{"id":81583,"date":"1999-10-12T00:00:00","date_gmt":"1999-10-12T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/mathematical-analisis-of-relaxation-and-flow-near-boundaries-in-nematic-liquid-crystals\/"},"modified":"1999-10-12T00:00:00","modified_gmt":"1999-10-12T00:00:00","slug":"mathematical-analisis-of-relaxation-and-flow-near-boundaries-in-nematic-liquid-crystals","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/fisica\/mathematical-analisis-of-relaxation-and-flow-near-boundaries-in-nematic-liquid-crystals\/","title":{"rendered":"Mathematical analisis of relaxation and flow near boundaries in nematic liquid crystals"},"content":{"rendered":"<h2>Tesis doctoral de <strong>  Diez Casas Marta M. <\/strong><\/h2>\n<p>En este trabajo de investigaci\u00f3n se hace una an\u00e1lisis matematico de comportamiento dinamico de los cristales liquidos de tipo nem\u00e1tico. Las ecuaciones que definen el comportamiento de estos cristales -las ecuaciones de equilibrio junto con las ecuaciones constitutivas cuando los efectos t\u00e9rminos se consideran despreciables- se resuelven para distintas condiciones iniciales y de contorno, usando diversas t\u00e9cnicas matem\u00e1ticas como an\u00e1lisis de perturbaci\u00f3n singular, desarrollos asint\u00f3ticos, principios variacionales y principios de m\u00e1ximo y minimo para ecuaciones diferenciales en derivadas parciales.  partiendo de la teor\u00eda del continuo propuesta por ericksen y leslie para describir el comportamiento din\u00e1mico de los cristales l\u00edquidos de tipo nem\u00e1tico, se estudia el cambio de orientaci\u00f3n y flujo de un cristal nematico en las proximidades de un substrato r\u00edgido. Se consideran situaciones en las que la superficie del substrato recibe un tratamiento especial para que las mol\u00e9culas del cristal en contacto con \u00e9l tengan una orientaci\u00f3n distinta a la que tienen inicialmente en el resto del fluido. Se observa que, cuando el campo electromagn\u00e9tico que manten\u00eda la orientaci\u00f3n inicial de las moleculas del cristal se desconecta, la condici\u00f3n de contorno en la superficie del substrato se difunde en el resto de la masa del cristal y por tanto, las mol\u00e9culas tienden a orientarse con el substrato. Es m\u00e1s, cuando la inercia se desprecia, el angulo polar que da la orientaci\u00f3n de las mol\u00e9culas satisface una ecuaci\u00f3n de difusi\u00f3n. La aplicaci\u00f3n de un principio de m\u00e1ximo y minimo variacional permite acotar la soluci\u00f3n de esta ecuaci\u00f3n. la introducci\u00f3n de la inercia, necesaria para satisfacer la condici\u00f3n inicial de reposo, se realiza mediante un metodo de perturbacion singular. Se dan resultados para los casos de no deslizamiento y de deslizamiento perfecto mol\u00e9culas del cristal en contacto con el substrato r\u00edgido.  por otra p<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Mathematical analisis of relaxation and flow near boundaries in nematic liquid crystals<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Mathematical analisis of relaxation and flow near boundaries in nematic liquid crystals <\/li>\n<li><strong>Autor:<\/strong>\u00a0  Diez Casas Marta M. <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Navarra<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 10\/12\/1999<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Colin Atkinson<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: javier Gil sevillano <\/li>\n<li>lain Steward (vocal)<\/li>\n<li>frank Leppington (vocal)<\/li>\n<li>Jos\u00e9 Manuel Martinez esnaola (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Diez Casas Marta M. En este trabajo de investigaci\u00f3n se hace una an\u00e1lisis matematico de comportamiento dinamico [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[199,202,28680,17749],"tags":[61036,174014,174016,17773,32035,174015],"class_list":["post-81583","post","type-post","status-publish","format-standard","hentry","category-fisica","category-mecanica","category-mecanica-de-medios-continuos","category-navarra","tag-colin-atkinson","tag-diez-casas-marta-m","tag-frank-leppington","tag-javier-gil-sevillano","tag-jose-manuel-Martinez-esnaola","tag-lain-steward"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/81583","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=81583"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/81583\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=81583"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=81583"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=81583"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}