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class="label">Followers</p><p class="data">68</p></div></a><a><div class="stat-container js-profile-followees" data-broccoli-component="user-info.followees-count" data-click-track="profile-expand-user-info-following"><p class="label">Following</p><p class="data">0</p></div></a><a><div class="stat-container js-profile-coauthors" data-broccoli-component="user-info.coauthors-count" data-click-track="profile-expand-user-info-coauthors"><p class="label">Co-authors</p><p class="data">9</p></div></a><span><div class="stat-container"><p class="label"><span class="js-profile-total-view-text">Public Views</span></p><p class="data"><span class="js-profile-view-count"></span></p></div></span></div><div class="user-bio-container"><div class="profile-bio fake-truncate js-profile-about" style="margin: 0px;">https://www.researchgate.net/profile/Alexander-Balankin<br /><div class="js-profile-less-about u-linkUnstyled u-tcGrayDarker u-textDecorationUnderline u-displayNone">less</div></div></div><div class="ri-section"><div class="ri-section-header"><span>Interests</span></div><div class="ri-tags-container"><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="31879133" href="https://www.academia.edu/Documents/in/Leer_y_caminar_en_la_naturaleza"><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://independent.academia.edu/AlexanderBalankin","location":"/AlexanderBalankin","scheme":"https","host":"independent.academia.edu","port":null,"pathname":"/AlexanderBalankin","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Leer y caminar en la naturaleza"]}" data-trace="false" data-dom-id="Pill-react-component-80af5087-962f-4ee6-9197-f7e5acb136e6"></div> <div 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href="https://www.academia.edu/124810902/Effect_of_pore_closing_dynamics_on_high_speed_densification_of_powder_material"><img alt="Research paper thumbnail of Effect of pore closing dynamics on high-speed densification of powder material" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/124810902/Effect_of_pore_closing_dynamics_on_high_speed_densification_of_powder_material">Effect of pore closing dynamics on high-speed densification of powder material</a></div><div class="wp-workCard_item"><span>Combustion, Explosion, and Shock Waves</span><span>, 1985</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b84ad85fc94a9dd40111d45c9c9654e1" 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href="https://www.academia.edu/122161944/Reply_to_Comment_on_Hydrodynamics_of_fractal_continuum_flow_and_Map_of_fluid_flow_in_fractal_porous_medium_into_fractal_continuum_flow_"><img alt="Research paper thumbnail of Reply to “Comment on ‘Hydrodynamics of fractal continuum flow’ and ‘Map of fluid flow in fractal porous medium into fractal continuum flow’ ”" class="work-thumbnail" src="https://attachments.academia-assets.com/116912483/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161944/Reply_to_Comment_on_Hydrodynamics_of_fractal_continuum_flow_and_Map_of_fluid_flow_in_fractal_porous_medium_into_fractal_continuum_flow_">Reply to “Comment on ‘Hydrodynamics of fractal continuum flow’ and ‘Map of fluid flow in fractal porous medium into fractal continuum flow’ ”</a></div><div class="wp-workCard_item"><span>Physical Review E</span><span>, Nov 21, 2013</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1eef6178fe351f092fd2d78f4884a3aa" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116912483,"asset_id":122161944,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116912483/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161944"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span 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WowProfile.WorkStripView({ el: this, workJSON: {"id":122161944,"title":"Reply to “Comment on ‘Hydrodynamics of fractal continuum flow’ and ‘Map of fluid flow in fractal porous medium into fractal continuum flow’ ”","translated_title":"","metadata":{"publisher":"American Physical Society","grobid_abstract":"The aim of this Reply is to elucidate the difference between the fractal continuum models used in the preceding Comment and the models of fractal continuum flow which were put forward in our previous articles [Phys. Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically, inconsistencies in the definitions of the fractal derivative, the Jacobian of transformation, the displacement vector, and angular momentum are revealed. The proper forms of the Reynolds' transport theorem and angular momentum principle for the fractal continuum are reaffirmed in a more illustrative manner. Consequently, we emphasize that in the absence of any internal angular momentum, body couples, and couple stresses, the Cauchy stress tensor in the fractal continuum should be symmetric. Furthermore, we stress that the approach based on the Cartesian product measured and used in the preceding Comment cannot be employed to study the path-connected fractals, such as a flow in a fractally permeable medium. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161943"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122161943/Stresses_and_strains_in_a_deformable_fractal_medium_and_in_its_fractal_continuum_model"><img alt="Research paper thumbnail of Stresses and strains in a deformable fractal medium and in its fractal continuum model" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161943/Stresses_and_strains_in_a_deformable_fractal_medium_and_in_its_fractal_continuum_model">Stresses and strains in a deformable fractal medium and in its fractal continuum model</a></div><div class="wp-workCard_item"><span>Physics Letters</span><span>, Nov 1, 2013</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT The model of fractal continuum accounting the topological, metric, and dynamic propertie...