Cette thèse est dédiée à la modélisation et à l'analyse mathématique de modèles asymptotiques utilisés en océanographie décrivant la propagation des ondes internes à l'interface entre deux couches de fluides de densités différentes, soumis à la seule force de gravité.L'objectif de cette thèse est de construire et justifier de nouveaux modèles asymptotiques prenant en compte la variation de la topographie. Pour ce faire, on pose plusieurs hypothèses de petitesse sur la profondeur de l'eau et sur les déformations à l'interface et au fond. On s'intéresse plus particulièrement à deux régimes de variations topographiques, celui de moyenne amplitude et celui de lentes variations de grande amplitude.La première partie de cette thèse consiste à justifier rigoureusement et étudier mathématiquement (existence, unicité, stabilité et convergence de la solution) deux classes de modèles asymptotiques. Une classe de modèles couplés et une classe de modèles scalaires. Cette dernière classe est caractérisée par la description de la propagation unidirectionnelle des ondes internes.Dans la deuxième partie on propose un schéma numérique pour résoudre le modèle asymptotique couplé dérivé dans la première partie dans le cadre d'un font plat. Ce modèle existant dans la littérature a été reformulé d'une façon plus appropriée pour la résolution numérique en gardant le même ordre de précision que l'original et en améliorant ses propriétés de dispersion. Enfin nous présentons plusieurs simulations numériques pour valider notre schéma. / This thesis is dedicated to the modeling and the mathematical analysis of asymptotic models used in oceanography describing the propagation of internal waves at the interface between two layers of fluids of different densities, under the only influence of gravity.We aim here at constructing and justifying new asymptotic models taking into account variable topography. To this end, we assume several smallness assumptions on the depth of the water and on the deformations at the interface and at the bottom. We are interested in two topographic regimes, one for variations of medium amplitude and one for slow variations with large amplitude.In the first part of this thesis we rigorously justify and mathematically study (existence, uniqueness, stability and convergence of the solution) two classes of asymptotic models. A class of coupled models and a class of scalar models. The latter class is characterized by the description of the propagation of unidirectional internal waves. In the second part we propose a numerical resolution for the coupled asymptotic model derived in the first part restricted to the flat bottom case. This existing model in the literature has been rewritten under a new formulation more suitable for numericalresolution with the same order of precision as the standard one but with improved frequency dispersion. Finally, we present several numerical simulations to validate our scheme.

Neste trabalho, são caracterizadas as soluções do tipo ondas planas e modais de modelos matemáticos referentes à teoria de linhas de transmissão, com e sem perdas, e à teoria de vigas, modelo de Timoshenko e modelo não local de Eringen. Os modelos são formulados matricialmente, e as ondas em questão são determinadas em termos da base gerada pela resposta matricial fundamental de sistemas de equações diferenciais ordinárias de primeira, segunda e quarta ordem. A resposta matricial fundamental é utilizada numa forma fechada que envolve o acoplamento de um número finito de matrizes e uma função escalar geradora e suas derivadas. A função escalar geradora é bem comportada para mudanças em torno de frequências críticas e sua robustez é exibida através da técnica de Liouville. As ondas modais são decompostas em termos de uma parte que viaja para frente e uma parte que viaja para trás. Essa decomposição é utilizada para fornecer matrizes de reflexão e transmissão em descontinuidades e condições de contorno. No contexto das linhas de transmissão são consideradas uma junção de linhas com impedâncias características diferentes ou uma carga em uma extremidade da linha. Na teoria de Timoshenko são consideradas uma fissura ou condições de contorno em uma das extremidades. Exemplos numéricos com descontinuidade são considerados na viga. Na teoria de linhas de transmissão exemplos com multicondutores são considerados e observações são realizadas sobre a decomposição das ondas modais. No modelo não local de Eringen, para vigas bi-apoiadas é discutida a existência do segundo espectro de frequências. / Plane type solutions and modal waves of mathematical models, which refer to transmission lines theory, both lossless and lossy, and to beam theory, using both Timoshenko and nonlocal Eringen models, are being characterized in this work. The models are formulated in matrix form, and the waves are determined in terms of matrix basis generated by fundamental matrix response of systems of ordinary differential equations of first, second and fourth order. The fundamental matrix response is used in the closed-form, which involve the coupling between a number finite of matrices of a generating scalar function and its derivatives. The generating scalar function is well behaved for changes around critical frequencies and its robustness is exhibited through the Liouville technique. Modal waves are decomposed in forward and backward parts. This decomposition is used for providing reflection and transmission matrices when dealing with discontinuities and boundary conditions. In the context of transmission lines junction of lines with different characteristic impedances or a load at one end of the line are being considered. In Timoshenko’s theory the crack problem or boundary conditions at one end are also being considered. Numerical examples with discontinuities are considered in the context of beams. Numerical examples with discontinuities and boundary value problems were approached using modal wave decomposition. In transmission line theory examples with multiconductors are considered and observations are made about decomposition of the modal waves. In the nonlocal of Eringen model, for bi-supported beams, the existence of the second frequency spectrum is discussed.

