Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 101-103).

Orientadores: Djairo Guedes de Figueiredo, João Marcos Bezerra do Ó / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-16T16:52:57Z (GMT). No. of bitstreams: 1 Ribeiro_BrunoHenriqueCarvalho_D.pdf: 1676664 bytes, checksum: 8517caa733a0141397500732b70a6ae6 (MD5) Previous issue date: 2010 / Resumo: Estudamos problemas do tipo Ambrosetti-Prodi para classes de sistemas elípticos gradientes com não-linearidades em crescimento crítico unilateral de Sobolev e de Trudinger-Moser. Com uso de métodos variacionais, provamos multiplicidade de solução para problemas homogêneos sem ressonância na parte linear e existência de solução não-trivial para problemas homogêneos com ressonância / Abstract: We study Ambrosetti-Prodi problems for classes of gradient elliptic systems with nonlinearities in the critical growth range of Sobolev and Trudinger-Moser types. Using variational methods, we prove multiplicity of solutions for nonhomogeneous problems without resonance in the linear part and homogeneous problems involving resonance / Doutorado / Analise / Doutor em Matemática

Orientadores: João Marcos Bezerra do O, Orlando Francisco Lopes / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-09T00:03:49Z (GMT). No. of bitstreams: 1 Severo_UberlandioBatista_D.pdf: 985878 bytes, checksum: 9d6e8a161a83e2812687d6ed4364bda1 (MD5) Previous issue date: 2007 / Resumo: Neste trabalho, estudamos questões relacionadas à existência, multiplicidade e comportamento de concentração de soluções do tipo onda estacionária, para uma classe de equações de Schrödinger quase-lineares, as quais modelam fenômenos físicos, por exemplo, na F³sica de Plasmas. Na obtenção de nossos resultados, usamos métodos variacionais, tais como, teoremas do tipo mini-max, bem como, teoria de regularidade de equações elípticas de segunda ordem / Abstract: In this work, we study questions related to existence, multiplicity and concentration behavior of standing waves, for a class of quasilinear Schrödinger equations, arising, for example, in Plasma Physics. To obtain our results, we use variational methods, such as, minimax theorems and also regularity theory of elliptic equations of second order / Doutorado / Analise / Doutor em Matemática

Orientadores: João Marcos Bezerra do O, Djairo Guedes de Figueiredo / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-15T15:20:37Z (GMT). No. of bitstreams: 1 Moraes_ElisandradeFatimaGlossde_D.pdf: 1261630 bytes, checksum: 516f800553b6eff1f3462fe4be134e8a (MD5) Previous issue date: 2010 / Resumo: Neste trabalho, estudamos questões relacionadas com existência e concentração de soluções positivas para algumas classes de problemas elípticos quase-lineares. Na obtenção de nossos resultados usamos um método variacional que permite estudar soluções do tipo "singlepeak" e "multiple-peak" para uma classe bem geral de não linearidades que não satisfazem necessariamente a condição clássica de Ambrosetti-Rabinowitz bem como nenhuma hipótese de monotonicidade. Problemas deste tipo aparecem em vários modelos da física e biologia, onde a presença de pequenos parâmetros de difusão ocorre naturalmente. Na Física de Plasmas, por exemplo, surgem no estudo de ondas estacionárias para certas classes de problemas envolvendo equações de Schrödinger quase-lineares / Abstract: In this work we study questions related with existence and concentration of positive solutions for some classes of quasilinear elliptic problems. To obtain our results we use a variational method that allows us to study solutions of the "single-peak" and "multiple-peak" type for a more general class of nonlinearities which do not satisfy necessarily the Ambrosetti-Rabinowitz condition and monotonicity hypothesis. Problems of this type appear in several models of physics and biology where the presence of small parameters of difusion occurs naturally. In plasma physics for example, they arise in the study of stationary waves for certain classes of quasilinear Schrödinger equations / Doutorado / Analise / Doutor em Matemática

