{"id":92940,"date":"2018-03-11T10:12:08","date_gmt":"2018-03-11T10:12:08","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/dynamics-and-stability-of-dissipative-nonlinear-waves\/"},"modified":"2018-03-11T10:12:08","modified_gmt":"2018-03-11T10:12:08","slug":"dynamics-and-stability-of-dissipative-nonlinear-waves","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/dynamics-and-stability-of-dissipative-nonlinear-waves\/","title":{"rendered":"Dynamics and stability of dissipative nonlinear waves"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Adrian Alexandrescu <\/strong><\/h2>\n<p>Hemos estudiado el comportamiento de las ondas no lineales untilizando tres modelos extendidos de la ecuaci\u00f3n nls: (i) un modelo con modulaci\u00f3n peri\u00f3dica de la no linealidad, (ii) un modelo con t\u00e9rminos de disipaci\u00f3n (perdidas) no lineal, y (iii) un modelo que incluye no linealidades de tipo c\u00fabico-qu\u00edntico.  se ha intentado estabilizar la soluci\u00f3n de simetr\u00eda radial y de un nodo. Hemos probado varias configuraciones, incluyendo sistemas de una y de dos componentes. En el sistema de dos componentes se ha utilizado la soluci\u00f3n fundamental (denominada como el solit\u00f3n de townes) para implementar una gu\u00eda no lineal para la soluci\u00f3n con un nodo. Tambien se ha estudiado la posibilidad de estabilizar soluciones estacionarias de simetr\u00eda rotacional discreta.  utilizando herramientas anal\u00edticas y num\u00e9ricas hemos investigado el papel de las perdidas no lineales en la din\u00e1mica de las ondas descritas por la ecuaci\u00f3n nls.  Las soluciones estacionarias del modelo nls con perdidas no lineales se han calculado para no linealidad nula, negativa y positiva, para escenarios en dos y tres dimensiones, y ademas de las soluciones de tipo fundamental, se han construido soluciones de tipo vortice.  la interacci\u00f3n de un medio coherentes de cuatro niveles con los campos electromagn\u00e9ticos se ha planteado en el regimen no perturbativo y se han calculado numericamente las susceptibilidades del medio de cuatro niveles. La propagaci\u00f3n de los campos se ha descrito por un sistema de ecuaciones nls. Mediante una serie de simulaciones num\u00e9ricas se ha comprobado que los haces \u00f3pticos muestran propiedades parecidas a los l\u00edquidos: formaci\u00f3n y extracci\u00f3n de gotas, rebotes, coalescencia y evaporaci\u00f3n por la superficie.  utilizando el sistema de ecuaciones nls para la propagaci\u00f3n por el medio coherente de cuatro niveles se han construido solitones vectoriales formados por los dos campos que interaccionan con el medio. Se han establecido dominio de existencia para los estados estacionarios vectoriales. El analisis de la estabilidad lineal de los solitones vectoriales se hizo utilizando un conjunto de dos t\u00e9cnicas: la pseudo-propagaci\u00f3n para estimar la tasa de crecimiento de los modos de perturbaci\u00f3n y la relajaci\u00f3n num\u00e9rica para construir por continuidad las curvas de inestabilidad. El estudio de las estabilidad din\u00e1mica se hizo propagando unos estados estacionarios inicialmente perturbados por un ruido de 1%.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Dynamics and stability of dissipative nonlinear waves<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Dynamics and stability of dissipative nonlinear waves <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Adrian Alexandrescu <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Castilla-la mancha<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 23\/04\/2009<\/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>Victor Manuel Perez Garcia<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: humberto Michinel \u00e1lvarez <\/li>\n<li>german Jos\u00e9 de Valcarcel gonzalvo (vocal)<\/li>\n<li>Jos\u00e9 Mar\u00eda Soto crespo (vocal)<\/li>\n<li>gabriel Fern\u00e1ndez calvo (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Adrian Alexandrescu Hemos estudiado el comportamiento de las ondas no lineales untilizando tres modelos extendidos de la [&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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