Suite à la découverte du boson de Higgs en Juin 2012 au Large Hadron Collider, l’accélérateur de particules situé à la frontière franco-suisse, l’étude du secteur scalaire des particules élémentaires a connu un regain d’intérêt. En particulier, le boson de Higgs étant une particule clef au sein du Modèle Standard des particules, les expérimentateurs étudient ses propriétés avec beaucoup de soin.Le Modèle Standard, dont le but est de décrire les interactions entre particules élémentaires, n’est cependant pas une théorie complète. En effet, en plus de quelques problèmes d’ordre théorique, certains phénomènes observés expérimentalement ne peuvent pas être expliqués par ce modèle. Les théoriciens en physique des particules cherchent donc à établir une nouvelle théorie venant le compléter et permettant d’expliquer pleinement les observations expérimentales.Cette thèse est axée sur l’étude du secteur scalaire de modèles au-delà du Modèle Standard des particules. J’ai plus particulièrement travaillé sur un modèle à deux doublets de Higgs – modèle purement effectif mais qui peut être inclus dans d’autres théories plus abouties – ainsi que sur un modèle construit comme une combinaison entre les théories déjà très proches de techicouleur et de Higgs composites, et ce dans le cas particulier d’une brisure de symétrie SU (4) ? Sp(4). J’ai étudié ce dernier modèle d’un point de vue effectif mais la théorie complète est capable depallier un certain nombre des limitations du Modèle Standard.Chacun de ces modèles inclut un secteur scalaire plus riche que celui du Modèle Standard et contient au moins une particule pouvant être assimilée au boson de Higgs découvert au LHC. J’ai réalisé l’étude phénoménologique de chacun de ces modèles et les ai confrontés à des contraintes tant théoriques qu’expérimentales – en particulier celles obtenues grâce aux études les plus récentes, portant sur le boson de Higgs et sur de potentielles particules scalaires additionnelles, réalisées par les équipes du LHC. Cela m’a permis de contraindre les paramètres libres des modèles et en particulier de restreindre les valeurs possibles pour la masse des autres particules scalaires, permettant de mieux cibler les zones où ces nouvelles particules, si elles existent, pourraient être détectées au LHC.Ces deux théories, bien que très contraintes par les données expérimentales, ne sont toujours pas exclues par les contraintes expérimentales les plus récentes / Following the discovery of the Higgs boson in June 2012 at the Large Hadron Collider, the particle collider located beneath the France-Switzerland border, interest in the study of the scalar sector in elementary particle physics significantly increased. In particular, as the Higgs boson plays a very special role in the Standard Model of particle physics, experimentalists study its properties with great care.The goal of the Standard Model is to describe the interactions between elementary particles. However the theory is not quite complete. Indeed, in addition to some purely theoretical problems, a number of experimental observations cannot be explained by the Standard Model. Theorists are therefore looking for a more comprehensive theory able to fully explain the observations.This thesis is based on the study of the scalar sector of two different extensions of the Standard Model of particle physics. I have worked on the Two-Higgs Doublet Model – this model is purely effective but can be included in more comprehensive theories – as well as on a model based on a combination of Technicolor and Composite Higgs theories in the framework of the SU (4) ? Sp(4) symmetry breaking pattern. I studied the latter via an effective approach but the full theory is able to get rid of some of the pitfalls of the Standard Model.These two models include a scalar sector that is richer than the one found in the Standard Model and contain at least one particle which can be assimilated to the Higgs boson discovered at the LHC.I performed a phenomenological study for these two models and tested them against both theoretical and experimental constraints. In particular I used the latest studies on the 125 GeV Higgs boson and on possible additional scalars performed by the ATLAS and CMS collaborations. The application of all these constraints drastically reduced the available parameter space of the two models. In particular it narrowed the possible mass range of the additional scalars, allowing to know more accurately where to search them experimentally in order to prove or rule out their possible existence.As of today the two theories I worked on are still not excluded by the latest experimentaldata

