{"id":112,"date":"2016-04-14T13:28:36","date_gmt":"2016-04-14T13:28:36","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/swngsn\/?p=112"},"modified":"2016-04-14T13:28:36","modified_gmt":"2016-04-14T13:28:36","slug":"entropic-gradient-flow-formulation-for-non-linear-diffusion-marios-stamatakis-bath","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/2016\/04\/14\/entropic-gradient-flow-formulation-for-non-linear-diffusion-marios-stamatakis-bath\/","title":{"rendered":"Entropic gradient flow formulation for non-linear diffusion, Marios Stamatakis (Bath)"},"content":{"rendered":"<div class=\"page\" title=\"Page 1\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p>Nonlinear diffusion \u2202t\u03c1 = \u2206(\u03a6(\u03c1)) is considered as the hydrodynamic limit of the zero- range process. It is shown that for suitable choices of \u03a6, a metric can be defined with respect to which the non-linear diffusion is the gradient flow of the thermodynamic entropy of the zero-range process. Hence we call this metric the thermodynamic metric. This exhibits the thermodynamic entropy as a Lyapunov functional. The thermodynamic metric is also linked to the large deviation principle for the hydrodynamic limit of the underlying zero range process<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page\" title=\"Page 2\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Nonlinear diffusion \u2202t\u03c1 = \u2206(\u03a6(\u03c1)) is considered as the hydrodynamic limit of the zero- range process. It is shown that for suitable choices of \u03a6, a metric can be defined with respect to which the non-linear diffusion is the gradient flow of the thermodynamic entropy of the zero-range process. Hence we call this metric the\u2026 <span class=\"read-more\"><a href=\"https:\/\/sites.maths.cf.ac.uk\/swngsn\/2016\/04\/14\/entropic-gradient-flow-formulation-for-non-linear-diffusion-marios-stamatakis-bath\/\">Read More &raquo;<\/a><\/span><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-112","post","type-post","status-publish","format-standard","hentry","category-abstracts"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts\/112","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/comments?post=112"}],"version-history":[{"count":0,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts\/112\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/media?parent=112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/categories?post=112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/tags?post=112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}