Made available in DSpace on 2015-05-14T12:13:59Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 989729 bytes, checksum: 3e97939bd59206a6ed90c89ca0467d17 (MD5) Previous issue date: 2011-05-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Cosmological models involving scalar fields allow the description of a phase of accelerated cosmic expansion and thus appear as a promising alternative for the study of the cosmic inflation and dark energy. We are interested here in analyzing these cosmological models. In particular, we will explore cosmological solutions based on the first order formalism. The inclusion of this method favors the search for analytic solutions with scalar fields in cosmology, and this is particularly important when we consider the component of nonrelativistic matter (dust) in the presence of dark energy, in order to construct a cosmological model capable of explaining, in good agreement with observational data, the current phase of cosmic acceleration. Considering a regime of Lorentz violation, the use of this method allowed us to verify that new considerations must be implemented so that the inflationary regime can now solve the problem of initial conditions. Another question of interest, which can be addressed with the aid of the first order formalism, takes into account the possibility of the dark energy equation of state parameter to be a constant other than −1 and in this case we get that a lot of fine-tuning is needed, which should be interpreted as strong evidence in favor of a dynamic model of dark energy. We also introduce the so-called deformation method on the slow-roll inflationary models, and we explore this framework in applications of current interest to this branch of research. / Modelos cosmológicos envolvendo campos escalares permitem a descrição de uma fase de expansão cósmica acelerada e, portanto, se apresentam como uma alternativa promissora no estudo da inflação cósmica e da energia escura. Estamos aqui interessados em analisar esses modelos cosmológicos; em especial, vamos explorar soluções cosmológicas baseadas no formalismo de primeira ordem. A inclusão desse método favorece a busca por soluções analíticas na cosmologia com campos escalares e isso é particularmente interessante no caso em que consideramos o componente de matéria não relativística (poeira) na presença da energia escura, afim de construir um modelo cosmológico capaz de explicar, em bom acordo com os dados observacionais, a atual fase de aceleração cósmica. Considerando um regime de violação de Lorentz, a utilização desse método nos permitiu verificar que novas considerações devem ser implementadas, para que o regime inflacionário possa resolver o problema das condições iniciais. Outra questão de interesse, que pode ser analisada com auxílio do formalismo de primeira ordem, leva em conta a possibilidade da equação de estado da energia escura ser um constante qualquer diferente de −1 e, nesse caso, obtemos que uma grande quantidade de ajuste fino é necessária, o que deve ser interpretado como uma forte evidência em favor de um modelo dinâmico de energia escura. Também introduzimos o chamado método de deformação a modelos inflacionários sob o regime de rolagem lenta e exploramos essa ferramenta em aplicações de corrente interesse na literatura.