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT The model of fractal continuum accounting the topological, metric, and dynamic properties of deformable physical fractal medium is suggested. The kinematics of fractal continuum deformation is developed. The corresponding geometric interpretations are provided. The concept of stresses in the fractal continuum is defined. The conservation of linear and angular momentums is established. 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In the present study, the principal results are obtained in the context of a general synergetic approach, and explicit expressions for parameters are derived by treating thermodynamic density fluctuations as quasi-particles with a finite correlation radius in an inhomogeneous field of mechanical stresses. The need for a revision of certain theoretical concepts associated with the penetration of a cumulative jet is emphasized.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161942"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161942"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161942; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122161942]").text(description); $(".js-view-count[data-work-id=122161942]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122161942; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122161942']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122161942, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=122161942]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122161942,"title":"Physical aspects of the cumulation effect","translated_title":"","metadata":{"abstract":"A new approach to the problem of axisymmetric cumulation is proposed which is based on the kinetic concept of the physicomechanical behavior of solids. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161937"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122161937/Effective_degrees_of_freedom_of_a_random_walk_on_a_fractal"><img alt="Research paper thumbnail of Effective degrees of freedom of a random walk on a fractal" class="work-thumbnail" src="https://attachments.academia-assets.com/116882925/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161937/Effective_degrees_of_freedom_of_a_random_walk_on_a_fractal">Effective degrees of freedom of a random walk on a fractal</a></div><div class="wp-workCard_item"><span>Physical Review E</span><span>, Dec 29, 2015</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9295967435a8145275b09d7179a07bd8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116882925,"asset_id":122161937,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116882925/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161937"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161937"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161937; 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This allows us to define the fractional dimensional space allied to the fractal as the ν-dimensional space F ν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in F ν is inferred. The Laplacian operator in F ν is constructed. This allows us to map physical problems on fractals into the corresponding problems in F ν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.","publication_date":{"day":29,"month":12,"year":2015,"errors":{}},"publication_name":"Physical Review E","grobid_abstract_attachment_id":116882925},"translated_abstract":null,"internal_url":"https://www.academia.edu/122161937/Effective_degrees_of_freedom_of_a_random_walk_on_a_fractal","translated_internal_url":"","created_at":"2024-07-18T12:39:20.164-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":31879133,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":116882925,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/116882925/thumbnails/1.jpg","file_name":"fulltext.pdf","download_url":"https://www.academia.edu/attachments/116882925/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Effective_degrees_of_freedom_of_a_random.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/116882925/fulltext-libre.pdf?1721333800=\u0026response-content-disposition=attachment%3B+filename%3DEffective_degrees_of_freedom_of_a_random.pdf\u0026Expires=1733020772\u0026Signature=e8MqFN8rKKyX~OhQrAHIyvpVnlAy9GIyr5R1bHCCCHudICrqqYkY3OOgq9T3qGbWZ1IRDdT600Q1kxtrdHwvLvk~ribSLy8InJbYU69pcHuzg5gwKwRUS0gMB7ao5IhDWTTu0e7W3tmV~vXBMnLgDu4h0JuupJcZQymDSlq72hHF~UAM7-XFzxjcj5lZZrHl2CpEocIx9f6oMwgqrfHAxjBGsT~kqX7L5kzaMh5Qil2c-OnpvrGFKzalV2oB4d4a~t3Qx9ETyc6Jup3uokXoK4CKvcAh8AUOFY7rlTAymL3PSaTaKeHzemAv4~iHMDcKriSB0QjFqTwcGhYImALZmQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Effective_degrees_of_freedom_of_a_random_walk_on_a_fractal","translated_slug":"","page_count":11,"language":"en","content_type":"Work","owner":{"id":31879133,"first_name":"Alexander","middle_initials":null,"last_name":"Balankin","page_name":"AlexanderBalankin","domain_name":"independent","created_at":"2015-06-04T13:48:09.347-07:00","display_name":"Alexander Balankin","url":"https://independent.academia.edu/AlexanderBalankin"},"attachments":[{"id":116882925,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/116882925/thumbnails/1.jpg","file_name":"fulltext.pdf","download_url":"https://www.academia.edu/attachments/116882925/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Effective_degrees_of_freedom_of_a_random.