Neste trabalho, construímos novas soluções com simetria esférica ou axial para as equações do campo gravitacional induzido num cenário brana do tipo Randall-Sundrum, onde uma 3-brana com constante cosmológica está imersa num espaço-tempo 5-dimensional conhecido como bulk. Para o caso esfericamente simétrico, com constante cosmológica negativa, obtivemos uma família de soluções numa brana assintoticamente anti-de Sitter, sendo que cada membro desta é diferenciado de outro por uma constante integração C, que fixada proveu-nos soluções de buracos negros ou buracos de minhocas. Com a mesma simetria, geometrias que descrevem buracos de minhoca foram encontradas numa brana assintoticamente de Sitter. Para o caso axialmente simétrico, métricas assintoticamente anti-de Sitter e de Sitter foram construídas no contexto citado. Propriedades óticas, como a rotação do vetor de polarização, foram estudadas, mostrando-nos algumas diferenças entre os mundos brana, tratados como uma teoria de gravitação modificada, e a relatividade geral. / In this work we have constructed new solutions, with axial or spherical symmetry, to the induced gravitational field equations within a Randall-Sundrum type brane world scenario, where a 3-brane with cosmological constant is embedded in a 5-dimensional space-time called bulk. For the spherical case with negative cosmological constant, we have found a family of solutions in an anti-de Sitter brane, where each member of the family is different from another when C is fixed. With a fixed C we have black holes or wormholes. In this same case, with spherical symmetry, we have obtained wormhole solutions in a de Sitter brane. In the same context, for the axially symmetric case, metrics asymptotically anti-de Sitter and de Sitter were built. Optics features, like rotation of polarization vector, have been studied. These features showed some differences between brane worlds, a theory of modified gravity, and the General Relativity.

Mecanismos flexíveis, nos quais a deformação elástica é aproveitada na atuação cinemática, têm grande empregabilidade em dispositivos de mecânica de precisão, engenharia biomédica, e mais recentemente em microeletromecanismos (MEMS). Entre as diversas técnicas empregadas para o seu projeto, a otimização topológica tem se mostrado a mais genérica e sistemática. A grande dificuldade destes projetos é conciliar os requisitos cinemáticos com a resistência mecânica da estrutura. Neste trabalho, é implementado um critério de resistência dentro da formulação do problema de otimização, com o intuito de gerar mecanismos que cumpram a tarefa cinemática desejada mas ao mesmo tempo não ultrapassem limites de tensão predeterminados. Esta restrição adicional também visa aliviar o problema bastante conhecido do aparecimento de articulações. Não linearidade geométrica e de material (hiperelasticida de compressível) são implementadas na solução das equações através do método dos elementos finitos para levar em conta os grandes deslocamentos do mecanismo. O método das assíntotas móveis é usado para a atualização das variáveis de projeto. As derivadas do problema de otimização são calculadas analiticamente, pelo método adjunto. Técnicas de projeção são aplicadas para a garantia de topologias livres de instabilidades numéricas comuns em otimização topológica, e projetos otimizados mais próximos de um espaço 0/1 para as densidades físicas. / Compliant me hanisms, in whi h the elasti strain is the basis for kinemati a tua- tion are widely used in pre ision me hani s devi es, biomedi al engineering, and re ently in mi roele trome hani al systems (MEMS). Among several te hniques applied in ompliant me hanisms design, topology optimization has been one of the most general and systemati . The great hallenge in these designs is to ouple both the kinemati s and the me hani al strength riteria requirements. In this work, a strength riteria for the optimization problem is applied, with the aim of generating ompliant me hanisms that ful ll the desired kine- mati tasks while omplying with a stress threshold. The addition of a stress onstraint to the formulation for ompliant me hanisms in topology optimization also aims to allevi- ate the appearan e of hinges in the optimized topology, a well known issue in the design of ompliant me hanisms. Geometri al and material ( ompressible hyperelasti ity) nonlin- earities are applied to the nite element equilibrium equations, to take into a ount large displa ements. The method of moving asymptotes is applied for design variables updating. The derivatives are al ulated analyti ally, by the adjoint method. Proje tion ltering te h- niques are applied, in order to guarantee topologies free of ommon numeri al instabilities in topology optimization, and optimized designs near the 0/1 solution for the physi al densities.