Made available in DSpace on 2015-05-14T12:14:03Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 3752182 bytes, checksum: 63a51d4864db299b4b98e396d8d6e622 (MD5) Previous issue date: 2012-03-13 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we do an investigation of new features of so-called k-defects, which are topological defects with non-canonical kinetic term. Specifically, we study a class of k-defects in models of scalar field theories distinct from standard theory but discribing, case to case, the very same defect structure with the very same energy density as that described by the theory governed by standard Lagrange density. In teories which presents such relationships, distinct models support the same topological structure; why call them of twinlike models. We then build a model of twin theory, which we call ALTW model, and find the relationships between them, including relations between the potentials of both, which, although distinct, they present minima that are connected by the same field solution, for the case of static and stable configurations. The results are ilustrated with several examples. In order to distinguish between theories, we analyze the situation in which the component T11 of the energy-momentum tensor is nonzero, which is equivalent to breaking the pressureless condition required to ensure stability of static solutions. With the same purpose of distinction, we did a study of linear stability of defects and we found that, although representing the same defect structure, case to case, a theory is not a simple reparametrization of the other. We also made an extension of the twin nature between more general models of real scalar field theries and an application to braneworld scenario. We also investigated the behavior twin between standard and tachyonic models in FRW cosmology, where the scalar field evolves over time. / No presente trabalho fazemos uma investigação de novas características dos chamados kdefeitos, que são defeitos topológicos com termo cinético não-canônico. Especificamente, estudamos uma classe de k-defeitos em modelos de teorias de campos escalares distintos da teoria padrão mas que descrevem, caso a caso, o mesmo defeito com a mesma densidade de energia daquele descrito pela teoria governada pela densidade lagrangiana padrão. Em teorias que apresentam tais relações, modelos distintos suportam a mesma estrutura topológica; daí chamá-los de modelos gêmeos. Construímos, então, um modelo de teoria gêmea, que denominamos modelo ALTW, e encontramos as relações existentes entre eles, incluindo as relações entre os potenciais de ambos, que, embora distintos, apresentam mínimos conectados pelo mesmo campo solução, para o caso de configurações estáticas e estáveis. Os resultados são ilustrados com vários exemplos. Com a finalidade de distinguir as teorias, analisamos a situação em que a componente T11 do tensor energia-momento é não-nula, o que é equivalente a quebrar a condição de pressão nula necessária para garantir a estabilidade das soluções estáticas. Com o mesmo objetivo de distinção, fizemos um estudo da estabilidade linear dos defeitos e obtivemos que, embora representem o mesmo defeito, caso a caso, uma teoria não é uma simples reparametrização da outra. Fizemos ainda uma extensão da natureza gêmea entre modelos mais gerais de teorias de campo escalar real e uma aplicação ao cenário de brana. Investigamos também o comportamento gêmeo entre os modelos padrão e taquiônico em cosmologia FRW, onde o campo escalar evolui com o tempo.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Nosso objetivo nesse trabalho à apresentar um teorema que caracteriza os solitons gradiente rÃgidos para caso nÃo compacto. Como aplicaÃÃo provaremos que os solitons gradiente homogÃneos sÃo rÃgidos e apresentaremos um exemplar de soliton de Ricci que nÃo pode ser gradiente. / Our goal in this work is to present a theorem which characterizes the gradient solitons rigid for non-compact case. As an application we prove that the homogeneous gradient solitons are rigid and provide an example of the Ricci soliton can not be gradient.

A adequada quantificação do transporte interfacial de escalares em escoamentos turbulentos é de interesse prático para os processos industriais e para a gestão dos problemas ambientais. O fenômeno é matematicamente complexo devido ao uso de equações governantes estatísticas não lineares e não fechadas. Neste estudo, analisam-se detalhes do método de Ondas Quadradas Aleatórias (OQA), o qual fornece uma quantificação estatística que permite fechar as equações e obter um perfil normalizado da grandeza de interesse para a transferência unidimensional turbulenta de escalares, que, num caso idealizado, depende de apenas dois parâmetros adimensionais, A e k (neste caso, k representa um coeficiente de transferência e A depende da interação entre os fenômenos de transporte molecular e turbulento). Simulações numéricas foram realizadas no intuito de se verificar a influência das derivadas de ordem superior para a função normalizada de concentração. A sensibilidade do modelo e a análise de aspectos intrínsecos ao mesmo foram também realizadas. Importante análise das condições de contorno empregadas foi desenvolvida com a inserção de um contorno adicional, com base física, no seio líquido. Como os estudos iniciais tinham se concentrado em exemplos de transferência de massa, uma extensão para o caso de transporte de calor foi considerada. Os resultados obtidos reproduzem o comportamento dos dados experimentais observados na literatura. / The adequate quantification of interfacial scalar transport in turbulent flows is of practical interest for industrial processes and in environmental problems. The phenomenon is mathematically complex due to the use of unclosed nonlinear statistical equations. In this study, we analyze details of the method of Random Square Waves (RSW), which provides a statistical quantification that allows closing the set of equations and getting the normalized scalar profile of the one-dimensional turbulent scalar variable, which, in an idealized case, depends on only two nondimensional parameters, k and A (in this case, k represents a transfer coefficient and A depends on the interaction between the molecular and turbulent transports). Numerical simulations were performed in order to verify the influence of the higher order of derivatives over the normalized concentration function. The sensitivity of the model to the relevant parameters and the analysis of its intrinsic parameters were also performed. An important aspect is the analysis of the boundary conditions, for which an additional condition was proposed and employed in the bulk liquid (with based on physical grounds). Because the initial studies have focused on examples of mass transfer, an extension to the case of heat transport was here considered. The results reproduce the behavior of experimental data reported in the literature.

