Cette thèse de doctorat s’intéresse aux mécanismes d’amélioration des transferts dans des géométries de dissipateurs thermiques à plaques et ailettes. Une première partie est consacrée à l’étude d’une configuration académique à l’aide de simulations numériques visant à obtenir une amélioration du transfert de chaleur conjugué en modifiant uniquement par des découpes la forme géométrique des ailettes planes conductrices. Une analyse locale approfondie de l’écoulement et des champs thermiques a été effectuée avec notamment le principe de synergie locale, des champs de vitesse et de gradients thermiques, pour comprendre l’effet des modifications géométriques. Ce mémoire présente également le développement de dissipateurs aux performances thermo-aérauliques augmentées pour des applications de refroidissement de coffrets électronique embarqués. L’intensification des transferts thermiques est obtenue par la génération d’écoulements secondaires qui provoquent un brassage de fluide et réduisent la résistance thermique à la paroi en perturbant le développement de la couche limite thermique. Différentes configurations de dissipateurs avec deux types de générateurs d’écoulements secondaires, paires d’ailettes Delta et protrusions, ont été étudiées numériquement, en employant une modélisation de type « RANS ». Les performances thermo-aérauliques des géométries munies de générateurs de vorticité ont été comparées à celle d’un dissipateur thermique de référence « lisse ». Des prototypes ont également été fabriqués et testés sur un banc expérimental spécifiquement développé pour réaliser des mesures des performances globales en termes de puissance thermique et de pertes de charge. Les résultats expérimentaux et numériques ont été confrontés afin de qualifier les simulations réalisées. Par la suite, une étude d’optimisation employant l’analyse factorielle Taguchi a été utilisée afin d’optimiser les paramètres géométriques des dissipateurs retenus. Deux fonctions objectif ont été considérées : la maximisation du facteur de performance thermique à iso puissance de ventilation (PEC) et la réduction de la température moyenne de paroi du dissipateur par rapport au cas de référence. L’analyse des performances thermo-aérauliques globales des géométries étudiées a été complétée par une analyse qualitative locale des champs thermiques et d’écoulement notamment avec le principe de synergie. / This doctoral thesis focuses on mechanisms of heat transfer enhancement in plate and fin heat sink geometries. First part of the thesis is dedicated to study an academic configuration using numerical simulations to achieve an improvement in conjugate heat transfer by modifying only the geometrical shape (through punching) of the conductive plane fins. An in-depth local analysis of the flow and thermal fields was carried out with the local synergy principle, velocity and thermal gradients, to understand the effect of geometric modifications. This thesis also presents the development of heat sinks with increased thermo-hydraulic performance for on-board electronic box cooling applications. The intensification of the heat transfer is obtained by the generation of secondary flows which cause an intensive mixing of fluid and reduces the thermal resistance to the wall by disrupting the development of the thermal boundary layer. Different heat sink geometries with two types of secondary flow generators : delta winglet pair and protrusions were numerically studied using RANS approach. The thermo-hydraulic performances of the geometries equipped with vortex generators were compared with that of a smooth reference heat sink. The prototypes were also manufactured and tested on an experimental bench specifically designed to perform global performance measurements in terms of thermal power and pressure drops. Experimental and numerical results were compared to qualify the simulations performed. Subsequently, an optimization study using Taguchi factorial analysis was used to optimize the geometrical parameters of the chosen dissipaters. Two objective functions were considered : maximization of either iso-pumping power performance criteria (PEC) or average wall temperature of the dissipaters compared to the reference case. The global thermo-hydraulic performance analysis of the studied geometries was completed by a qualitative analysis of local flow and thermal fields, in particular with the local field synergy principle.