Neste trabalho desenvolveu-se e implementou-se um modelo computacional paralelo multifísica para a simulação do transporte de substâncias e do escoamento hidrodinâmico, bidimensional (2D) e tridimensional (3D), em corpos de água. Sua motivação está centrada no fato de que as margens e zonas costeiras de rios, lagos, estuários, mares e oceanos são locais de aglomerações de seres humanos, dada a sua importância para as atividades econômica, de transporte e de lazer, causando desequilíbrios a esses ecossistemas. Esse fato impulsiona o desenvolvimento de pesquisas relativas a esta temática. Portanto, o objetivo deste trabalho é o de construir um modelo computacional com alta qualidade numérica, que possibilite simular os comportamentos da hidrodinâmica e do transporte escalar de substâncias em corpos de água com complexa configuração geométrica, visando a contribuir para seu manejo racional. Visto que a ênfase nessa tese são os aspectos numéricos e computacionais dos algoritmos, analisaram-se as características e propriedades numérico-computacionais que as soluções devem contemplar, tais como a estabilidade, a monotonicidade, a positividade e a conservação da massa. As estratégias de soluções enfocam os termos advectivos e difusivos, horizontais e verticais, da equação do transporte. Desse modo, a advecção horizontal é resolvida empregando o método da limitação dos fluxos de Sweby, e o transporte vertical (advecção e difusão) é resolvido com os métodos beta de Gross e de Crank-Nicolson. São empregadas malhas com distintas resoluções para a solução do problema multifísica. O esquema numérico resultante é semi-implícito, computacionalmente eficiente, estável e fornece acurácia espacial e temporal de segunda ordem. Os sistemas de equações resultantes da discretização, em diferenças finitas, das equações do escoamento e do transporte 3D, são de grande porte, lineares, esparsos e simétricos definidos-positivos (SDP). No caso 2D os sistemas são lineares, mas os sistemas de equações para a equação do transporte não são simétricos. Assim, para a solução de sistemas de equações SDP e dos sistemas não simétricos empregam-se, respectivamente, os métodos do subespaço de Krylov do gradiente conjugado e do resíduo mínimo generalizado. No caso da solução dos sistemas 3-diagonal, utiliza-se o algoritmo de Thomas e o algoritmo de Cholesky. A solução paralela foi obtida sob duas abordagens. A decomposição ou particionamento de dados, onde as operações e os dados são distribuídos entre os processos disponíveis e são resolvidos em paralelo. E, a decomposição de domínio, onde obtém-se a solução do problema global combinando as soluções de subproblemas locais. Em particular, emprega-se neste trabalho, o método de decomposição de domínio aditivo de Schwarz, como método de solução, e como pré-condicionador. Para maximizar a relação computação/comunicação, visto que a eficiência computacional da solução paralela depende diretamente do balanceamento de carga e da minimização da comunicação entre os processos, empregou-se algoritmos de particionamento de grafos para obter localmente os subproblemas, ou as partes dos dados. O modelo computacional paralelo resultante mostrou-se computacionalmente eficiente e com alta qualidade numérica. / A multi-physics parallel computational model was developed and implemented for the simulation of substance transport and for the two-dimensional (2D) and threedimensional (3D) hydrodynamic flow in water bodies. The motivation for this work is focused in the fact that the margins and coastal zones of rivers, lakes, estuaries, seas and oceans are places of human agglomeration, because of their importance for economic, transport, and leisure activities causing ecosystem disequilibrium. This fact stimulates the researches related to this topic. Therefore, the goal of this work is to build a computational model of high numerical quality, that allows the simulation of hydrodynamics and of scalar transport of substances behavior in water bodies of complex configuration, aiming at their rational management. Since the focuses of this thesis are the numerical and computational aspects of the algorithms, the main numerical-computational characteristics and properties that the solutions need to fulfill were analyzed. That is: stability, monotonicity, positivity and mass conservation. Solution strategies focus on advective and diffusive terms, horizontal and vertical terms of the transport