{"id":113414,"date":"2012-12-11T00:00:00","date_gmt":"2012-12-11T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/point-set-manifold-processing-for-computational-mechanics-thin-shells-reduced-order-modeling-cell-motility-and-molecular-conformations\/"},"modified":"2012-12-11T00:00:00","modified_gmt":"2012-12-11T00:00:00","slug":"point-set-manifold-processing-for-computational-mechanics-thin-shells-reduced-order-modeling-cell-motility-and-molecular-conformations","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/geometria-diferencial\/point-set-manifold-processing-for-computational-mechanics-thin-shells-reduced-order-modeling-cell-motility-and-molecular-conformations\/","title":{"rendered":"Point-set manifold processing for computational mechanics: thin shells, reduced order modeling, cell motility and molecular conformations"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Ra\u00fal Daniel Mill\u00e1n <\/strong><\/h2>\n<p>En diversas aplicaciones de inter\u00e9s pr\u00e1ctico se requieren realizar c\u00e1lculos sobre variedades suaves de peque\u00f1a dimensi\u00f3n, d, inmersas en espacios de gran dimensi\u00f3n, d. A menudo, no se posee una descripci\u00f3n suave de estas variedades, en su lugar estas son descriptas por un conjunto de puntos no estructurados en alta dimensi\u00f3n, lo que conlleva serias dificultades. En esta tesis se utilizan m\u00e9todos de aprendizaje estad\u00edstico y m\u00e9todos sin malla para construir una aproximaci\u00f3n continua de la variedad a trav\u00e9s del solapamiento de descripciones param\u00e9tricas suaves. Una ventaja inherente de esta aproximaci\u00f3n es el hecho de no utilizar una parametrizaci\u00f3n global, siendo tal aproximaci\u00f3n aplicable a variedades de cualquier g\u00e9nero y de geometr\u00eda compleja. La metodolog\u00eda combina cuatro ingredientes: (1) partici\u00f3n del conjunto de puntos en subregiones de topolog\u00eda simple, (2) detecci\u00f3n autom\u00e1tica de la estructura geom\u00e9trica que describe la variedad localmente, por medio de  t\u00e9cnicas no lineales de reducci\u00f3n de la dimensi\u00f3n, (3) parametrizaci\u00f3n local de la variedad utilizando aproximantes suaves sin malla (en particular m\u00e9todos de m\u00e1xima entrop\u00eda local), y (4) uni\u00f3n de las representaciones locales de la variedad por medio de la partici\u00f3n de la unidad.  La generalidad, precisi\u00f3n y flexibilidad de la metodolog\u00eda propuesta se ilustra a trav\u00e9s de cuatro problemas de distinta naturaleza. En primer lugar, se aplica la metodolog\u00eda en problemas de l\u00e1minas delgadas modeladas mediante la teor\u00eda de kirchhoff-love, (d=2, d=3). Se consideran problemas cl\u00e1sicos de l\u00e1minas lineales como as\u00ed tambi\u00e9n problemas no lineales, con los cuales se ilustra la habilidad del m\u00e9todo para manipular superficies descriptas por puntos que poseen gran complejidad geom\u00e9trica o una dif\u00edcil topolog\u00eda. En segundo lugar, el m\u00e9todo se aplica en la reducci\u00f3n no lineal de modelos. En particular, se considera el caso de grandes deformaciones elastodin\u00e1micas de un material neo-hookeano (d=2, d=10000), los resultados se comparan con los obtenidos por m\u00e9todos est\u00e1ndares basados en el an\u00e1lisis de componentes principales (pca, por sus siglas en ingl\u00e9s). El tercer problema se centra en el estudio de los mecanismos de locomoci\u00f3n de cuatro microorganismos, de la familia de euglenids. Esto se lleva a cabo por medio de un an\u00e1lisis cuantitativo de videos experimentales que describen los cambios de forma que realizan para nadar (d=1, d~30000). Finalmente, en el campo de din\u00e1mica molecular, se determina de forma autom\u00e1tica las variables colectivas que describen las conformaciones moleculares (d=1\u00c2\u00bf6, d~30, 1000), las cuales pueden ser empleadas para mejorar el muestreo y acelerar la din\u00e1mica molecular.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Point-set manifold processing for computational mechanics: thin shells, reduced order modeling, cell motility and molecular conformations<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Point-set manifold processing for computational mechanics: thin shells, reduced order modeling, cell motility and molecular conformations <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Ra\u00fal Daniel Mill\u00e1n <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de catalunya<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 12\/11\/2012<\/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>fehmi Cirak (vocal)<\/li>\n<li>  (vocal)<\/li>\n<li>  (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Ra\u00fal Daniel Mill\u00e1n En diversas aplicaciones de inter\u00e9s pr\u00e1ctico se requieren realizar c\u00e1lculos sobre variedades suaves de [&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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