Grâce à leurs propriétés physiques/chimiques uniques, les nanoparticules colloïdales sont au cœur de nombreuses applications innovantes. Afin de faciliter leur caractérisation ou de les intégrer dans des dispositifs fonctionnels, il est nécessaire de les assembler de manière dirigée sur des surfaces solides. Dans ce contexte, l’objectif de cette thèse est de mieux comprendre et d’optimiser la technique de nanoxérographie, méthode d’assemblage dirigé où des nanoparticules sont piégées sur des motifs de charges électrostatiques. Après un premier travail consistant à améliorer le procédé de nanoxérographie, trois problématiques spécifiques ont été adressées : (i) l’assemblage de particules micrométriques. Le couplage de simulations numériques et de manipulations expérimentales a permis d’identifier les paramètres clés de l’assemblage de telles particules colloïdales et d’élargir (facteur 100) la gamme de tailles de particules assemblables par nanoxérographie. (ii) l’analyse de l’assemblage multicouche. Par le biais de nanoparticules modèles luminescentes et par la mise en place d’un nouveau protocole d’assemblage, les critères clés génériques pour l’assemblage 3D de colloïdes par nanoxérographie ont été dégagés. (ii) l’assemblage dirigé de nanogels sensibles à un stimulus environnemental extérieur. L’utilisation d’un protocole d’assemblage optimisé a permis d’élaborer des assemblages de nanogels interactifs avec leur environnement et du faire du tri sélectif de ces nanoparticules sur une même surface. / Owing to their unique physico-chemical properties, colloidal nanoparticles are building blocks for the creation of plentiful innovative devices. In order to make easier their characterization and to incorporate them into functional nano-devices, it is necessary to perfectly control their directed assemblies onto solid surfaces. In this context, this thesis’ purpose is to simultaneously better understand and optimize the nanoxerography method, which allows electrostatic and selective directing assemblies of nanoparticles onto charged patterns. After an optimization of the nanoxerography process, three specific problematics have been addressed: (1) micron-sized particles assembly. The combined use of numerical simulations and experiments enabled to unveil the key parameters involved in micron-sized particles assembly and to expend the particle size range foreseeable for an assembly by nanoxerography (factor 100). (2) the 3D assembly analysis. The influence of diverse parameters on the 3D assembly of luminescent model nanoparticles was quantified by using a new assembly protocol. The results gave the generic key criterions for the 3D assembly of colloids by nanoxerography. (3) directed assembly of nanogels sensitive to an external environmental stimulus. The use of an optimized protocol allowed elaborating nanogels assemblies interactive with their environment and to sort these nanoparticles onto the same surface.

L’apparition accidentelle d’un arc électrique dans le système de distribution électrique d’un aéronef peut compromettre la sécurité du vol. Il existe peu de travaux liés à cette problématique.Le but de ce travail est donc d’étudier le comportement d’un arc électrique, en conditions aéronautiques,par des approches théorique, numérique, et expérimentale. Dans ce travail, un modèle MHD de la colonne d’arc à l’ETL a été utilisé, et résolu à l’aide du logiciel commercial comsolMultiphysics. Afin de décrire l’interaction plasma-électrodes, le modèle a dû étendu pour inclure les écarts à l’équilibre près des électrodes. Ces zones ont été prises en compte en considérant la conservation du courant et de l’énergie dans la zone hors-équilibre. L’approche choisie et le développement du modèle ont été détaillés. La validation du modèle dans le cas d’un arc libre a montré un excellent accord avec les résultats numériques et expérimentaux de la littérature.Ce modèle d’arc libre a été étendu au cas de l’arc se propageant entre des électrodes en configuration rails et en géométrie 3D. Une description auto-cohérente du déplacement de l’arc entre les électrodes a été réalisée. La simulation numérique a été faite pour des arcs en régimes DC, pulsé et AC à des pressions atmosphériques et inférieures. Les principales caractéristiques de l’arc ont été analysées et discutées. Les résultats obtenus ont été comparés avec les résultats expérimentaux et ont montré un bon accord.Ce modèle d’arc électrique est capable de prédire le comportement d’un arc de défaut dans des conditions aéronautiques. Des améliorations du modèle sont discutées comme perspectives de ce travail. / The ignition of an electric arc in the electric distribution system of an aircraft can be a serious problem for flight safety. The amount of information on this topic is limited, however. Therefore,the aim of this work is to investigate the electric arc behavior by means of experiment and numerical simulations.The MHD model of the LTE arc column was used and resolved numerically using the commercial software comsol Multiphysics. In order to describe plasma-electride interaction, the model had to be extended to include non-equilibrium effects near the electrodes. These zones were taken into account by means of current and energy conservation in the non-equilibrium layer. The correct matching conditions were developed and are described in the work. Validation of the model in the case of a free burning arc showed excellent agreement between comprehensive models and the experiment.This model was then extended to the case of the electric arc between rail electrodes in a 3D geometry. Due to electromagnetic forces the electric arc displaces along the electrodes. A self-consistent description of this phenomenon was established. The calculation was performed for DC, pulsed and AC current conditions at atmospheric and lower pressures. The main characteristics of the arc were analyzed and discussed. The results obtained were compared with the experimental measurements and showed good agreement.The model of electric arcs between busbar electrodes is able to predict the behavior of a fault arc in aeronautical conditions. Further improvements of the model are discussed as an outlook of the research.