equation. In this way, horizontal advection is solved using Sweby’s flow limiting method; and the vertical transport (advection and diffusion) is solved with Gross and Crank-Nicolson’s beta methods. Meshes of different resolutions are employed in the solution of the multi-physics problem. The resulting numerical scheme is semi-implicit, computationally efficient, stable and provides second order accuracy in space and in time. The equation systems resulting of the discretization, in finite differences, of the flow and 3D transport are of large scale, linear, sparse and symmetric positive definite (SPD). In the 2D case, the systems are linear, but the equation systems for the transport equation are not symmetric. Therefore, for the solution of SPD equation systems and of the non-symmetric systems we employ, respectively, the methods of Krylov’s sub-space of the conjugate gradient and of the generalized minimum residue. In the case of the solution of 3-diagonal systems, Thomas algorithm and Cholesky algorithm are used. The parallel solution was obtained through two approaches. In data decomposition or partitioning, operation and data are distributed among the processes available and are solved in parallel. In domain decomposition the solution of the global problem is obtained combining the solutions of the local sub-problems. In particular, in this work, Schwarz additive domain decomposition method is used as solution method and as preconditioner. In order to maximize the computation/communication relation, since the computational efficiency of the parallel solution depends directly of the load balancing and of the minimization of the communication between processes, graph-partitioning algorithms were used to obtain the sub-problems or part of the data locally. The resulting parallel computational model is computationally efficient and of high numerical quality.

This dissertation has as base Jocelino Sato and Vicente de Souza Neto's paper called Complete and Stable O(p + 1) x O(q + 1)-Invariant Hypersurfaces with Zero Scalar Curvature in Euclidean Space Rp+q+2, published on the Annals of Global Analysis and Geometry - 29 in 2006. The main result of this dissertation is the Classi_cation Theorem, which states: The O(p+1) x O(q+1)-Invariant Hypersurfaces in Rp+q+2, p; q > 1, with zero scalar curvature belong to one of the following classes: (1) Cones with a singularity at the orign of Rp+q+2; (2) Hypersurfaces having one orbit of singularity and asymptoting both of the cones Cα and Cβ; (3) Regular hypersurfaces asymptoting the cone Cα; (4) Regular hypersurfaces asymptoting the cone Cβ; (5) Regular hypersurfaces asymptoting both of the cones Cα and Cβ. It was reached by the studies of the ordinary differential equation on R2, involving the coordenate curves that generate these hypersurfaces. Such differential equation, in its turn, is associated with a vector field X : R22 → R2 on the plan. The study of the orbits space in this field is essential; after all, because of it, it was possible to translate the X orbits' behavior into information concerning the profile curves and, finally, reach the theorem. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Esta dissertação está baseada no artigo de Jocelino Sato e Vicente de Souza Neto intitulado Complete and Stable O(p+1) x O(q+1) - Invariant Hypersurfaces with Zero Scalar Curvature in Euclidean Space Rp+q+2, publicado na revista Annals of Global Analysis and Geometry, volume 29, em 2006. O principal resultado desta dissertação é o Teorema de Classicação, que afirma o seguinte: Uma hipersuperfície Mp+q+1 que é invariante pela açãoao do grupo O(p + 1) x O(q + 1), p; q > 1, com curvatura escalar identicamente nula deve pertencer a uma das seguintes classes: (1) Cones com uma singularidade na origem de Rp+q+2; (2) Hipersuperfícies possuindo uma órbita de singularidades e assintotando ambos os cones Cα e Cβ; (3) Hipersuperfícies regulares que assintotam o cone Cα; (4) Hipersuperfícies regulares que assintotam o cone Cβ; (5) Hipersuperfícies regulares que assintotam ambos os cones Cα e Cβ. A demonstração do teorema requer um estudo de uma equação diferencial ordinária envolvendo as coordenadas das curvas, no plano, que geram estas hipersuperfícies. Esta equação diferencial, por sua vez, está associada a um campo de vetores X : R2 → R2 no plano. O estudo do retrato de fase deste campo é fundamental. Através dele, foi possível traduzir o comportamento das trajetórias de X em informações com respeito às curvas geratrizes e desta maneira obter o teorema.