Orientador: Marcelo da Silva Montenegro / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-23T11:08:01Z (GMT). No. of bitstreams: 1 Abreu_RafaeldosReis_D.pdf: 1052192 bytes, checksum: 6fe840dfe507b4cc6c5ad9f908da486a (MD5) Previous issue date: 2013 / Resumo: Neste trabalho, tratamos de resultados de existência de soluções ground state para algumas classes de problemas elípticos sobre espaços euclidianos ou sobre domínios exteriores. Nos casos em que consideramos um domínio exterior, consideramos a condição de fronteira de Dirichlet ou de Neumann. O fato de se considerar domínios não limitados naturalmente implica em algumas dificuldades como, por exemplo, a falta de compacidade. Quando isso ocorre, em geral, a condição Palais-Smale não é válida. Para contornar esta e outras dificuldades, usamos o Teorema do Passo da Montanha sem condição Palais-Smale, Lema de Lions e Teorema de Vitali. Em nosso estudo, utilizamos métodos variacionais explorando diversas técnicas para a obtenção de pontos críticos de funcionais associados a cada problema. Pontos críticos não nulos de cada funcional são soluções de seu respectivo problema / Abstract: In this work, we deal with existence of ground state solutions for some classes of elliptic problems on Euclidean spaces or on exterior domains. In cases where we consider an exterior domain, we consider the Dirichlet boundary condition or the Neumann boundary condition. Elliptic problems involving unbounded domains naturally have some difficulties, por example, the lack of compactness. When it occurs, in general, the Palais-Smale condition is not valid. To overcome this difficulty and others, we use the Mountain Pass Theorem without Palais-Smale condition, results due to Lions and the Vitali's Theorem. In our study, we use variational methods exploring techniques to obtain critical points of functionals related to each problem. Nonzero critical points of each functional are solutions of its respective problem / Doutorado / Matematica / Doutor em Matemática

This dissertation deals with the use of Shewhart control charts, modified to have variable sampling intervals, to simultaneously monitor a set of parameters. Fixed sampling interval control charts are modified to utilize sampling intervals that vary depending on what is being observed from the data. Two problems are emphasized, namely, the simultaneous monitoring of the mean and the variance and the simultaneous monitoring of several means. For each problem, two basic strategies are investigated. One strategy uses separate control charts for each parameter. A second strategy uses a single statistic which combines the information in the entire sample and is sensitive to shifts in any of the parameters. Several variations on these two basic strategies are studied. Numerical studies investigate the optimal number of sampling intervals and the length of the sampling intervals to be used. Each procedure is compared to corresponding fixed interval procedures in terms of time and the number of samples taken to signal. The effect of correlation on multiple means charts is studied through simulation. For both problems, it is seen that the variable sampling interval approach is substantially more efficient than fixed interval procedures, no matter which strategy is used. / Ph. D.

Die vorliegende Arbeit befasst sich mit der Entwicklung physikalisch fundierter, variations-basierter Modelle zur Beschreibung von magneto-aktiven Polymeren bei finiten Deformationen. Die Erarbeitung einer theoretisch und numerisch instruktiven Abhandlung zur Modellierung von nicht-dissipativen sowie dissipativen magneto-mechanischen Systemen stellt dabei einen zentralen Aspekt dieser Arbeit dar. Die konstitutive Modellierung erfolgt in kanonischer Form im Rahmen einer Theorie erster Ordnung auf Basis zweier skalarwertiger Tensorfunktionen -- der totalen Energiedichtefunktion und dem Dissipationspotential -- welche das komplexe konstitutive Verhalten des Systems vollständig charakterisieren. Die Entwicklung fundierter, konstitutiver Makroskalenmodelle für nicht-dissipative sowie dissipative magneto-aktive Polymere erfolgt dabei mikrostrukturgeleitet und im Falle nicht-dissipativer magneto-aktiver Polymere explizit auf Basis eines umfangreichen -- mittels numerischer Homogenisierung erzeugten -- Datensatzes. Das im Rahmen der konstitutiven Modellierung genutzte energie-basierte Setting stellt die natürliche Umgebung für Stabilitätsbetrachtungen dar und erlaubt die Diskussion der materiellen Stabilität der entwickelten konstitutiven Modelle auf Grundlage verallgemeinerter Konvexitätskonzepte. Im Mittelpunkt der numerischen Behandlung der vorliegenden Problemstellungen steht die Konstruktion primaler Variationsprinzipien auf Basis der entwickelten konstitutiven Funktionen in Verbindung mit deren konformen Finite-Elemente-Approximationen. Die zugehörigen diskreten Variationsformulierungen zeichnen sich durch ihre Minimaleigenschaften aus, wodurch diese nicht durch die diskrete inf-sup Stabilitätsbedingung eingeschränkt sind. Die Leistungsfähigkeit und Validität der entwickelten Modelle wird anhand von Benchmark- und Konvergenzstudien im Detail untersucht. Der Fokus weiterer numerischer Studien liegt auf der makrostrukturellen Analyse des magnetostriktiven und magnetorheologischen Effektes. / The present work covers the development of physically motivated, variational-based models for the description of magneto-active polymers at finite deformations. A key aspect of this thesis is to develop a unified theoretical and computational framework for the modeling of non-dissipative and dissipative magneto-active polymers. Within a classical first order theory, a strong emphasis is put on a unifying constitutive modeling framework based on two scalar valued tensor functions, namely the total energy density function and the dissipation potential. This two potential ansatz allows the canonical derivation of thermodynamically consistent constitutive models for a broad spectrum of complex systems in a mathematically elegant manner. The development of a family of constitutive macroscale models for non-dissipative and dissipative magneto-active polymers is based on a microstructure-guided approach, whereby the parametrization of the developed non-dissipative constitutive model is explicitly based on a comprehensive material data set generated via computational homogenization. The energy-based setting provides the natural environment for stability analysis and allows the discussion of the material stability of the developed constitutive models based on generalized notions of convexity. The focus of the variational and computational framework lies on the construction of primal variational principles and their conforming finite element approximations. The associated discrete variational formulations are characterized by their minimization structure and are therefore not restricted by the discrete inf-sup stability condition. The performance and validity of the developed models are investigated in detail by benchmark and convergence studies. The main emphasis of further numerical studies lies on the macrostructural analysis of the magnetostrictive and magnetorheological effect.