Ce travail porte sur le problème des partitions minimales, à l'interface entre théorie spectrale et optimisation de forme. Une introduction générale précise le problème et présente des résultats, principalement dûs à B. Helffer, T. Hoffmann-Ostenhof et S. Terracini, qui sont utilisés dans le reste de la thèse.Le premier chapitre est une étude spectrale asymptotique du laplacien de Dirichlet sur une famille de domaines en dimension deux qui tend vers un segment. L'objectif est d'obtenir une localisation des lignes nodales dans la limite des domaines minces. En appliquant les résultats de Helffer, Hoffmann-Ostenhof et Terracini, on montre ainsi que les domaines nodaux des premières fonctions propres forment des partitions minimales.Le deuxième chapitre étudie les valeurs propres de certains opérateurs de Schrödinger sur un domaine plan avec condition au bord de Dirichlet. On considère des opérateurs qui ont un potentiel électrique nul et un potentiel magnétique d'un type particulier, dit d'Aharonov-Bohm, avec des singularités en un nombre fini de points appelés pôles. On démontre que les valeurs propres dépendent continuement des pôles. Dans le cas de pôles distincts et éloignés du bord, on prouve que cette dépendance est analytique lorsque la valeur propre est simple. On exprime de plus une condition suffisante pour que la fonction qui aux pôles associe une valeur propre présente un point critique. On utilise alors la caractérisation magnétique des partitions minimales pour montrer que l'énergie minimale est une valeur critique d'une de ces fonctions.Le troisième chapitre est un article écrit en collaboration avec Virginie Bonnaillie-Noël. Il porte sur une famille d'exemples, les secteurs angulaires de rayon unité et d'ouverture variable, dont on tente de déterminer les partitions minimales. On applique pour cela les théorèmes généraux rappelés dans l'introduction afin de déterminer les partitions nodales qui sont minimales. On s'intéresse plus particulièrement aux partitions minimales en trois domaines. En appliquant les idées du deuxième chapitre, on montre que pour certaines valeur de l'angle, il n'existe aucune partition minimale qui soit symétrique par rapport à la bissectrice du domaine. D'un point de vue quantitatif, on obtient des encadrements précis de l'énergie minimale.Le quatrième chapitre consiste en l'étude des partitions minimales de tores plats dont on fait varier le rapport entre longueur et largeur. On utilise une méthode numérique très différente de celle du troisième chapitre, basée sur un article de B. Bourdin, D. Bucur et É. Oudet. Elle consiste en une relaxation suivie d'une optimisation par un algorithme de gradient projeté. On peut ainsi tester des résultats théoriques antérieurs. Les résultats présentés suggèrent de plus la construction explicite de familles de partitions (en liaison avec des pavages du tore) qui donnent une nouvelle majoration de l'énergie minimale.Un dernier chapitre de perspectives présente plusieurs applications possibles des méthodes décrites dans la thèse. / This work is concerned with the problem of minimal partitions, at the interface between spectral theory and shape optimization. A general introduction gives a precise statement of the problem and recall results, mainly due to B. Helffer, T. Hoffmann-Ostenhof and S.Terracini, that are used in the rest of the thesis.The first chapter is an asymptotic spectral study of the Dirichlet Laplacian on a familly of two-dimensional domains converging to a line segment. The aim is to localize the nodal lines when the domains become very thin. With the help of the results of Helffer, Hoffmann-Ostenhof, and Terracini, we then show that the nodal domains of the first eigenfunctions give minimal partitions.The second chapter studies the eigenvalues of some Schrödinger operators on a domain with Dirichlet boundary conditions. We consider operators that have no electric potential and a so-called Aharonov-Bohm magnetic potential, which has singularities at a finite number of points called poles. We prove that the eigenvalues are continuous functions of the poles. When the poles are distinct and far from the boundary, we prove that this function is analytic, assuming the eigenvalue is simple. We also