SANTOS, A. S. L. Problema de Yamabe modificado em variedades compactas de dimensão quatro e métricas críticas do funcional curvatura escalar. 2017. 58 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-05-25T19:34:47Z No. of bitstreams: 1 2017_tese_aslsantos.pdf: 535461 bytes, checksum: 8c3ddbdd33d74c4eb7b265354b3bafb3 (MD5) / Rejected by Rocilda Sales (rocilda@ufc.br), reason: Boa tarde, Eu revisei a Tese de ALEX SANDRO LOPES SANTOS, e encontrei um pequeno erro na capa, ele colocou os seguintes elementos: UNIVERSIDADE FEDERAL DO CEARÁ CENTRO DE CIÊNCIAS PROGRAMA DE PÓS-GRADUAÇÃO EM MATEMÁTICA DOUTORADO EM MATEMÁTICA Mas deve ser alterado para: UNIVERSIDADE FEDERAL DO CEARÁ CENTRO DE CIÊNCIAS DEPARTAMENTO DE MATEMÁTICA PROGRAMA DE PÓS-GRADUAÇÃO EM MATEMÁTICA Com os demais elementos da Tese, não há nenhum problema de formatação. Atenciosamente, on 2017-05-26T15:06:03Z (GMT) / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-05-29T13:47:44Z No. of bitstreams: 1 2017_tese_aslsantos.pdf: 536279 bytes, checksum: f37ece7d8035a2d9c788c45d2e7807ae (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-05-29T14:08:17Z (GMT) No. of bitstreams: 1 2017_tese_aslsantos.pdf: 536279 bytes, checksum: f37ece7d8035a2d9c788c45d2e7807ae (MD5) / Made available in DSpace on 2017-05-29T14:08:17Z (GMT). No. of bitstreams: 1 2017_tese_aslsantos.pdf: 536279 bytes, checksum: f37ece7d8035a2d9c788c45d2e7807ae (MD5) Previous issue date: 2017-05-19 / In the fisrt part of this work we investigate the modified Yamabe problem on four-dimensional manifolds whose the modifiers invariants depending on the eigenvalues of the Weyl curvature tensor and they are described in terms of maximum and minimum of the biorthogonal (sectional) curvature. We provide some geometrical and topological properties on four-dimensional manifolds in terms of these invariants. In the second part we investigate the critical points of the total scalar curvature functional restricted to space of metrics with constant scalar curvature of unitary volume, for simplicity CPE metrics. It was conjectured in the 1980’s that every CPE metric must be Einstein. We prove that such a conjecture is true under a second-order vanishing condition on the Weyl tensor. / Na primeira parte deste trabalho investigamos o problema de Yamabe modificado em variedades de dimensão quatro cujos invariantes modificadores dependem dos autovalores do tensor de Weyl e são descritos em termos do máximo e mínimo da curvatura biortogonal (seccional). Fornecemos algumas propriedades geométricas e topológicas para tais variedades em termos destes invariantes. Na segunda parte investigamos os pontos críticos do funcional curvatura escalar total restrito ao espaço de métricas com curvatura escalar constante e volume unitário, abreviadamente chamamos de métricas CPE. Conjecturou-se na década de 1980 que toda métrica CPE deve ser Einstein. Provamos que tal conjectura é verdadeira sob uma condição de nulidade sobre o divergente de segunda ordem do tensor de Weyl.