This doctoral thesis presents an extensive study on the applications of generalized coherent states (GCS) for the quantum dynamics of many-body systems. The research starts with exploring the fundamental properties of generalized coherent states, which are created by generators of the SU($M$) group acting on an extreme state, and demonstrating their role in representing ideal quantum condensates. A significant feature is the relationship between generalized coherent states and the more standard Glauber coherent states (CS). Similarities in their overcomplete and non-orthogonal nature are shown, alongside crucial differences with respect to $U(1)$ symmetry and entanglement properties, which generalized coherent states solely adhere to. Furthermore, this thesis delves into the nonequilibrium dynamics of GCS as well as Glauber CS under nonlinear interactions. Combining analytical analysis and numerical calculations, it is found that while their two-point correlation functions are equivalent in the thermodynamic limit, their autocorrelation functions exhibit distinctly different characteristics. It is proven analytically that the autocorrelation functions of the evolved GCS relate to the ones of the corresponding Glauber CS through a Fourier series relation, which arises due to the $U(1)$ symmetry of the GCS. A substantial part of this thesis is dedicated to investigating the dynamics of the Bose-Hubbard model, incorporating both nonlinear interaction and tunneling term. This investigation introduces a novel approach which employs an Ansatz for the wave function in terms of a linear combination of GCS, where the differential equations of all the variables are determined by the time-dependent variational principle without truncation. This innovative method is adeptly applied to the nonequilibrium dynamics in various scenarios, from the bosonic Josephson Junction model where some fundamental quantum effects can be revealed by a handful of GCS basis functions, to large system size implementations of the Bose-Hubbard model, where the phenomenon of thermalization can be observed. The proposed variational approach provides an alternative way to study the time-dependent dynamics in many-body quantum systems conserving particle number. The final focus of this thesis is on the boson sampling problem within a linear optical network framework. Again adapting a linear combination of GCS, an exact analytical formula for the output state in standard boson sampling scenarios is derived by means of Kan's formula, showcasing a computational complexity that increases less severely with particle and mode number than the super-exponential scaling of the Fock state Hilbert space. The reduced density matrix of the output state is obtained by tracing out one subsystem. This part of the study extends to examining the properties of the subsystem entanglement creation, and offering novel perspectives on entanglement entropy differences between global and local optical networks. This thesis makes several contributions to the field of quantum many-body systems, particularly highlighting the potential applications of GCS. The presented research offers a new variational method to the nonequilibrium dynamics, and paves the way for future explorations and applications in quantum simulations, quantum computing and beyond.

Utilizando a representação funcional de schrodinger e um ansatz gaussiano simples, obtemos um conjunto de equações finitas para a matéria e gravitação em espaços homogêneos e inomogêneos. / Using the formalism of functional Schrödinger representation and a simple Ansatz, we obtain a set of finite equations to the matter and gravitation in homogeneous and inhomogeneous spaces.

Utilizando a representação funcional de schrodinger e um ansatz gaussiano simples, obtemos um conjunto de equações finitas para a matéria e gravitação em espaços homogêneos e inomogêneos. / Using the formalism of functional Schrödinger representation and a simple Ansatz, we obtain a set of finite equations to the matter and gravitation in homogeneous and inhomogeneous spaces.