give a sufficient condition for the function to have a critical point. Using the magnetic characterization of minimal partitions, we show that the minimal enery is a critical value for one of these functions.The third chapter in an article written in collaboration with Virginie Bonnaillie-Noël. It studies minimal partitions for sectors of unit radius with a variable angular opening. We apply the general results presented in the introduction, together with numerical computations, to determine nodal partitions that are minimal. We focus on partitions into three domains. Using ideas from the second chapter, we show that, for some values of the angle, there is no minimal partition that is symmetric with respect to the bisector. Form a quantitative point of view, we obtain precise bounds on the minimal energy.The fourth chapter studies the minimal partitions of flat tori in function of the ratio between width and length. We use a numerical method that is quite different from chapter three, and is based on an article by B. Bourdin, D. Bucur, and É. Oudet. It consists in a relaxation of the problem, followed by optimization with the help of a projected gradient algorithm. The results shown here additionally suggest explicit families of partitions, which consist in tilings of tori by polygons, that give upper bounds on the minimal energy. In the last chapter we consider several possible applications of the methods described in the thesis.

O presente trabalho tem por objetivo a caracterização dinâmica dos sistemas múltiplos de planetas extrassolares. O critério de classificação escolhido é baseado na proposta publicada inicialmente em Ferraz-Mello et al. (2005) e posteriormente modicada em Michtchenko et al. (2007). Para a obtenção dos parâmetros planetários orbitais foi feita uma pesquisa em diversos catálogos e artigos disponíveis para posterior criação de um catálogo próprio. Este incluiu somente sistemas extrassolares múlltiplos, ou seja, sistemas que contêm dois ou mais planetas orbitando a estrela. Foram feitas simulações numéricas de estabilidade dinâmica dos sistemas do catálogo próprio com tempos de integração de 200 mil até 21 milhões de anos. Ao todo, foram analisados 37 sistemas múltiplos extrassolares, divididos em 50 subsistemas considerando-se a estrela e dois planetas em órbitas consecutivas. Ao todo, foram analisados 37 sistemas múltiplos extrassolares, divididos em 50 subsistemas considerando-se a estrela e dois planetas em órbitas consecutivas. Estes foram submetidos ao total de 68 simulações computacionais. Os sistemas que apresentaram um cenário de estabilidade dinâmica foram posteriormente separados em três classes: ressonantes, seculares ou hierárquicos. Mais ainda, o comportamento secular desses sistemas foi classificado conforme o movimento do ângulo \"Deltavarpi\" : oscilatório em torno de 0º, oscilatório em torno de 180º ou circulatório. Os resultados das simulações são mostrados para todos os sistemas estudados. / The aim of the present work is a dynamic classification of multiple extrasolar systems. The characterization criterion used is based on a criterion proposed initially in Ferraz-Mello et al. (2005) and modified in Michtchenko et al. (2007). To obtain orbital parameters of the extrasolar systems, a search was done into several available catalogues and the scientific literature. A new catalogue was compiled containing only multiple extrasolar systems, that is, systems with two or more planets in orbit of the host star. Numerical simulations of dynamical stability of the cataloged systems were done considering pairs of planets on the consecutive orbits. Totally, 37 multiple extrasolar systems were analyzed, decomposed in 50 sub-systems each one consisting of the host star and two planets. The time evolution of those were simulated over time spans from 200 thousand years to 21 million years in 68 numerical simulations. The systems which have presented a dynamical stability were subsequently classified in resonants, secular or hierarchical and their secular behavior was classified with respect of the angle \"Deltavarpi\" as oscillation around 0º, oscillation around 180º or circulation. The result of all simulations are presented here for the analyzed systems.