Neste trabalho estudamos a continuidade da dinâmica assintótica relativamente a perturbações e, em particular, exploramos a obtenção de melhorias para as taxas de convergência de atratores globais através da introdução de fatores de correção, inspirados pelos resultados da teoria de homogeneização e nos trabalhos de (BABIN; VISHIK, 1992) e (CARVALHO; CHOLEWA, 2011), e através da introdução de mecanismos que melhoram a transferência da taxa de convergência de semigrupos para a taxa de convergência de atratores, inspirados pelos trabalhos (SANTAMARÍA, 2013) e (BABIN; VISHIK, 1992; CARVALHO; CHOLEWA, 2011). A proposta inicial está centrada na obtenção de melhores taxas de convergência de atratores globais através da obtenção de equiatração e da melhoria da taxa de convergência dos semigrupos. Para isto, buscamos melhorar a taxa de convergência do resolvente dos operadores setoriais envolvidos, por meio de uma perturbação singular do resolvente limite que ainda gere uma família de operadores setoriais com resolventes que aproximam o resolvente do problema limite e aproximam melhor os resolventes das perturbações iniciais. Feito isto, obtemos uma melhora imediata de convergência dos semigrupos lineares, depois dos não lineares (através da fórmula da variação das constantes). Motivados pelos resultados de (SANTAMARÍA, 2013), que oferecem uma menor perda na transferência das taxas de convergência dos semigrupos para as taxas de convergência dos atratores, buscamos melhor compreender a propriedade Lipschitz Shadowing, que é responsável direta pela obtenção da taxa de convergência dos atratores diretamente da taxa de convergência dos semigrupos. Isto nos levou a descobrir que podemos obter as propriedade Lipschitz Shadowing e estabilidade estrutural para perturbações Lipschitz de semigrupos Morse-Smale. / Here we compare the continuity of the asymptotic dynamics with respect to perturbations and, in particular, we explored to obtain improvement of rates of convergence of the global attractor through the introduction of correction factors, inspired by the results of homogenization theory and work of (BABIN; VISHIK, 1992) and (CARVALHO; CHOLEWA, 2011), and the introduction of mechanisms that improve the transference of the convergence rate of semigroups to the convergence rate of attractors, inspired by the work of (SANTAMARÍA, 2013) and (BABIN; VISHIK, 1992; CARVALHO; CHOLEWA, 2011). The initial proposal is focused on achieving best rates of convergence of the global attractors by obtaining equi-atraction and improving the convergence rate of semigroups. For this, we seek to improve the rate of convergence of the resolvents of sectorial operators, through a singular perturbation of the resolvent associated with the limit problem and generate a new family of sectorial operators whose resolvents both approximate the resolvent of the limit problem as they were closer to the resolvents the initial perturbation. Having done this, we obtain an immediate improvement of convergence of linear semigroups, after the non-linear (using the variation of constants formula). Motivated by the results of (SANTAMARÍA, 2013), which offer an improvement in obtaining convergence rates, we seek to study property better Lipschitz Shadowing, which is basically responsible for obtaining the distance of the attractors directly from the convergence rate of the semigroups. This has led us to discover that we can both preserve the Lipschitz Shadowing property under Lipschitz perturbations of Morse-Smale semigroups, and The geometric stability of the attractors.

