{"id":72971,"date":"2018-03-09T23:17:51","date_gmt":"2018-03-09T23:17:51","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/metodos-geometricos-en-teorias-clasicas-de-campos-e-integracion-numerica\/"},"modified":"2018-03-09T23:17:51","modified_gmt":"2018-03-09T23:17:51","slug":"metodos-geometricos-en-teorias-clasicas-de-campos-e-integracion-numerica","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/metodos-geometricos-en-teorias-clasicas-de-campos-e-integracion-numerica\/","title":{"rendered":"Metodos geometricos en teorias clasicas de campos e integracion numerica"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Aitor Santamaria Merino <\/strong><\/h2>\n<p>En esta tesis se profundiza en la descripci\u00f3n de las teor\u00edas cl\u00e1sicas de campos en t\u00e9rminos de geometr\u00eda multisimpl\u00e9ctica. Adem\u00e1s, se realiza un an\u00e1lisis de las propiedades geom\u00e9tricas de ciertos problemas en mec\u00e1nica, interesante para la construcci\u00f3n de una nueva familia de integradores num\u00e9ricos cuyas propiedades de convergencia superan a las de los algoritmos cl\u00e1sicos. se espera en el futuro extenderlos a las teor\u00edas de campos.  comienza con una breve exposici\u00f3n de la geometr\u00eda simpl\u00e9ctica y aplicaciones a la mec\u00e1nica, acompa\u00f1ada de una exposici\u00f3n paralela de la geometr\u00eda multisimpl\u00e9ctica y los fibrados de jets, que son la base que describe las teor\u00edas cl\u00e1sicas de campos en t\u00e9rminos multisimpl\u00e9cticos. En particular, la tesis completa la descripci\u00f3n con teoremas nuevos relativos a la existencia de coordenadas de darboux, y una extensi\u00f3n de los triples de tulczyjew a las teor\u00edas de campos.  a continuaci\u00f3n, se analizan los conceptos de simetr\u00eda y cantidad conservada para las ecuaciones de la din\u00e1mica de las teor\u00edas cl\u00e1sicas de campos. Asimismo, se analiza la din\u00e1mica en presencia de superficies de cauchy.  finalmente, se utilizan propiedades de las funciones generatrices para obtener nuevos m\u00e9todos num\u00e9ricos geom\u00e9tricos, particularizando para mec\u00e1nica no hol\u00f3noma y control \u00f3ptimo, con mejor comportamiento a largo plazo, tal y como se prueba en algunos on ejemplos.  la tesis concluye con una descripci\u00f3n de problemas abiertos en este campo.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Metodos geometricos en teorias clasicas de campos e integracion numerica<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Metodos geometricos en teorias clasicas de campos e integracion numerica <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Aitor Santamaria Merino <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Carlos III de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 28\/02\/2005<\/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>Manuel Leon Rodriguez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: alberto Ibort latre <\/li>\n<li>frans Cantrijn (vocal)<\/li>\n<li> Marrero gonzalez Juan  Carlos (vocal)<\/li>\n<li>narciso Roman roy (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Aitor Santamaria Merino En esta tesis se profundiza en la descripci\u00f3n de las teor\u00edas cl\u00e1sicas de campos [&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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