Nesta pesquisa, o método geofísico GPR Ground Penetrating Radar foi utilizado para caracterizar tambores metálicos e plásticos enterrados numa área de testes controlados, denominada de Sítio Controlado de Geofísica Rasa SCGR do IAG instalado no campus da Universidade de São Paulo, em São Paulo. Os alvos foram escolhidos visando simular estudos de contaminação ambiental e obras de engenharia dentro do contexto urbano. Os tambores metálicos (vazios) foram dispostos na vertical e horizontal e os tambores plásticos (vazios, preenchidos com água salgada e com água doce) foram dispostos na vertical. Foram realizadas simulações numéricas GPR 2D para auxiliar na escolha dos parâmetros ótimos referentes à aquisição dos dados e verificar se os contrastes existentes entre os alvos (tambores metálicos e plásticos) e o background poderiam produzir reflexões significativas. As aquisições foram realizadas antes e depois da instalação dos alvos no SCGR-IAG utilizando as antenas de 100 MHz, 200 MHz e 500 MHz. Após as aquisições, os dados GPR foram processados e em seguida analisados visando estabelecer respostas típicas para cada alvo, considerando o tipo de material, a sua composição e/ou preenchimento. Os resultados foram comparados com as informações das profundidades reais dos alvos enterrados e as simulações numéricas, os quais apresentaram uma excelente concordância. Além disso, permitiram identificar com clareza todos os alvos e diferenciá-los quanto ao padrão de reflexão. Nos tambores plásticos foi possível distinguir os que estavam vazios e os preenchidos com água doce ou com água salgada. Essas respostas obtidas em uma área de testes controlados podem ser consideradas como típicas para os alvos, podendo ser extrapoladas para áreas onde não se tem nenhuma informação da subsuperfície. / In this research, geophysical method GPR - Ground Penetrating Radar was used to characterize metallic and plastic drums buried in an area of controlled tests, called \"Controlled Site of Shallow Geophysics (SCGR-IAG Sítio Controlado de Geofísica Rasa) installed in the campus of the University of São Paulo, in São Paulo. The targets were chosen aiming to simulate studies of environmental contamination and works of engineering inside the urban context. The metallic drums (empty) were disposed in the vertical and the horizontal position, and the plastic tubes (empty, filled with salty water and cool water) were disposed in the vertical position. 2D GPR numerical simulations were carried through to assist in the choice of the excellent parameters referring to the acquisition of the data, and to verify if the contrasts between the targets (metallic and plastic tubes) and the background could produce significant reflections. The acquisitions were carried through \"before\" and \"after\" the installation of the targets at the SCGR-IAG using 100 MHz, 200 MHz and 500 MHz antennas. After the acquisitions, GPR data were processed and then analyzed to establish typical answers to each target, considering the type of material, its composition and/or fulfilling. The results were compared with the information of the real depths of the buried targets and the numerical simulations, which matched in an excellent agreement. Moreover, the results allowed to identify with clarity all the targets and differentiate them according to the reflection standard. In the plastic drums it was possible to distinguish the ones that were empty and the filled ones with cool water or salty water. These answers gotten in an area of controlled tests can be considered as typical for the targets, being able to be surpassed for areas where no information of the subsurface is had.