Este trabalho aborda a formulação geométrica das teorias clássicas de calibre, ou Yang-Mills, considerando-as como uma importante classe de modelos que deve ser incluída em qualquer tentativa de estabelecer um formalismo matemático geral para a teoria clássica dos campos. Tal formulação deve vir em (pelo menos) duas variantes: a versão hamiltoniana, que passou por uma fase de desenvolvimento rápido durante os últimos 10-15 anos, levando ao que hoje é conhecido como o ``formalismo multissimplético\'\', e a mais tradicional versão lagrangiana utilizada nesta tese. O motivo principal justificando tal investigação é que teorias de calibre constituem os mais importantes exemplos de sistemas dinâmicos que são altamente relevantes na Física e onde a equivalência entre a versão lagrangiana e a versão hamiltoniana, que no caso de sistemas não-singulares é estabelecida pela transformação de Legendre, deixa de ser óbvia, pois teorias de calibre são sistemas degenerados do ponto de vista lagrangiano e são sistemas vinculados do ponto de vista hamiltoniano. Esta propriedade característica das teorias de calibre é uma consequência direta do seu alto grau de simetria, isto é, da sua invariância de calibre. No entanto, numa formulação plenamente geométrica da teoria clássica dos campos, capaz de incorporar situações topologicamente não-triviais, a invariância sob transformações de calibre locais (transformações de calibre de segunda espécie) e, surpreendentemente, até mesmo a invariância sob as transformações de simetria globais correspondentes (transformações de calibre de primeira espécie) não podem ser adequadamente descritas em termos de grupos de Lie e suas ações em variedades, mas requerem a introdução e o uso sistemático de um novo conceito, a saber, fibrados de grupos de Lie e suas ações em fibrados (sobre a mesma variedade base). A meta principal da presente tese é tomar os primeiros passos no desenvolvimento de ferramentas matemáticas adequadas para lidar com este novo conceito de simetria e, como uma primeira aplicação, dar uma definição clara e simples do procedimento de ``acoplamento mínimo\'\' e uma demonstração simples do teorema de Utiyama, segundo o qual lagrangianas para potenciais de calibre (conexões) de primeira ordem (i.e., que dependem apenas dos próprios potenciais de calibre e de suas derivadas parciais até primeira ordem) que são invariantes sob transformações de calibre são necessariamente funções dos campos de calibre (i.e., do tensor de curvatura) invariantes sob as transformações de simetria globais correspondentes. / This thesis deals with the geometric formulation of classical gauge theories, or Yang-Mills theories, regarded as an important class of models that must be included in any attempt to establish a general mathematical framework for classical field theory. Such a formulation must come in (at least) two variants: the hamiltonian version which has gone through a phase of rapid development during the last 10-15 years, leading to what is now known as the ``multisymplectic formalism\'\', and the more traditional lagrangian version studied in this thesis. The main motivation justifying this kind of investigation is that gauge theories constitute the most important examples of dynamical systems that are highly relevant in physics and where the equivalence between the lagrangian and the hamiltonian version, which for non-singular systems is established through the Legendre trans% formation, is far from obvious, since gauge theories are degenerate systems from the lagrangian point of view and are constrained systems from the hamiltonian point of view. This characteristic property of gauge theories is a direct consequence of their high degree of symmetry, that is, of gauge invariance. However, in a fully geometric formulation of classical field theory, capable of incorporating topologically non-trivial situations, invariance under local gauge transformations (gauge transformations of the second kind) and, surprisingly, even invariance under the corresponding global symmetry transformations (gauge transformations of the first kind) cannot be described adequately in terms of Lie groups and their actions on manifolds but requires the introduction and systematic use of a new concept, namely Lie group bundles and their actions on fiber bundles (over the same base manifold). The main goal of the present thesis is to take the first steps in developing adequate mathematical tools for handling this new concept of symmetry and, as a first application, give a simple clear-cut definition for the prescription of ``minimal coupling\'\' and a simple proof of Utiyama´s theorem, according to which lagrangians for gauge potentials (connections) that are gauge invariant and of first order, i.e., dependent only on the gauge potentials themselves and on their partial derivatives up to first order, are necessarily functions of the gauge field strengths (i.e., the curvature tensor) invariant under the corresponding global symmetry transformations.