SILVA, Adam Oliveira da. Rigidez de métricas críticas para funcionais riemannianos. 2017. 78 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-09-19T19:08:04Z No. of bitstreams: 1 2017_tese_aosilva.pdf: 481005 bytes, checksum: 2bdfc6ab68b042a5cfd4f67caf1e21e4 (MD5) / Rejected by Rocilda Sales (rocilda@ufc.br), reason: Bom dia, Estou devolvendo a Tese de ADAM OLIVEIRA DA SILVA, para que o arquivo seja substituído, pois o aluno já veio na BCM e orientei quais eram as correções a serem feitas. Atenciosamente, on 2017-09-20T14:03:26Z (GMT) / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-09-20T16:47:21Z No. of bitstreams: 1 2017_tese_aosilva.pdf: 480774 bytes, checksum: a1267dd82f8a82a19f79902004e1afb5 (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-09-21T12:26:34Z (GMT) No. of bitstreams: 1 2017_tese_aosilva.pdf: 480774 bytes, checksum: a1267dd82f8a82a19f79902004e1afb5 (MD5) / Made available in DSpace on 2017-09-21T12:26:35Z (GMT). No. of bitstreams: 1 2017_tese_aosilva.pdf: 480774 bytes, checksum: a1267dd82f8a82a19f79902004e1afb5 (MD5) Previous issue date: 2017-09-15 / The aim of this work is to study metrics that are critical points for some Riemannian functionals. In the first part, we investigate critical metrics for functionals which are quadratic in the curvature on closed Riemannian manifolds. It is known that space form metrics are critical points for these functionals, denoted by F t,s (g). Moreover, when s = 0, always Einstein metrics are critical to F t (g). We proved that under some conditions the converse is true. For instance, among others results, we prove that if n ≥ 5 and g is a Bach-flat critical metric to F −n/4(n−1) , with second elementary symmetric function of the Schouten tensor σ 2 (A) > 0, then g should be Einstein. Furthermore, we show that a locally conformally flat critical metric with some additional conditions are space form metrics. In the second part, we study the critical metrics to volume functional on compact Riemannian manifolds with connected smooth boundary. We call such critical points of Miao-Tam critical metrics due to the variational study making by Miao and Tam (2009). In this work, we show that the geodesics balls in space forms Rn , Sn and Hn have the maximum possible boundary volume among Miao-Tam critical metrics with connected boundary provided that the boundary be an Einstein manifold. In the same spirit, we also extend a rigidity theorem due to Boucher et al. (1984) and Shen (1997) to n-dimensional static metrics with positive constant scalar curvature, which give us another way to get a partial answer to the Cosmic no-hair conjecture already obtained by Chrusciel (2003). / Este trabalho tem como principal objetivo estudar métricas que são pontos críticos de alguns funcionais Riemannianos. Na primeira parte, investigaremos métricas críticas de funcionais que são quadráticos na curvatura sobre variedades Riemannianas fechadas. É de conhecimento que métricas tipo formas espaciais são pontos críticos para tais funcionais, denotados aqui por F t,s (g). Além disso, no caso s = 0, métricas de Einstein são sempre críticas para F t (g). Provamos que sob algumas condições, a recíproca destes fatos são verdadeiras. Por exemplo, dentre outros resultados, provamos que se n ≥ 5 e g é uma métrica Bach-flat crìtica para F−n/4(n−1) com segunda função simétrica elementar do tensor de Schouten σ 2 (A) > 0, então g tem que ser métrica de Einstein. Ademais, mostramos que uma métrica crítica localmente conformemente plana, com algumas hipóteses adicionais, tem que ser tipo forma espacial. Na segunda parte, estudamos as métricas críticas do funcional volume sobre variedades Riemannianas compactas com bordo suave conexo. Chamamos tais pontos críticos de métricas críticas de Miao-Tam, devido ao estudo variacional feito por Miao e Tam (2009). Neste trabalho provamos que as bolas geodésicas das formas espaciais Rn , S n e H n possuem o valor máximo para o volume do bordo dentre todas as métricas críticas de Miao-Tam com bordo conexo, desde que o bordo seja uma variedade de Einstein. No mesmo sentido, também estendemos um teorema de rigidez devido à Boucher et al. (1984) e Shen (1997) para métricas estáticas de dimensão n e com curvatura escalar constante positiva, o qual nos fornece outra maneira para obter uma resposta parcial para a Cosmic no-hair conjecture já obtida por Chrusciel (2003).