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/116882925/fulltext-libre.pdf?1721333800=\u0026response-content-disposition=attachment%3B+filename%3DEffective_degrees_of_freedom_of_a_random.pdf\u0026Expires=1733020772\u0026Signature=e8MqFN8rKKyX~OhQrAHIyvpVnlAy9GIyr5R1bHCCCHudICrqqYkY3OOgq9T3qGbWZ1IRDdT600Q1kxtrdHwvLvk~ribSLy8InJbYU69pcHuzg5gwKwRUS0gMB7ao5IhDWTTu0e7W3tmV~vXBMnLgDu4h0JuupJcZQymDSlq72hHF~UAM7-XFzxjcj5lZZrHl2CpEocIx9f6oMwgqrfHAxjBGsT~kqX7L5kzaMh5Qil2c-OnpvrGFKzalV2oB4d4a~t3Qx9ETyc6Jup3uokXoK4CKvcAh8AUOFY7rlTAymL3PSaTaKeHzemAv4~iHMDcKriSB0QjFqTwcGhYImALZmQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering"},{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":16460,"name":"Statistical Physics","url":"https://www.academia.edu/Documents/in/Statistical_Physics"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine"},{"id":78086,"name":"Random Walk","url":"https://www.academia.edu/Documents/in/Random_Walk"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":172625,"name":"Fractal","url":"https://www.academia.edu/Documents/in/Fractal"}],"urls":[{"id":43582976,"url":"https://doi.org/10.1103/physreve.92.062146"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161936"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122161936/Map_of_fluid_flow_in_fractal_porous_medium_into_fractal_continuum_flow"><img alt="Research paper thumbnail of Map of fluid flow in fractal porous medium into fractal continuum flow" class="work-thumbnail" src="https://attachments.academia-assets.com/116904911/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161936/Map_of_fluid_flow_in_fractal_porous_medium_into_fractal_continuum_flow">Map of fluid flow in fractal porous medium into fractal continuum flow</a></div><div class="wp-workCard_item"><span>Physical Review E</span><span>, May 30, 2012</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="51a4ebe10d9b0c2b6878829b04337b22" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116904911,"asset_id":122161936,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116904911/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161936"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161936"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161936; 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Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d s is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.","publication_date":{"day":30,"month":5,"year":2012,"errors":{}},"publication_name":"Physical Review E","grobid_abstract_attachment_id":116904911},"translated_abstract":null,"internal_url":"https://www.academia.edu/122161936/Map_of_fluid_flow_in_fractal_porous_medium_into_fractal_continuum_flow","translated_internal_url":"","created_at":"2024-07-18T12:39:19.767-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":31879133,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":116904911,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/116904911/thumbnails/1.jpg","file_name":"fulltext.pdf","download_url":"https://www.academia.edu/attachments/116904911/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Map_of_fluid_flow_in_fractal_porous_medi.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/116904911/fulltext-libre.pdf?1721424170=\u0026response-content-disposition=attachment%3B+filename%3DMap_of_fluid_flow_in_fractal_porous_medi.pdf\u0026Expires=1733020772\u0026Signature=SjudrfFuqLT8Mi4nHpsGDXPXUO~rkzho-isZPxDO9-amc6agvLANOBXXsZVrk~YEV9I7D02tgQnQQK3ai3P~4QcCaSvygq6b54JuQhLjDB7ROTGZ~RT7pIwD61ANUhBTHfKbQbXgurvU2ISdXoRiMJS-NNgNJIHHGI4MaBUfpgNgnWXB036YWeagAGpG3N8oYjcHCUYzp30lWXdGnAA09u5N4Rfmlkg2CXDI5Nb17C9l-TTm2IoSNsNZdkEoF5lxneX5U~Lzzm5JypOp4FdEeGGqmIQJnmr-x3FFJfCTWh7uEeSjzzpIzULlPJi2P3Ijm4euMnjo5OXkgHoLj6pHnA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Map_of_fluid_flow_in_fractal_porous_medium_into_fractal_continuum_flow","translated_slug":"","page_count":21,"language":"en","content_type":"Work","owner":{"id":31879133,"first_name":"Alexander","middle_initials":null,"last_name":"Balankin","page_name":"AlexanderBalankin","domain_name":"independent","created_at":"2015-06-04T13:48:09.347-07:00","display_name":"Alexander Balankin","url":"https://independent.academia.edu/AlexanderBalankin"},"attachments":[{"id":116904911,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/116904911/thumbnails/1.jpg","file_name":"fulltext.pdf","download_url":"https://www.academia.edu/attachments/116904911/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Map_of_fluid_flow_in_fractal_porous_medi.