Ce travail de thèse est une contribution au projet national AMOCOPS, financé par l’ANR. Le thème central du projet est la diffusion de lumière par des particules de formes complexes et de grandes tailles (plusieurs dizaines de µm au moins), domaine où les méthodes de simulation numérique existantes trouvent leurs limites d’applicabilité. Nous abordons le problème par le biais des effets mécaniques de la lumière, autrement dit les forces et couples créés par la pression de radiation. Etant la conséquence du transfert d’impulsion entre l’onde et la matière, ces effets sont directement liés à la diffusion de lumière. La thèse comprend une partie expérimentale –majoritaire- concernant les réponses mécaniques de particules de polystyrène de forme ellipsoïdale et d’allongement variable sous illumination par un ou deux faisceaux laser. Les cas de faisceaux faiblement focalisés (lévitation optique) et d’un faisceau très fortement focalisé (pincette optique) sont examinés successivement. Nous caractérisons différents types d’équilibre statique, certains d’entre eux non décrits auparavant, obtenus dans les deux géométries. Par ailleurs nous confirmons l’existence de réponses purement dynamiques, où la particule oscille en permanence. Trois nouveaux modes sont observés, deux dans la géométrie lévitation optique et un autre sous pincette optique. Cette étude nous permet de distinguer les oscillations dites de Simpson-Hanna dans le régime linéaire de celles non linéaires mises en évidence avant nous par Mihiretie et al..Les résultats de nos expériences sont comparés à ceux obtenus par les simulations de J.C. Loudet, sur la base de la simple optique géométrique (OG) et limitées à 2 dimensions (2d). Nous montrons que ces simulations permettent de reproduire qualitativement et comprendre physiquement la plupart des comportements observés dans nos expériences. La principale limitation de ces calculs tient à ce que l’OG ignore le caractère ondulatoire de la lumière. Pour faire mieux et aller vers des simulations fiables quantitativement, il faut développer un modèle alliant optique géométrique et optique ondulatoire. C’est la fonction du modèle VCRM (Vectorial Complex Ray Model) développé récemment par K.F. Ren en 2d. Le but du projet Amocops est de mettre au point la version 3d de la méthode et de la valider sur la base d’expériences comme celles que nous avons conduites. La deuxième partie de la thèse est consacrée à la méthode VCRM. Nous en exposons les principes, et nous présentons quelques résultats des travaux en cours avec une version intermédiaire entre 2d et 3d, dite « 2d+ ». Quelques illustrations sont proposées sur des exemples impliquant des sphères et ellipsoïdes de grandes tailles. / This work is a contribution to the “AMOCOPS” project, funded by Agence Nationale de la Recherche. AMOCOPS is dedicated to the development of new computation schemes to simulate the light scattering patterns of large complexly shaped particles. Particle sizes are of the order of several 10s of micrometres, which is at the limit, or beyond the capabilities of currently available computation techniques.Our work indirectly deals with light scattering through the corresponding mechanical effects of light. Light scattering is the source of momentum transfer between light and matter, and therefore of the forces and torques acting on the exposed particles. The majority of Part A of this thesis is about the mechanical responses of ellipsoidal polystyrene particles of varying aspect ratios, under illumination by one or two laser beams. We investigate the case of weakly focused beams (optical levitation), and that of a single large aperture beam (optical tweezers). Different types of static equilibria, some of which are new, are observed and characterized in both geometries. We confirm the existence of dynamic states, whereby the particle permanently oscillates within the laser beam(s). Three new oscillation modes are observed, two of them in the conditions of optical levitation, and another one in the optical tweezer geometry. The study allows us to make a distinction between noise-driven oscillations in the linear regime, of the type predicted by Simpson and Hanna, and nonlinear oscillations such as those evidenced prior to this work, by Mihiretie et al..Results from our experiments are compared to simulations by J.C. Loudet, using simple ray-optics (RO) in two dimensions (2D). We show that results from 2D-RO qualitatively match most of our observations, and allow us to physically understand the main mechanisms at work in the observed phenomena. The simulations cannot be quantitatively exact, due to the 2D limitation, and because RO essentially ignores the wave nature of light. In Part B of the manuscript, we present the principles of the Vectorial Complex Ray Model (VCRM), which was recently developed by K.F. Ren in 2d. The goal of AMOCOPS is to develop a full 3D version of VCRM, able to simulate light scattering by particles of any shape with a smooth surface. We explain the basics of the model, as well as the “2D+” version, which is an extension of the basic 2D-VCRM. A few illustrative examples of light scattering patterns computed with 2d+-VCRM for large-sizes spheres and ellipsoids are presented