L’optimisation de l’efficacité énergétique des machines électriques constitue un domaine de recherche bien développé et fait partie des objectifs de plusieurs accords internationaux comme le projet Energie-Climat de la Commission Européenne visant l’amélioration de 20% d’efficacité pour 2020, encore étendu pour 2030 avec des objectifs plus importants. Ainsi, cette thèse propose un procédé d’optimisation du rendement du moteur asynchrone en agissant sur les paramètres du contrôle. Pour atteindre cet objectif, le flux dans l’entrefer est adapté selon un tableau de flux optimal calculé hors ligne pour tous les points de fonctionnement possibles. Ce flux est déterminé avec le plus haut degré de précision possible en se basant sur un modèle dynamique de la machine développé dans ces travaux. Ce dernier pallie le point faible du modèle dynamique classique, en prenant en compte l’effet des pertes fer. Le modèle des pertes fer utilisé est celui de Bertotti, qui les évalue en fonction de la fréquence et de l’amplitude du champ magnétique. Les pertes sont alors représentées par une résistance variable, continuellement évaluée selon le point de fonctionnement. Le tableau de flux optimal obtenu est fonction des conditions d’opération repérées dans le plan couple-vitesse. Ainsi l’étude montre que le flux peut être optimisé pour des valeurs de couple sensiblement inférieures à environ la moitié du couple nominal, ce seuil variant en fonction de la vitesse. La méthode d’optimisation proposée est simulée puis testée pour le contrôle scalaire et le contrôle vectoriel indirect par orientation de flux rotorique, afin de montrer la généricité de l’approche. La validation est conduite sur une maquette expérimentale d’une puissance de 5.5 kW et pour 2 machines asynchrones de générations différentes (IE2 et IE3). Les résultats obtenus montrent la réduction des pertes dans la machine et donc une amélioration du rendement global, tout en préservant un comportement dynamique satisfaisant. L’optimisation de l’efficacité énergétique est ainsi validée pour les deux structures de contrôle et pour les deux types de machine. Outre une comparaison avec la simulation, la solution proposée est comparée aux méthodes existantes afin d’en apprécier l’efficacité. / 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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This master thesis proposes a control method of scalar direct torque control and a technique of current control to maximize the aerodynamic efficiency of wind energy conversion systems (WECS) using permanent magnets synchronous generators (PMSG) with non-salient poles. The maximum power point tracking (MPPT) is possible to apply optimum torque to the generator by just controlling the static converter. Two topologies are addressed: The first one is a boost converter, widely used in WECS, where the MPPT method is implemented by the controlling the boost inductor current; and the second is a three phase AC boost converter where the scalar direct torque control is proposed. Aims to reduce the mechanic speed sensor a work with sensorless algorithms, is proposed. First an observer in the continuous time domain in coordinates αβ is developed containing two observers: a current sliding mode whose function is to determine the electromotive force (EMF) and EMF observer which aims to determine the rotor speed based on the direct method of Lyapunov. After, in the discrete time domain, sliding mode observers of speed and rotor position are described. Simulation and experimental results are presented to validate the theoretical analysis and demonstrate the good performance of the techniques to drive PMSG. / Esta dissertação propõe um método de controle escalar direto de conjugado e uma técnica de controle de corrente para maximização da eficiência aerodinâmica de sistemas de conversão de energia eólica (WECS) que utilizam geradores síncronos de ímãs permanente (PMSG) com polos não salientes. O rastreamento do ponto de máxima potência (MPPT), impõe o conjugado ótimo ao gerador apenas por meio do controle do conversor estático. Duas topologias são abordadas: conversor boost, amplamente utilizado em WECS, em que o método de MPPT é implementado por meio do controle da corrente do indutor boost, e um conversor boost trifásico CA, com controle escalar direto de torque. Buscando reduzir os sensores mecânicos do sistema, estimadores para obtenção da velocidade e da posição rotórica são propostos. Primeiramente um observador no domínio de tempo contínuo em coordenadas αβ é desenvolvido, contendo dois observadores: um de corrente por modos deslizantes, cuja função é determinar a força eletromotriz (EMF) e um observador de EMF, baseado no método direto de Lyapunov, com objetivo de determinar a velocidade rotórica. Posteriormente são descritos observadores por modos deslizantes no domínio de tempo discreto de velocidade e posição rotórica. Resultados de simulação e experimentais são apresentados para validar a análise teórica e demonstrar o desempenho das técnicas de controle e estimação propostas.