Energy efficiency optimization of electric machines is an important research field and is part of the objectives of several international projects such as the European Commission Climate and Energy package which has set itself a 20% energy savings target by 2020, and was extended for 2030 with higher targets. Therefore, this thesis proposes an efficiency optimization method of the Induction Machine (IM) through the variation of the control parameters. To achieve this goal, the flux in the airgap is modified according to an optimal flux table computed off-line for all possible operating points. The flux table is calculated with the best possible accuracy through an improved dynamic model of the IM, developed in these works. The latter avoids the main drawback of the classic dynamic model, by considering the effect of core losses. The core loss model established by Bertotti is used. It depends on the frequency and the amplitude of the magnetic field. The losses are then represented by a variable resistor, continuously evaluated according to the operating point. The established optimal flux table is a function of the operating conditions in terms of torque and speed. Indeed, the results show that the flux can be optimized for torque values less than about half the rated torque, and that this threshold is influenced by the speed. The proposed optimization method is simulated, then tested for the scalar control and the field-oriented control, in order to show the genericity of the proposed approach. The validation is carried on an experimental test bench for two 5.5 kW induction motors of different efficiency standards (IE2 and IE3). The results obtained show the reduction of the losses in the motor, thus an improvement of the overall efficiency while preserving a satisfactory dynamic behavior. Consequently, the optimization of the energy efficiency is validated for the two control structures and for the two studied motors. In addition to the validation of the simulation results, the proposed approach is compared to existing methods to assess its effectiveness

Cette thèse est consacrée à l'étude d'une famille des flots géométriques associés au problème de la courbure scalaire prescrite sur une variété riemannienne compacte. Plus précisément, si on désigne par (M,g0) une variété riemannienne compacte de dimension n≥3, et si F∈C∞ (M) est une fonction donnée, le problème de la courbure scalaire prescrite consiste à trouver une métrique g conforme à g0 telle que F soit sa courbure scalaire. Ce problème est équivalent à la résolution de l'EDP suivante :-4 (n-1)/(n-2) ∆u+R0 u=Fu((n+2)/(n-2 )) , u>0 , (E), Où R0 est la courbure scalaire de la métrique initiale g0 et ∆ est le laplacien associé à g0. Il s'agit d'une équation elliptique non-linéaire dont la difficulté principale provient du terme u((n+2)/(n-2 )). Hormis le cas de la sphère standard Sn , tous les travaux consacrés à l'étude de l'équation (E) sont basés sur la méthode variationnelle. Dans cette thèse, on développe une autre approche basée sur l'étude d'une famille de flots géométriques qui permet, entre autres, de résoudre l'équation (E). La question dépend bien entendu de la métrique initiale g0 et en particulier du signe de sa courbure scalaire R0. Les flots introduits sont des flots de gradient associés à deux fonctionnelles distinctes dépendant du signe de R0. La première partie de cette thèse est consacrée au cas R0<0 et dans la deuxième partie on traite le cas R0>0. Dans les deux cas, on démontre l'existence globale du flot et on étudie son comportement asymptotique à l'infini. / This thesis is devoted to the study of a family of geometric flows associated with the prescribed scalar curvature problem. More precisely, if we denote by (M,g0) a compact riemannian manifold with dimension n≥3, and if F∈C∞ (M) is a given function, the prescribed scalar curvature problem consists of finding a conformal metric g to g0 such that F is its scalar curvature. This problem is equivalent to the resolution of the following PDE : -4 (n-1)/(n-2) ∆u+R0 u=Fu((n+2)/(n-2 )) , u>0 , (E), Where R0 is the scalar curvature of the initial metric g0 and ∆ is the laplacian associated with g0.It is a nonlinear elliptic equation, whose the main difficulty comes from the term u((n+2)/(n-2 )). Apart from the case of the standard sphere Sn all the works that study the equation (E) are based on the variational method. In this thesis, we develop another approach based on the study of a family of geometric flows which allows to solve equation (E).The flows introduced are gradient flows associated with two distinct functional functions depending on the sign of R0.The first part of this thesis is devoted to the case R0<0 and in the second part we treat the case R0>0. In both cases, our aim is to proof the global existence of the flow and study its asymptotic behavior at infinity.