The present thesis is divided into two parts. Part I is devoted to the study of Gribov ambiguity in gauge systems and its relation with the appearance of degeneracies in the symplectic structure of the corresponding reduced phase space after gauge fixation. Part II is concerned with classical dual field theories for three-dimensional Einstein gravity and the symplectic structure on coadjoint orbits of the corresponding asymptotic symmetry group.In Part I, the Gribov problem is studied in the context of finite temperature QCD and the structure of the gluon propagator is analyzed. The standard confined scenario is found for low temperatures, while for high enough temperatures deconfinement takes place and a free gluon propagator is obtained. Subsequently, the relation between Gribov ambiguity and degeneracies in the symplectic structure of gauge systems is analyzed. It is shown that, in finite-dimensional systems, the presence of Gribov ambiguities in regular constrained systems always leads to a degenerate symplectic form upon Dirac reduction. The implications for the Gribov-Zwanziger approach to QCD and the symplectic structure of the theory are discussed. In Part II, geometrical actions for three-dimensional Einstein gravity are constructed by studying the symplectic structure on coadjoint orbits of the asymptotic symmetry group. The geometrical action coming from the Kirillov-Kostant symplectic form on coadjoint orbits is analyzed thought Dirac's algorithm for constrained systems. By studying the case of centrally extended groups and semi-direct products, the symplectic structure on coadjoint orbits of the Virasoro and the BMS3 group are analyzed. This allows one to associate separate geometric actions to each coadjoint orbit of the solution space, leading to two-dimensional dual fiel theories for asymptotically AdS and asymptotically flat three-dimensional gravity respectively. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Aujourd’hui, l’accès à l’espace constitue un enjeu scientifique, technologique et politique d’importance. Il est primordial de pouvoir garantir le succès de la mise sur orbite des satellites pour un coût de transport minimal. Les lanceurs tels qu’Ariane 5 sont soumis à des fluctuations de pression pouvant induire des efforts instationnaires repris par les vérins du moteur Vulcain. Ces efforts s’exercent notamment dans la zone décollée du culot du lanceur normalement à l’axe de la poussée et sont qualifiés de charges latérales. Du point de vue de la simulation numérique, l’étape de discrétisation des éléments technologiques du lanceur rend la génération de maillages structurés particulièrement complexe. Cette constatation conduit à la présente étude. Dans le but d’évaluer l’influence des effets technologiques sur la prévision des charges latérales pour des configurations réalistes de lanceur, la thématique des frontières immergées est étudiée. L’objectif est de développer une stratégie numérique permettant d’accroître le niveau de complexité de la géométrie considérée tout en conservant la précision des résultats des études antérieures sur des configurations simplifiées. Cette stratégie s’inscrit dans le cadre de simulations numériques ZDES d’écoulements massivement décollés d’arrière-corps, à haut nombre de Reynolds et en régime compressible. Les capacités de la méthodologie développée sont évaluées sur des cas tests numériques canoniques avant d’être éprouvées sur des configurations simplifiées de lanceur. Enfin, l’effet de cette stratégie sur la prévision des charges latérales est étudié. / Nowadays, access to space has become a great issue in scientific, technological and political framework. It is essential to ensure the success of the placing of orbiting satellites with a minimal flight cost. Launchers, as the Ariane 5 space launcher, are subject to pressure fluctuations which can lead to unsteady loads on the actuators of the Vulcain engine. These loads occur especially in the separated zone of the launcher base flow and act normally to the thrust axis. They are referred to as side loads. From the numerical simulation perspective, the launcher technological elements discretization process makes the generation of structured mesh particularly difficult. The present study lies within such a framework. In order to assess the influence of the technological effects on the side loads prediction for realistic launcher configurations, immersed boundaries are studied. The aim is to develop a numerical strategy able to increase the level of geometrical complexity of the geometry at stake while maintaining the accuracy of the results of previous studies on simplified configurations. This strategy fits into numerical simulations of ZDES type of separating/reattaching flows at high Reynolds number and compressible regime. The abilities of the methodology are first assessed on canonical numerical test cases. Then, the strategy is applied on simplified launcher configurations. Finally, the effect of this strategy on the side loads prediction is assessed.

