{"id":110073,"date":"2011-11-07T00:00:00","date_gmt":"2011-11-07T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/developments-in-maximum-entropy-approximants-and-application-to-phase-field-models\/"},"modified":"2011-11-07T00:00:00","modified_gmt":"2011-11-07T00:00:00","slug":"developments-in-maximum-entropy-approximants-and-application-to-phase-field-models","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/analisis-numerico\/developments-in-maximum-entropy-approximants-and-application-to-phase-field-models\/","title":{"rendered":"Developments in maximum entropy approximants and application to phase field models"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Adrian Martin Rosolen <\/strong><\/h2>\n<p>Los aproximantes de m\u00e1xima entrop\u00eda local pertenecen a la familia de m\u00e9todos sin malla, son \u00f3ptimos desde el punto de vista de teor\u00eda de la informaci\u00f3n, y se caracterizan por la no negatividad y suavidad de las funciones de forma. Este car\u00e1cter no negativo unido a la capacidad de reproducir en forma exacta funciones afines dota a los esquemas de aproximaci\u00f3n con una estructura propia de geometr\u00eda convexa. Los aproximantes presentan tambi\u00e9n ciertas ventajas en comparaci\u00f3n a otros m\u00e9todos sin malla, como ser la posibilidad de imponer directamente condiciones de contorno de dirichlet, la propiedad de variaci\u00f3n decreciente, y la ausencia de oscilaciones, que introducen dificultades en la integraci\u00f3n num\u00e9rica. En esta tesis se presentan nuevos desarrollos para la familia de aproximantes de m\u00e1xima entrop\u00eda. Adem\u00e1s, se propone un m\u00e9todo para resolver ecuaciones en derivadas parciales de cuarto orden que modelan la mec\u00e1nica de biomembranas a trav\u00e9s de una aproximaci\u00f3n de campo de fase. a continuaci\u00f3n se enumeran las contribuciones m\u00e1s significativas de esta tesis. En primer lugar, se propone un m\u00e9todo racional para determinar el tama\u00f1o de soporte \u00f3ptimo de las funciones de forma de m\u00e1xima entrop\u00eda local. Dicho m\u00e9todo est\u00e1 basado en conceptos de adaptividad variacional y es aplicable a problemas modelados con ecuaciones diferenciales obtenidas a partir de un principio de m\u00ednimo. En segundo lugar, se formula un esquema de m\u00e1xima entrop\u00eda no negativo de segundo order que siempre satisface las condiciones de factibilidad. Este nuevo esquema permite generar funciones de forma para distribuciones de puntos no estucturadas y no uniformes. En tercer lugar, se propone un esquema de aproximaci\u00f3n que combina el an\u00e1lisis isogeom\u00e9trico y los aproximantes de m\u00e1xima entrop\u00eda local. Este nuevo esquema re\u00fane las mejores caracter\u00edsticas de ambos m\u00e9todos: la alta fidelidad para representar el borde del dominio (geometr\u00eda de cad exacta) propia del an\u00e1lisis isogeom\u00e9trico, y la facilidad para discretizar volum\u00e9tricamente con distribuciones de puntos considerando posible refinamiento local. En \u00faltimo lugar, se presenta una estrategia adaptativa para calcular soluciones num\u00e9ricas de un modelo de campo de fase de cuarto orden que modela la mec\u00e1nica de biomembranas. La suavidad de los aproximantes de m\u00e1xima entrop\u00eda local, su monotonicidad, y su habilidad para tratar distribuciones de puntos no uniformes permite discretizar el problema con el m\u00e9todo de galerkin y resolver con precisi\u00f3n los cambios bruscos de frente generados por el modelo de campo de fase.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Developments in maximum entropy approximants and application to phase field models<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Developments in maximum entropy approximants and application to phase field models <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Adrian Martin Rosolen <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de catalunya<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 11\/07\/2011<\/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>Marino Arroyo Balaguer<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Antonio Huerta cerezuela <\/li>\n<li>timon Rabczuk (vocal)<\/li>\n<li>h\u00e9ctor G\u00f3mez d\u00edaz (vocal)<\/li>\n<li>elias Cueto prendes (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Adrian Martin Rosolen Los aproximantes de m\u00e1xima entrop\u00eda local pertenecen a la familia de m\u00e9todos sin malla, [&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 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