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/116904911/fulltext-libre.pdf?1721424170=\u0026response-content-disposition=attachment%3B+filename%3DMap_of_fluid_flow_in_fractal_porous_medi.pdf\u0026Expires=1733020772\u0026Signature=SjudrfFuqLT8Mi4nHpsGDXPXUO~rkzho-isZPxDO9-amc6agvLANOBXXsZVrk~YEV9I7D02tgQnQQK3ai3P~4QcCaSvygq6b54JuQhLjDB7ROTGZ~RT7pIwD61ANUhBTHfKbQbXgurvU2ISdXoRiMJS-NNgNJIHHGI4MaBUfpgNgnWXB036YWeagAGpG3N8oYjcHCUYzp30lWXdGnAA09u5N4Rfmlkg2CXDI5Nb17C9l-TTm2IoSNsNZdkEoF5lxneX5U~Lzzm5JypOp4FdEeGGqmIQJnmr-x3FFJfCTWh7uEeSjzzpIzULlPJi2P3Ijm4euMnjo5OXkgHoLj6pHnA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering"},{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":172625,"name":"Fractal","url":"https://www.academia.edu/Documents/in/Fractal"},{"id":890611,"name":"Fractal Dimension","url":"https://www.academia.edu/Documents/in/Fractal_Dimension"}],"urls":[{"id":43582975,"url":"https://doi.org/10.1103/physreve.85.056314"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161935"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122161935/Fractal_fracture_mechanics_A_review"><img alt="Research paper thumbnail of Fractal fracture mechanics—A review" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161935/Fractal_fracture_mechanics_A_review">Fractal fracture mechanics—A review</a></div><div class="wp-workCard_item"><span>Engineering Fracture Mechanics</span><span>, Aug 1, 1995</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The revolution in geometry, which has recently created the notion of the fractional dimension of ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The revolution in geometry, which has recently created the notion of the fractional dimension of real world bodies and has formed fractal geometry, has substantially influenced fracture science. An experimentally measured crack in real materials has appeared to be substantially a fractal, that is, a geometrical object of fractional dimension. In the present paper, an attempt has been undertaken to</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161935"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161935"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161935; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122161935]").text(description); $(".js-view-count[data-work-id=122161935]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122161935; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122161935']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122161935, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=122161935]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122161935,"title":"Fractal fracture mechanics—A review","translated_title":"","metadata":{"abstract":"The revolution in geometry, which has recently created the notion of the fractional dimension of real world bodies and has formed fractal geometry, has substantially influenced fracture science. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161934"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122161934/Scale_effects_in_the_impact_fracture_and_explosion_kinetics_of_solids_and_the_problem_of_strongly_nonequilibrium_process_modeling"><img alt="Research paper thumbnail of Scale effects in the impact fracture and explosion kinetics of solids and the problem of strongly nonequilibrium process modeling" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161934/Scale_effects_in_the_impact_fracture_and_explosion_kinetics_of_solids_and_the_problem_of_strongly_nonequilibrium_process_modeling">Scale effects in the impact fracture and explosion kinetics of solids and the problem of strongly nonequilibrium process modeling</a></div><div class="wp-workCard_item"><span>Zhurnal Tekhnicheskoi Fiziki</span><span>, Dec 1, 1989</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161934"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161934"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161934; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122161934]").text(description); $(".js-view-count[data-work-id=122161934]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122161934; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122161934']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122161934, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161933"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122161933/Fractal_dynamics_of_deformable_media"><img alt="Research paper thumbnail of Fractal dynamics of deformable media" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161933/Fractal_dynamics_of_deformable_media">Fractal dynamics of deformable media</a></div><div class="wp-workCard_item"><span>Pisma v Zhurnal Tekhnischeskoi Fiziki</span><span>, Mar 1, 1991</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161933"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161933"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161933; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161932"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/122161932/Kinetic_fluctuation_nature_of_the_hydrodynamic_regime_of_the_high_rate_deformation_of_solids"><img alt="Research paper thumbnail of Kinetic (fluctuation) nature of the hydrodynamic regime of the high-rate deformation of solids" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/122161932/Kinetic_fluctuation_nature_of_the_hydrodynamic_regime_of_the_high_rate_deformation_of_solids">Kinetic (fluctuation) nature of the hydrodynamic regime of the high-rate deformation of solids</a></div><div class="wp-workCard_item"><span>Pisma v Zhurnal Tekhnischeskoi Fiziki</span><span>, Jul 1, 1988</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The hydrodynamic regime of deformation realized under high pressures and strain rates (e.g. explo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The hydrodynamic regime of deformation realized under high pressures and strain rates (e.g. explosive welding or cumulative jet formation) is described in terms of a model allowing for the dynamics of density fluctuations in the solid under deformation. The model proposed here is an extension of Zhurkov&#x27;s (1983) model to the case of a large deviation of the deformed solid from the thermodynamic equilibrium. In contrast to the thermal fluctuation theory of fracture, which considers spontaneous (thermal) density fluctuations only, the present model includes both spontaneous and induced density fluctuations.