Esta dissertação de Mestrado tem por objetivo principal investigar as possibilidades de uso dos programas de simulação computacional no campo de isomeria geométrica no contexto da escola pública. Para contemplar esse objetivo, a referida pesquisa foi constituída a partir de uma pesquisa bibliográfica e de um estudo de caso numa escola pública. O referencial teórico foi construído para investigar os efeitos do uso de programas computacionais no ensino de isomeria geométrica; realizamos entrevistas semiestruturadas com três professores de uma escola, situada na cidade de Caxias do Sul, no estado do Rio Grande do Sul, a fim de contrastar os interlocutores teóricos e empíricos. A partir do conjunto de informações oriundas do contexto escolar, associadas à fundamentação teórica, foi possível apontar um conjunto de resultados: i) a escola apresenta baixo nível de utilização da tecnologia no ensino; ii) o acesso ao laboratório de química e de informática é prejudicado pela burocracia; iii) o professor atua com sobrecarga de trabalho; iv) as capacitações ou formações continuadas para os professores são insuficientes; v) a carga horária para o ensino de Química foi drásticamente reduzida em comparação a anos anteriores; vi) há falta de empenho dos estudantes. Dentro desse contexto, classifica-se essa pesquisa por meio de uma abordagem exploratória, onde usou-se a técnica qualitativa de Análise Textual Discursiva (ATD) para compreender o corpus de pesquisa. Além disso, no que tange ao uso de programas de simulação, os resultados da consulta à bibliografia atestam que os programas computacionais são importantes ferramentas de apoio ao ensino de isomeria geométrica, pois melhoram a visualização entre os três níveis de representação da Química (macroscópico, microscópico e simbólico) meio da criação de moléculas em duas dimensões e a conversão destas para a forma tridimensional. Observamos que os estudantes, nativos digitais, são hábeis no manuseio de aplicativos computacionais. Complementarmente os professores entrevistados declararam não fazer uso de programas computacionais por uma série de razões: horários de aula reduzidos, desconhecimento dos programas e seu uso, poucas oportunidades de formação continuada. Portanto, nosso estudo sugere que se deva romper a visão tradicional do ensino da química (segundo a qual bastaria dotar as escolas de recursos de informática) para mudar as práticas pedagógicas. É necessário transgredir esse modelo e pensar em metodologias que se voltem aos fundamentos das disciplinas, que atendam ao processo de construção do conhecimento, promovendo assim a ascensão de um ensino de Química voltado à formação de estudantes críticos. / This dissertation main to investigate possibilities in apply computer simulation programs based on geometrical isomerism in the context of public school. A literature review and case study in public school was carried out to attend that target. Literature review had been focused on computer programs effects in teaching geometrical isomerism; we also made individual semi-structured interviews with three teachers at High school in Caxias do Sul city, Rio Grande do Sul state, to contrast the theoretical and empirical interlocutors. Based on these set of answer and on literature review we find a group of results: i) the school applies a low level of teaching technology; ii) there is a lot of bureaucracy to access chemistry and technology information labs; iii) teacher has workload; iv) teachers continuous learning is less than expected; v) time for chemistry class has been reduced over years; vi) there are students with low interest. Looking for this context, we classify this research as exploratory approach, where a qualitative technique called Textual Discoursive Analysis (DTA) was applied to understand the contests of interviews. Moreover, regarding computer programs literature results show these programs such as important tools to teach geometrical isomerism, because they improve an overview between Chemistry three levels (macroscopic, microscopic and symbolic) representation and it creates dual dimension molecules and convert them for tri-dimension molecules. We observe that digital native students are more skilled in computer simulation than others. Teachers interviewed declare do not use computer simulation because: they do not have time at class, knowledge limited about computer programs and how to apply it, few opportunities to continuous learning. Therefore, our study proposes a break on traditional chemistry teaching (where information technology is implemented) to changes in the pedagogical practices. It is necessary to overpass that model and to think in methodologies focused on course fundaments, which meet to knowledge build process, and allow a Chemistry teaching applied to educate critical students.

In this paper we show how to give an intrinsic definition of a constructible circle on the sphere. The classical definition of constructible circle in the plane, using straight edge and compass is there by translated in ters of so called Lenart tools. The process by which we achieve our goal involves concepts from the algebra of Hermitian matrices, complex variables, and Sterographic projection. However, the discussion is entirely elementary throughout and hopefully can serve as a guide for teachers in advanced geometry.

This diploma thesis deals with analysis of the conformity assessment procedure of a torque converter body with its specification. The individual goals were to analyse the part specification, the current procedure for assessing compliance with the specification and to formulate practical recommendations. The first chapter is the introduction. The second chapter deals with the correct dimensioning of part geometry. In the third chapter, the customer's part specification was analysed. In the fourth chapter, the current conformity assessment procedure was analysed. In the last chapter, practical recommendations were presented.