{"id":419,"date":"2016-06-17T06:55:10","date_gmt":"2016-06-17T06:55:10","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/?p=419"},"modified":"2016-06-17T06:55:10","modified_gmt":"2016-06-17T06:55:10","slug":"uniaxial-versus-biaxial-character-of-landau-de-gennes-minimizers-in-three-dimensions","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/uniaxial-versus-biaxial-character-of-landau-de-gennes-minimizers-in-three-dimensions\/","title":{"rendered":"Uniaxial versus Biaxial Character of Landau-de Gennes Minimizers in Three Dimensions"},"content":{"rendered":"<p><em>Apala Majumdar (Bath, UK)<\/em><\/p>\n<p>We study global minimizers of the Landau-de Gennes energy functional for nematic liquid crystals, on arbitrary three-dimensional simply connected geometries with topologically non-trivial and physically relevant Dirichlet boundary conditions. Our results are speci\ufb01c to an asymptotic limit defined in terms of a re-scaled reduced temperature, t. We prove (i) that (re-scaled) global LdG minimizers converge uniformly to a (minimizing) limiting harmonic map, away from the singular set of the limiting map; (ii) we have points of maximal biaxiality and uniaxiality near each singular point of the limiting map (this improves recent results of Contreras and Lamy); (iii) estimates for the size of \u201cstrongly biaxial\u201d regions in terms of the reduced temperature t. This is joint work with Duvan Henao and Adriano Pisante.<\/p>\n<p><a href=\"http:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/programme\/\">Back to Programme<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Apala Majumdar (Bath, UK) We study global minimizers of the Landau-de Gennes energy functional for nematic liquid crystals, on arbitrary three-dimensional simply connected geometries with topologically non-trivial and physically relevant Dirichlet boundary conditions. Our results are speci\ufb01c to an asymptotic limit defined in terms of a re-scaled reduced temperature, t. We prove (i) that (re-scaled) &hellip; <a href=\"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/2016\/06\/17\/uniaxial-versus-biaxial-character-of-landau-de-gennes-minimizers-in-three-dimensions\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Uniaxial versus Biaxial Character of Landau-de Gennes Minimizers in Three Dimensions<\/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-419","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\/419","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=419"}],"version-history":[{"count":0,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/posts\/419\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/media?parent=419"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/categories?post=419"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/ntnlpde16\/wp-json\/wp\/v2\/tags?post=419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}