Scalar fields occur quite commonly in several application areas in both static and time-dependent forms. Hence a proper visualization of scalar fieldsneeds to be equipped with tools to extract and focus on important features of the data. Similarity detection and pattern search techniques in scalar fields present a useful way of visualizing important features in the data. This is done by isolating these features and visualizing them independently or show all similar patterns that arise from a given search pattern. Topological features are ideal for this purpose of isolating meaningful patterns in the data set and creating intuitive feature descriptors. The Merge Tree is one such topological feature which has characteristics ideally suited for this purpose. Subtrees of merge trees segment the data into hierarchical regions which are topologically defined. This kind of feature-based segmentation is more intelligent than pure data based segmentations involving windows or bounding volumes. In this thesis, we explore several different techniques using subtrees of merge trees as features in scalar field data. Firstly, we begin with a discussion on static scalar fields and devise techniques to compare features - topologically segmented regions given by the subtrees of the merge tree - against each other. Second, we delve into time-dependent scalar fields and extend the idea of feature comparison to spatio-temporal features. In this process, we also come up with a novel approach to track features in time-dependent data considering the entire global network of likely feature associations between consecutive time steps.The highlight of this thesis is the interactivity that is enabled using these feature-based techniques by the real-time computation speed of our algorithms. Our techniques are implemented in an open-source visualization framework Inviwo and are published in several peer-reviewed conferences and journals. / <p>QC 20171020</p>

Ces deux dernières décennies, les techniques de somme connexe essentiellement basées sur des outils d'analyse ont permis de faire des progrès importants dans la compréhension de nombreux problèmes non linéaires issus de la géométrie (étude des métriques à courbure scalaire constante en géométrie Riemannienne, métriques auto-duales, métrique ayant des groupes d'holonomie spéciaux, métriques extrémales en géométrie Kaehlerienne, équations de Yang-Mills, étude des surfaces minimales et des surfaces à courbure moyenne constante, métriques d'Einstein, etc.). Ces techniques se sont avérées être un outil puissant pour démontrer l'existence de solutions à des problèmes hautement non linéaires. Si les techniques permettant d'effectuer des sommes connexes en des points isolés sont bien comprises et fréquemment utilisées, les techniques permettant d'effectuer des sommes connexes le long de sous-variétés ne sont pas encore bien maîtrisées. Le principal objectif de cette thèse est de combler (partiellement) cette lacune en développant de telles techniques applicables dans le cadre de l'étude des métriques à courbure scalaire constante et aussi dans le cadre de l'étude des équations de comptabilité d'Einstein en relativité générale / These last two decades the connected sum techniques, essentially based on analytical tools, are revealed to be a powerful instrument to understand solutions of several nonlinear problem issued from the geometry (constant scalar curvature metrics in Riemannian geometry, self-dual metrics, metrics with special holonomy group, extremal Kaehler metrics, Yang-Mills equations, minimal and constant mean curvature surfaces, Einstein metrics, etc.). Even tough the techniques which allows one to consider the connected sum at points for solutions of nonlinear PDE's are frequently used and deeply understood, the analogous techniques for connected sums along sub-manifolds have not been mastered yet. The main purpose of this thesis is to (partially) plug this gap by developing such techniques in the context of the constant scalar curvature metrics and the Einstein constraint equations in general relativity

The equivalence principle has proven to be central to theories of gravity, with General Relativity being the simplest and most elegant theory to embody the principle. Most alternative theories of gravity struggle to satisfy the principle and still be distinct from GR. Extensions of cosmological and quantum theories question the irrefutably of the equivalence at every scale. The possibility of an equivalence principle violation at galactic scales would be an exciting prospect. In this thesis, we will carefully examine the equivalence principle through the study of chameleon scalar-tensor theories, this will include solutions for hypothetical stars known as boson stars. Such theories find varied application, especially in cosmology, where they model dark energy and inflation. The AWE hypothesis, is an instance of this. It is a nonuniversally coupled model in which violations of the equivalence principle on galactic scales may be apparent. We investigate spherically symmetric and static solutions within the framework of this theory. The constraints obtained from galactic rotation curves results in values of the couplings that show no significant violation of the equivalence principle or values consistent with a theory of dark energy

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