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161932"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161932"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161932; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122161932]").text(description); $(".js-view-count[data-work-id=122161932]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122161932; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122161932']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122161932, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=122161932]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122161932,"title":"Kinetic (fluctuation) nature of the hydrodynamic regime of the high-rate deformation of solids","translated_title":"","metadata":{"abstract":"The hydrodynamic regime of deformation realized under high pressures and strain rates (e.g. explosive welding or cumulative jet formation) is described in terms of a model allowing for the dynamics of density fluctuations in the solid under deformation. 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Doklady</span><span>, Feb 1, 1992</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161930"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161930"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161930; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122161930]").text(description); $(".js-view-count[data-work-id=122161930]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122161930; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122161930']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122161930, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=122161930]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122161930,"title":"Collective effects in the kinetics of metal fracture and spontaneous change in the fractal dimensionality of a dissipative structure during the viscobrittle transition","translated_title":"","metadata":{"publisher":"Springer Science+Business Media","publication_date":{"day":1,"month":2,"year":1992,"errors":{}},"publication_name":"Soviet physics. 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We can approximate this curve in two ways, with 1D gauge, or with uncertainty balls that give...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">... We can approximate this curve in two ways, with 1D gauge, or with uncertainty balls that give it a thickness. 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Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically, inconsistencies in the definitions of the fractal derivative, the Jacobian of transformation, the displacement vector, and angular momentum are revealed. The proper forms of the Reynolds' transport theorem and angular momentum principle for the fractal continuum are reaffirmed in a more illustrative manner. Consequently, we emphasize that in the absence of any internal angular momentum, body couples, and couple stresses, the Cauchy stress tensor in the fractal continuum should be symmetric. Furthermore, we stress that the approach based on the Cartesian product measured and used in the preceding Comment cannot be employed to study the path-connected fractals, such as a flow in a fractally permeable medium. 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The kinematics of fractal continuum deformation is developed. The corresponding geometric interpretations are provided. The concept of stresses in the fractal continuum is defined. The conservation of linear and angular momentums is established. 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In the present study, the principal results are obtained in the context of a general synergetic approach, and explicit expressions for parameters are derived by treating thermodynamic density fluctuations as quasi-particles with a finite correlation radius in an inhomogeneous field of mechanical stresses. The need for a revision of certain theoretical concepts associated with the penetration of a cumulative jet is emphasized.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161942"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161942"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161942; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122161942]").text(description); $(".js-view-count[data-work-id=122161942]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122161942; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122161942']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122161942, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=122161942]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122161942,"title":"Physical aspects of the cumulation effect","translated_title":"","metadata":{"abstract":"A new approach to the problem of axisymmetric cumulation is proposed which is based on the kinetic concept of the physicomechanical behavior of solids. