Zugl.: Saarbrücken, Univ., Diss., 2005

Zugl.: Bonn, Univ., Diss., 2007

Zugl.: Gent, Univ., Diss., 2006

Thesis (M.B.A.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf 53).

Zugl.: Berlin, Humboldt-Univ., Diss., 2008 / Includes bibliographical references (p. 466-502) and index.

Zugl.: Marburg, University, Diss., 1987. / Zugl.: Marburg, Univ., Diss., 1987.

Presented as Thesis (Ph. D.)--University of Wisconsin-Madison, 1911. / "Bibliography. Literature consulted in the course of this investigation": p. 110-112.

Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2005Bitstream added on 2014-06-13T18:55:33Z : No. of bitstreams: 1 benito_rn_me_sjrp.pdf: 385086 bytes, checksum: 17b116bfd36532f6c04131b8754908b3 (MD5) / O objetivo desse trabalho é aplicar a técnica da Redução de Liapunov-Schmidt no estudo da Bifurcação de Hopf. Primeiramente discutimos a Redução de Liapunov-Schmidt em espaços de dimensão finita e posteriormente em espaços de Banach de dimensão infinita. A conclusão do trabalho é a de monstração do Teorema de Hopf usando a Redução de Liapunov-Schmidt. / The main goal of this work is to apply the Liapunov-Schmidt Reduction technique in the study of the Hopf Bifurcation. First of all we discuss the Liapunov-Schmidt Reduction in finite dimensional spaces and after that in Banach spaces of infinite many dimensions. The conclusion of this work is the proof of the Hopf Theorem using the Liapunov-Schmidt Reduction.

Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática / En esta tesis doctoral se construyen soluciones rotacionalmente simétricas de la ecuación de Cahn-Hilliard en $ \R{^d} $ y se estudian sus propiedades de estabilidad. En el Capítulo \ref{ch1} se presenta la ecuación de Cahn-Hilliard y se explica su origen e interpretación física. Además se repasan varios resultados conocidos, se presenta la notación y se exponen los dos resultados más importantes de esta tesis: el primero establece la existencia de soluciones rotacionalmente simétricas cuyos conjuntos de nivel se aproximan a los unduloides de Delaunay. El segundo resultado afirma que las propiedades de estabilidad de los unduloides de Delanay heredan propiedades de estabilidad de las soluciones encontradas, en el sentido que son no degeneradas y tienen 6 campos de Jacobi con crecimiento moderado. En el Capítulo \ref{prel} se presentan en detalle los principales ingredientes que se necesitan para probar los Teoremas \ref{teo 1} y \ref{teo 2}, a saber las coordenadas de Fermi cerca de una superficie de curvatura media constante, los unduloides de Delaunay y su operador de Jacobi. También se muestra la primera aproximación de la solución anunciada en el Teorema \ref{teo 1}. En el Capítulo \ref{chap proof teo 1} se demuestra el Teorema \ref{teo 1}. Usamos una versión refinada del método de reducción del Lyapunov-Schmidt que simplifica varios aspectos técnicos de construcciones de problemas similares. Los resultados de este capítulo fueron obtenidos en colaboración con mi Profesor Guía, Dr. Micha\l\ Kowalczyk y fueron publicados en la revista \emph{Discrete and Continous Dynamical Systems} bajo el título \emph{Rotationally Symmetric Solutions to the Cahn-Hillard Equation}. Una demostración del Teorema \ref{teo 2} se da el Capítulo \ref{chap proof teo 2}. La clave es relacionar el núcleo del operador linearizado alrededor de nuestra solución con los campos de Jacobi que provienen de invariancias geométricas. Esta relación se puede realizar debido a que es posible separar las variables una vez que se ha aplicado la transformada de Laplace-Fourier. Los resultados de este capítulo también fueron obtenidos con mi profesor Guía y han sido aceptados para su publicación en la revista \emph{Indiana University Mathematics Journal} bajo el título \emph{Nondegeneracy and the Jacobi Fields of Rotationally Symmetric Solutions to the Cahn-Hillard Equation}. In this PhD thesis rotationally symmetric solutions to the Cahn-Hilliard equation are constructed. Also we study its stability properties. In Chapter \ref{ch1} we present the Cahn-Hilliard equation in $ \R^d $ and explain its origin and physical interpretation. We also review several known results, introduce some basic notation and present the two main results of this thesis. The first one states the existence of radially symmetric solutions to the Cahn-Hilliard equation which nodal sets approaches to Delaunay unduloids, and the second one claims that stability properties of the Delaunay unduloids inherit stability properties of the solutions we found in the sense that our solutions are non degenerated and have 6 Jacobi fields with temperate growth. Chapter \ref{prel} is devoted to present in detail the main ingredients we need to prove Theorem \ref{teo 1} and Theorem \ref{teo 2}, namely Fermi coordinates near a constant mean curvature (CMC), the Delaunay unduloids and its Jacobi operator. We also present the construction of the first approximation of the solutions announced in Theorem \ref{teo 1}. In Chapter \ref{chap proof teo 1} we prove Theorem \ref{teo 1}. We use a refined version of the Lyapunov-Schmidt reduction method which simplifies very technical aspects of previous constructions for similar problems. The results of this chapter were obtained in collaboration with my thesis advisor Dr. Micha\l\ Kowalczyk and published in \emph{Discrete and Continuous Dynamical Systems}. A proof of Theorem \ref{teo 2} is given in Chapter \ref{chap proof teo 2}. The key is to relate the kernel of the linearized operator about our solution with the Jacobi fields that comes from the geometric invariances. This relation can be performed since we are able to separate the variables once the Laplace-Fourier transform is applied. The results of this chapter were obtained in collaboration with my thesis advisor Dr. Micha\l\ Kowalczyk and admitted for publication in \emph{Indiana University Mathematics Journal}.

Stirling engines are an external combustion heat engine that converts thermal energy into mechanical work that a closed cycle is run by cyclic compression and expansion of a work fluid (commonly air or Helium) in which, the working fluid interacts with a heat source and a heat sink and produces network. The engine is based on the Stirling cycle which is a subset of the Carnot cycle. The Stirling cycle has recently been receiving renewed interest due to some of its key inherent advantages. In particular, the ability to operate with any form of heat source (including external combustion, flue gases, alternative (biomass, solar, geothermal) energy) provides Stirling engines a great flexibility and potential benefits since it is convinced as engines running with external heat sources. However, several aspects of traditional Stirling engine configurations (namely, the Alpha, Beta, and Gamma), specifically complexity of design, high cost, and relatively low power to size and power to volume ratios, limited their widespread applications to date. This study focuses on an innovative Stirling engine configuration that features a rotary displacer (as opposed to common reciprocating displacers), and aims to utilize analytical and numerical analysis to gain insights on its operation parameters. The results are expected to provide useful design guidelines towards optimization. The present study starts with an overview of the Stirling cycle and Stirling engines including both traditional and innovative rotary displacer configurations, and their major advantages and disadvantages. The first approach considers an ideal analytical model and implements the well-known Schmidt analysis assumptions for the rotary displacer Stirling engine to define the effects of major design and operation parameters on the performance. The analytical model resulted in identifying major variables that could affect the engine performance (such as the dead volume spaces, temperature ratios and the leading phase angle). It was shown that the dead volume could have a drastic effect over the engine performance and the optimum phase angle of the engine is 90o. The second approach considers a non-ideal analytical model and aims to identify and account the main sources of energy losses in the cycle to better represent the engine performance. The study showed that the ideal efficiency and the non-ideal efficiency could have 15% difference that could have as an enormous effect on the engine performance.