</a></li> <li><a href="/wiki/Software_framework" title="Software framework">Software framework</a></li> <li><a href="/wiki/Integrated_development_environment" title="Integrated development environment">Integrated development environment</a></li> <li><a href="/wiki/Software_configuration_management" title="Software configuration management">Software configuration management</a></li> <li><a href="/wiki/Library_(computing)" title="Library (computing)">Software library</a></li> <li><a href="/wiki/Software_repository" title="Software repository">Software repository</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Software_development" title="Software development">Software development</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Control_variable_(programming)" class="mw-redirect" title="Control variable (programming)">Control variable</a></li> <li><a href="/wiki/Software_development_process" title="Software development process">Software development process</a></li> <li><a href="/wiki/Requirements_analysis" title="Requirements analysis">Requirements analysis</a></li> <li><a href="/wiki/Software_design" title="Software design">Software design</a></li> <li><a href="/wiki/Software_construction" title="Software construction">Software construction</a></li> <li><a href="/wiki/Software_deployment" title="Software deployment">Software deployment</a></li> <li><a href="/wiki/Software_engineering" title="Software engineering">Software engineering</a></li> <li><a href="/wiki/Software_maintenance" title="Software maintenance">Software maintenance</a></li> <li><a href="/wiki/Programming_team" title="Programming team">Programming team</a></li> <li><a href="/wiki/Open-source_software" title="Open-source software">Open-source model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Theory_of_computation" title="Theory of computation">Theory of computation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Model_of_computation" title="Model of computation">Model of computation</a> <ul><li><a href="/wiki/Stochastic_computing" title="Stochastic computing">Stochastic</a></li></ul></li> <li><a href="/wiki/Formal_language" title="Formal language">Formal language</a></li> <li><a href="/wiki/Automata_theory" title="Automata theory">Automata theory</a></li> <li><a href="/wiki/Computability_theory" title="Computability theory">Computability theory</a></li> <li><a href="/wiki/Computational_complexity_theory" title="Computational complexity theory">Computational complexity theory</a></li> <li><a href="/wiki/Logic_in_computer_science" title="Logic in computer science">Logic</a></li> <li><a href="/wiki/Semantics_(computer_science)" title="Semantics (computer science)">Semantics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Algorithm" title="Algorithm">Algorithms</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algorithm_design" class="mw-redirect" title="Algorithm design">Algorithm design</a></li> <li><a href="/wiki/Analysis_of_algorithms" title="Analysis of algorithms">Analysis of algorithms</a></li> <li><a href="/wiki/Algorithmic_efficiency" title="Algorithmic efficiency">Algorithmic efficiency</a></li> <li><a href="/wiki/Randomized_algorithm" title="Randomized algorithm">Randomized algorithm</a></li> <li><a href="/wiki/Computational_geometry" title="Computational geometry">Computational geometry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mathematics of <a href="/wiki/Computing" title="Computing">computing</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Discrete_mathematics" title="Discrete mathematics">Discrete mathematics</a></li> <li><a href="/wiki/Probability" title="Probability">Probability</a></li> <li><a href="/wiki/Statistics" title="Statistics">Statistics</a></li> <li><a href="/wiki/Mathematical_software" title="Mathematical software">Mathematical software</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Mathematical_analysis" title="Mathematical analysis">Mathematical analysis</a></li> <li><a href="/wiki/Numerical_analysis" title="Numerical analysis">Numerical analysis</a></li> <li><a href="/wiki/Theoretical_computer_science" title="Theoretical computer science">Theoretical computer science</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Information_system" title="Information system">Information systems</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Database" title="Database">Database management system</a></li> <li><a href="/wiki/Computer_data_storage" title="Computer data storage">Information storage systems</a></li> <li><a href="/wiki/Enterprise_information_system" title="Enterprise information system">Enterprise information system</a></li> <li><a href="/wiki/Social_software" title="Social software">Social information systems</a></li> <li><a href="/wiki/Geographic_information_system" title="Geographic information system">Geographic information system</a></li> <li><a href="/wiki/Decision_support_system" title="Decision support system">Decision support system</a></li> <li><a href="/wiki/Process_control" class="mw-redirect" title="Process control">Process control system</a></li> <li><a href="/wiki/Multimedia_database" title="Multimedia database">Multimedia information system</a></li> <li><a href="/wiki/Data_mining" title="Data mining">Data mining</a></li> <li><a href="/wiki/Digital_library" title="Digital library">Digital library</a></li> <li><a href="/wiki/Computing_platform" title="Computing platform">Computing platform</a></li> <li><a href="/wiki/Digital_marketing" title="Digital marketing">Digital marketing</a></li> <li><a href="/wiki/World_Wide_Web" title="World Wide Web">World Wide Web</a></li> <li><a href="/wiki/Information_retrieval" title="Information retrieval">Information retrieval</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computer_security" title="Computer security">Security</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cryptography" title="Cryptography">Cryptography</a></li> <li><a href="/wiki/Formal_methods" title="Formal methods">Formal methods</a></li> <li><a href="/wiki/Security_hacker" title="Security hacker">Security hacker</a></li> <li><a href="/wiki/Security_service_(telecommunication)" title="Security service (telecommunication)">Security services</a></li> <li><a href="/wiki/Intrusion_detection_system" title="Intrusion detection system">Intrusion detection system</a></li> <li><a href="/wiki/Hardware_security" title="Hardware security">Hardware security</a></li> <li><a href="/wiki/Network_security" title="Network security">Network security</a></li> <li><a href="/wiki/Information_security" 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