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161937"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122161937/Effective_degrees_of_freedom_of_a_random_walk_on_a_fractal"><img alt="Research paper thumbnail of Effective degrees of freedom of a random walk on a fractal" class="work-thumbnail" src="https://attachments.academia-assets.com/116882925/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161937/Effective_degrees_of_freedom_of_a_random_walk_on_a_fractal">Effective degrees of freedom of a random walk on a fractal</a></div><div class="wp-workCard_item"><span>Physical Review E</span><span>, Dec 29, 2015</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9295967435a8145275b09d7179a07bd8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116882925,"asset_id":122161937,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116882925/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161937"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161937"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161937; 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This allows us to define the fractional dimensional space allied to the fractal as the ν-dimensional space F ν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in F ν is inferred. The Laplacian operator in F ν is constructed. This allows us to map physical problems on fractals into the corresponding problems in F ν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.","publication_date":{"day":29,"month":12,"year":2015,"errors":{}},"publication_name":"Physical Review E","grobid_abstract_attachment_id":116882925},"translated_abstract":null,"internal_url":"https://www.academia.edu/122161937/Effective_degrees_of_freedom_of_a_random_walk_on_a_fractal","translated_internal_url":"","created_at":"2024-07-18T12:39:20.164-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":31879133,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":116882925,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/116882925/thumbnails/1.jpg","file_name":"fulltext.pdf","download_url":"https://www.academia.edu/attachments/116882925/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Effective_degrees_of_freedom_of_a_random.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/116882925/fulltext-libre.pdf?1721333800=\u0026response-content-disposition=attachment%3B+filename%3DEffective_degrees_of_freedom_of_a_random.pdf\u0026Expires=1733020772\u0026Signature=e8MqFN8rKKyX~OhQrAHIyvpVnlAy9GIyr5R1bHCCCHudICrqqYkY3OOgq9T3qGbWZ1IRDdT600Q1kxtrdHwvLvk~ribSLy8InJbYU69pcHuzg5gwKwRUS0gMB7ao5IhDWTTu0e7W3tmV~vXBMnLgDu4h0JuupJcZQymDSlq72hHF~UAM7-XFzxjcj5lZZrHl2CpEocIx9f6oMwgqrfHAxjBGsT~kqX7L5kzaMh5Qil2c-OnpvrGFKzalV2oB4d4a~t3Qx9ETyc6Jup3uokXoK4CKvcAh8AUOFY7rlTAymL3PSaTaKeHzemAv4~iHMDcKriSB0QjFqTwcGhYImALZmQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Effective_degrees_of_freedom_of_a_random_walk_on_a_fractal","translated_slug":"","page_count":11,"language":"en","content_type":"Work","owner":{"id":31879133,"first_name":"Alexander","middle_initials":null,"last_name":"Balankin","page_name":"AlexanderBalankin","domain_name":"independent","created_at":"2015-06-04T13:48:09.347-07:00","display_name":"Alexander Balankin","url":"https://independent.academia.edu/AlexanderBalankin"},"attachments":[{"id":116882925,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/116882925/thumbnails/1.jpg","file_name":"fulltext.pdf","download_url":"https://www.academia.edu/attachments/116882925/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Effective_degrees_of_freedom_of_a_random.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/116882925/fulltext-libre.pdf?1721333800=\u0026response-content-disposition=attachment%3B+filename%3DEffective_degrees_of_freedom_of_a_random.pdf\u0026Expires=1733020772\u0026Signature=e8MqFN8rKKyX~OhQrAHIyvpVnlAy9GIyr5R1bHCCCHudICrqqYkY3OOgq9T3qGbWZ1IRDdT600Q1kxtrdHwvLvk~ribSLy8InJbYU69pcHuzg5gwKwRUS0gMB7ao5IhDWTTu0e7W3tmV~vXBMnLgDu4h0JuupJcZQymDSlq72hHF~UAM7-XFzxjcj5lZZrHl2CpEocIx9f6oMwgqrfHAxjBGsT~kqX7L5kzaMh5Qil2c-OnpvrGFKzalV2oB4d4a~t3Qx9ETyc6Jup3uokXoK4CKvcAh8AUOFY7rlTAymL3PSaTaKeHzemAv4~iHMDcKriSB0QjFqTwcGhYImALZmQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering"},{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":16460,"name":"Statistical Physics","url":"https://www.academia.edu/Documents/in/Statistical_Physics"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine"},{"id":78086,"name":"Random Walk","url":"https://www.academia.edu/Documents/in/Random_Walk"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":172625,"name":"Fractal","url":"https://www.academia.edu/Documents/in/Fractal"}],"urls":[{"id":43582976,"url":"https://doi.org/10.1103/physreve.92.062146"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161936"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122161936/Map_of_fluid_flow_in_fractal_porous_medium_into_fractal_continuum_flow"><img alt="Research paper thumbnail of Map of fluid flow in fractal porous medium into fractal continuum flow" class="work-thumbnail" src="https://attachments.academia-assets.com/116904911/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161936/Map_of_fluid_flow_in_fractal_porous_medium_into_fractal_continuum_flow">Map of fluid flow in fractal porous medium into fractal continuum flow</a></div><div class="wp-workCard_item"><span>Physical Review E</span><span>, May 30, 2012</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="51a4ebe10d9b0c2b6878829b04337b22" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":116904911,"asset_id":122161936,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/116904911/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161936"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161936"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161936; 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Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d s is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.","publication_date":{"day":30,"month":5,"year":2012,"errors":{}},"publication_name":"Physical Review E","grobid_abstract_attachment_id":116904911},"translated_abstract":null,"internal_url":"https://www.academia.edu/122161936/Map_of_fluid_flow_in_fractal_porous_medium_into_fractal_continuum_flow","translated_internal_url":"","created_at":"2024-07-18T12:39:19.767-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":31879133,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":116904911,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/116904911/thumbnails/1.jpg","file_name":"fulltext.pdf","download_url":"https://www.academia.edu/attachments/116904911/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Map_of_fluid_flow_in_fractal_porous_medi.