{"id":262,"date":"2016-06-17T07:10:10","date_gmt":"2016-06-17T07:10:10","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/?p=262"},"modified":"2016-06-17T07:10:10","modified_gmt":"2016-06-17T07:10:10","slug":"a-phase-field-model-for-willmores-energy-with-topological-constraint","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/a-phase-field-model-for-willmores-energy-with-topological-constraint\/","title":{"rendered":"A phase field model for Willmore\u2019s energy with topological constraint"},"content":{"rendered":"<p><em>Patrick Dondl (Freiburg, Germany)<\/em><\/p>\n<p>We consider the problem of minimizing Willmore\u2019s energy on confined and connected surfaces with prescribed surface area. To this end, we approximate the surface by a level set function u admitting the value +1 on the inside of the surface and -1 on its outside. The confinement of the surface is now simply given by the domain of definition of u. A diffuse interface approximation for the area functional, as well as for Willmore\u2019s energy are well known. We address the main difficulty, namely the topological constraint of connectedness by a penalization of a geodesic distance which is chosen to be sensitive to connected components of the phase field level sets and provide a proof of Gamma-convergence of our model to the sharp interface limit. Furthermore, we show some numerical results. This is joint work with Stephan Wojtowytsch (Durham University) and Antoine Lemenant (Universit Paris 7).<\/p>\n<p><a href=\"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/programme\/\">Back to Programme<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Patrick Dondl (Freiburg, Germany) We consider the problem of minimizing Willmore\u2019s energy on confined and connected surfaces with prescribed surface area. To this end, we approximate the surface by a level set function u admitting the value +1 on the inside of the surface and -1 on its outside. The confinement of the surface is &hellip; <a href=\"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/a-phase-field-model-for-willmores-energy-with-topological-constraint\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">A phase field model for Willmore\u2019s energy with topological constraint<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-262","post","type-post","status-publish","format-standard","hentry","category-abstracts"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts\/262","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/comments?post=262"}],"version-history":[{"count":0,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts\/262\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/media?parent=262"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/categories?post=262"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/tags?post=262"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}