Conformal Field Theories (CFT) are Quantum Field Theories characterized by enhanced (conformal) symmetries. They are interesting to Theoretical Physicists because they occur at critical points in phase transitions of various systems and also in the world sheet formulation of String Theory. CFTs allow Operator Product Expansion (OPE) in their correlators. The idea of Conformal Bootstrap is to solely use the conformal symmetries and crossing symmetry in the OPE to solve a conformal led theory and not explicitly use a lagrangian. Solving a CFT is equivalent to obtaining the anomalous dimensions and OPE coe client’s of the operators. The work presented in this thesis shows how ideas of bootstrap can be used to get analytic results for dimensions and OPE coe client’s of various operators in CFTs. In the conventional bootstrap program, the OPE in the direct (s-) channel is compared with the OPE of a crossed (t-) channel. This requirement of crossing symmetry is called the bootstrap equation. The flow of logic is somewhat reversed in the \new" idea that is formulated in this thesis. The trick is to expand a CFT correlator in terms of Witten diagrams, in all channels. This is a manifestly crossing symmetric description, and is in contrast to the usual expansion in terms of conformal blocks, which is in only one channel. For convenience we work with the Mellin transforms of Witten diagrams. For consistency of the Witten diagrams expansion with the conformal block expansion in a certain channel, we require the satisfaction of some equations, which we call the bootstrap equations in Mellin space. This scheme was rest chalked out by Polyakov in 1973, where he proposed the use of \unitary amplitudes" to expand a correlator. The unitary amplitudes had similar symmetry and analytic properties as the Witten diagrams. Even though he did not take his idea forward, replacing unitary amplitudes with Witten diagrams seems to work very well for obtaining analytic results. The working of bootstrap equations in Mellin space is demonstrated for the 4 Wilson-Fisher fixed point in d = 4 , O(N) theory at Wilson-Fisher point (in d = 4 ), as well as with large N (in general d), and large spin operators in strongly coupled and weakly coupled theories. For the case of global symmetry we have also analysed the somewhat unexplored case of cubic anisotropy. The results are obtained as perturbative series in , 1=N, or 1=` as applicable, and they are consistent with known results in literature. We also obtain various new results, for instance the OPE coe client’s of general higher spin operators. These results are otherwise very di cult to end from Feynman diagrams, but in this approach they come out very simply, essentially by solving some algebraic equations. We also show the use of the conventional bootstrap strategy, for analytically obtaining anomalous dimensions of large spin operators having higher twists, in a O(N) theory, by working in the light cone limit. One can question the validity of the proposal of using Witten diagrams to expand a correlator. One such issue is convergence of the sum over Witten diagrams. Convergence can be shown to hold for the operator spectrum we have worked with. Also there are operators that might upset convergence under some conditions. Resolutions of such cases, and ways to improve convergence have also been discussed. The conventional bootstrap method has been very successful in giving numerical results in nonpertur-bative CFTs, like the 3 dimensional Ising model. Numerical analysis can also be made possible with the new bootstrap in Mellin space approach. Having a convergent basis of expansion improves the prospect of numeric. The goal is to formulate a bootstrap scheme that, under a single framework, can make most of all the CFT properties. It should be systematic, so that one can obtain anomalous dimensions and OPE coe client’s of all operators up to any desired order, and works for all strongly/weakly coupled and perturbative/nonpertur-bative CFTS, both analytically and numerically. Finally, the use of Witten diagrams also indicates the possibility of Ising CFT or weakly coupled CFTs having connections with AdS/CFT, and hence String Theory. It does seem we have a right direction towards achieving our goal.