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/116904911/fulltext-libre.pdf?1721424170=\u0026response-content-disposition=attachment%3B+filename%3DMap_of_fluid_flow_in_fractal_porous_medi.pdf\u0026Expires=1733020772\u0026Signature=SjudrfFuqLT8Mi4nHpsGDXPXUO~rkzho-isZPxDO9-amc6agvLANOBXXsZVrk~YEV9I7D02tgQnQQK3ai3P~4QcCaSvygq6b54JuQhLjDB7ROTGZ~RT7pIwD61ANUhBTHfKbQbXgurvU2ISdXoRiMJS-NNgNJIHHGI4MaBUfpgNgnWXB036YWeagAGpG3N8oYjcHCUYzp30lWXdGnAA09u5N4Rfmlkg2CXDI5Nb17C9l-TTm2IoSNsNZdkEoF5lxneX5U~Lzzm5JypOp4FdEeGGqmIQJnmr-x3FFJfCTWh7uEeSjzzpIzULlPJi2P3Ijm4euMnjo5OXkgHoLj6pHnA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Map_of_fluid_flow_in_fractal_porous_medium_into_fractal_continuum_flow","translated_slug":"","page_count":21,"language":"en","content_type":"Work","owner":{"id":31879133,"first_name":"Alexander","middle_initials":null,"last_name":"Balankin","page_name":"AlexanderBalankin","domain_name":"independent","created_at":"2015-06-04T13:48:09.347-07:00","display_name":"Alexander Balankin","url":"https://independent.academia.edu/AlexanderBalankin"},"attachments":[{"id":116904911,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/116904911/thumbnails/1.jpg","file_name":"fulltext.pdf","download_url":"https://www.academia.edu/attachments/116904911/download_file?st=MTczMzAzMTI3OSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Map_of_fluid_flow_in_fractal_porous_medi.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/116904911/fulltext-libre.pdf?1721424170=\u0026response-content-disposition=attachment%3B+filename%3DMap_of_fluid_flow_in_fractal_porous_medi.pdf\u0026Expires=1733020772\u0026Signature=SjudrfFuqLT8Mi4nHpsGDXPXUO~rkzho-isZPxDO9-amc6agvLANOBXXsZVrk~YEV9I7D02tgQnQQK3ai3P~4QcCaSvygq6b54JuQhLjDB7ROTGZ~RT7pIwD61ANUhBTHfKbQbXgurvU2ISdXoRiMJS-NNgNJIHHGI4MaBUfpgNgnWXB036YWeagAGpG3N8oYjcHCUYzp30lWXdGnAA09u5N4Rfmlkg2CXDI5Nb17C9l-TTm2IoSNsNZdkEoF5lxneX5U~Lzzm5JypOp4FdEeGGqmIQJnmr-x3FFJfCTWh7uEeSjzzpIzULlPJi2P3Ijm4euMnjo5OXkgHoLj6pHnA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering"},{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":172625,"name":"Fractal","url":"https://www.academia.edu/Documents/in/Fractal"},{"id":890611,"name":"Fractal Dimension","url":"https://www.academia.edu/Documents/in/Fractal_Dimension"}],"urls":[{"id":43582975,"url":"https://doi.org/10.1103/physreve.85.056314"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161935"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122161935/Fractal_fracture_mechanics_A_review"><img alt="Research paper thumbnail of Fractal fracture mechanics—A review" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161935/Fractal_fracture_mechanics_A_review">Fractal fracture mechanics—A review</a></div><div class="wp-workCard_item"><span>Engineering Fracture Mechanics</span><span>, Aug 1, 1995</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The revolution in geometry, which has recently created the notion of the fractional dimension of ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The revolution in geometry, which has recently created the notion of the fractional dimension of real world bodies and has formed fractal geometry, has substantially influenced fracture science. An experimentally measured crack in real materials has appeared to be substantially a fractal, that is, a geometrical object of fractional dimension. In the present paper, an attempt has been undertaken to</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161935"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161935"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161935; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122161935]").text(description); $(".js-view-count[data-work-id=122161935]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122161935; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122161935']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122161935, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=122161935]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122161935,"title":"Fractal fracture mechanics—A review","translated_title":"","metadata":{"abstract":"The revolution in geometry, which has recently created the notion of the fractional dimension of real world bodies and has formed fractal geometry, has substantially influenced fracture science. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161934"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122161934/Scale_effects_in_the_impact_fracture_and_explosion_kinetics_of_solids_and_the_problem_of_strongly_nonequilibrium_process_modeling"><img alt="Research paper thumbnail of Scale effects in the impact fracture and explosion kinetics of solids and the problem of strongly nonequilibrium process modeling" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161934/Scale_effects_in_the_impact_fracture_and_explosion_kinetics_of_solids_and_the_problem_of_strongly_nonequilibrium_process_modeling">Scale effects in the impact fracture and explosion kinetics of solids and the problem of strongly nonequilibrium process modeling</a></div><div class="wp-workCard_item"><span>Zhurnal Tekhnicheskoi Fiziki</span><span>, Dec 1, 1989</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161934"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161934"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161934; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122161934]").text(description); $(".js-view-count[data-work-id=122161934]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122161934; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122161934']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122161934, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161933"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122161933/Fractal_dynamics_of_deformable_media"><img alt="Research paper thumbnail of Fractal dynamics of deformable media" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122161933/Fractal_dynamics_of_deformable_media">Fractal dynamics of deformable media</a></div><div class="wp-workCard_item"><span>Pisma v Zhurnal Tekhnischeskoi Fiziki</span><span>, Mar 1, 1991</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161933"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161933"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161933; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122161932"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/122161932/Kinetic_fluctuation_nature_of_the_hydrodynamic_regime_of_the_high_rate_deformation_of_solids"><img alt="Research paper thumbnail of Kinetic (fluctuation) nature of the hydrodynamic regime of the high-rate deformation of solids" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/122161932/Kinetic_fluctuation_nature_of_the_hydrodynamic_regime_of_the_high_rate_deformation_of_solids">Kinetic (fluctuation) nature of the hydrodynamic regime of the high-rate deformation of solids</a></div><div class="wp-workCard_item"><span>Pisma v Zhurnal Tekhnischeskoi Fiziki</span><span>, Jul 1, 1988</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The hydrodynamic regime of deformation realized under high pressures and strain rates (e.g. explo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The hydrodynamic regime of deformation realized under high pressures and strain rates (e.g. explosive welding or cumulative jet formation) is described in terms of a model allowing for the dynamics of density fluctuations in the solid under deformation. The model proposed here is an extension of Zhurkov&#x27;s (1983) model to the case of a large deviation of the deformed solid from the thermodynamic equilibrium. In contrast to the thermal fluctuation theory of fracture, which considers spontaneous (thermal) density fluctuations only, the present model includes both spontaneous and induced density fluctuations.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161932"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161932"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161932; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122161932]").text(description); $(".js-view-count[data-work-id=122161932]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122161932; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122161932']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122161932, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=122161932]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122161932,"title":"Kinetic (fluctuation) nature of the hydrodynamic regime of the high-rate deformation of solids","translated_title":"","metadata":{"abstract":"The hydrodynamic regime of deformation realized under high pressures and strain rates (e.g. explosive welding or cumulative jet formation) is described in terms of a model allowing for the dynamics of density fluctuations in the solid under deformation. 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Doklady</span><span>, Feb 1, 1992</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122161930"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122161930"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122161930; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122161930]").text(description); $(".js-view-count[data-work-id=122161930]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122161930; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122161930']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122161930, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=122161930]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122161930,"title":"Collective effects in the kinetics of metal fracture and spontaneous change in the fractal dimensionality of a dissipative structure during the viscobrittle transition","translated_title":"","metadata":{"publisher":"Springer Science+Business Media","publication_date":{"day":1,"month":2,"year":1992,"errors":{}},"publication_name":"Soviet physics. 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We can approximate this curve in two ways, with 1D gauge, or with uncertainty balls that give...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">... We can approximate this curve in two ways, with 1D gauge, or with uncertainty balls that give it a thickness. 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