Grâce aux progrès de la recherche, on sait aujourd’hui guérir près d’un cancer sur deux. Cependant, certaines tumeurs, telles que les glioblastomes restent parmi les plus agressives et les plus difficiles à traiter. La cause de cette résistance aux traitements pourrait provenir d’une sous-population de cellules ayant des caractéristiques communes aux cellules souches que l’on appelle cellules souches cancéreuses. De nombreux modèles mathématiques et numériques de croissance tumorale existent déjà mais peu tiennent compte de l’hétérogénéité intra-tumorale, qui est aujourd’hui un véritable challenge. Cette thèse s’intéresse à la dynamique des différentes sous-populations cellulaires d’un glioblastome. Elle consiste en l’élaboration d’un modèle mathématique de croissance tumorale reposant sur un processus de branchement de Bellman-Harris, à la fois multi-type et dépendant de l’âge. Ce modèle permet d’intégrer l’hétérogénéité cellulaire. Des simulations numériques reproduisent l’évolution des différents types de cellules et permettent de tester l’action de différents schémas thérapeutiques sur le développement tumoral. Une méthode d’estimation des paramètres du modèle numérique fondée sur le pseudo-maximum de vraisemblance a été adaptée. Cette approche est une alternative au maximum de vraisemblance dans le cas où la distribution de l’échantillon est inconnue. Enfin, nous présentons les expérimentations biologiques qui ont été mises en place dans le but de valider le modèle numérique / The latest advances in cancer research are paving the way to better treatments. However, some tumors such as glioblastomas remain among the most aggressive and difficult to treat. The cause of this resistance could be due to a sub-population of cells with characteristics common to stem cells. Many mathematical and numerical models on tumor growth already exist but few take into account the tumor heterogeneity. It is now a real challenge. This thesis focuses on the dynamics of different cell subpopulations in glioblastoma. It involves the development of a mathematical model of tumor growth based on a multitype, age-dependent branching process. This model allows to integrate cellular heterogeneity. Numerical simulations reproduce the evolution of different types of cells and simulate the action of several therapeutic strategies. A method of parameters estimation based on the pseudo-maximum likelihood has been developed. This approach is an alternative to the maximum likelihood in the case where the sample distribution is unknown. Finally, we present the biological experiments that have been implemented in order to validate the numerical model

Nesta pesquisa, o método geofísico GPR Ground Penetrating Radar foi utilizado para caracterizar tambores metálicos e plásticos enterrados numa área de testes controlados, denominada de Sítio Controlado de Geofísica Rasa SCGR do IAG instalado no campus da Universidade de São Paulo, em São Paulo. Os alvos foram escolhidos visando simular estudos de contaminação ambiental e obras de engenharia dentro do contexto urbano. Os tambores metálicos (vazios) foram dispostos na vertical e horizontal e os tambores plásticos (vazios, preenchidos com água salgada e com água doce) foram dispostos na vertical. Foram realizadas simulações numéricas GPR 2D para auxiliar na escolha dos parâmetros ótimos referentes à aquisição dos dados e verificar se os contrastes existentes entre os alvos (tambores metálicos e plásticos) e o background poderiam produzir reflexões significativas. As aquisições foram realizadas antes e depois da instalação dos alvos no SCGR-IAG utilizando as antenas de 100 MHz, 200 MHz e 500 MHz. Após as aquisições, os dados GPR foram processados e em seguida analisados visando estabelecer respostas típicas para cada alvo, considerando o tipo de material, a sua composição e/ou preenchimento. Os resultados foram comparados com as informações das profundidades reais dos alvos enterrados e as simulações numéricas, os quais apresentaram uma excelente concordância. Além disso, permitiram identificar com clareza todos os alvos e diferenciá-los quanto ao padrão de reflexão. Nos tambores plásticos foi possível distinguir os que estavam vazios e os preenchidos com água doce ou com água salgada. Essas respostas obtidas em uma área de testes controlados podem ser consideradas como típicas para os alvos, podendo ser extrapoladas para áreas onde não se tem nenhuma informação da subsuperfície. / In this research, geophysical method GPR - Ground Penetrating Radar was used to characterize metallic and plastic drums buried in an area of controlled tests, called \"Controlled Site of Shallow Geophysics (SCGR-IAG Sítio Controlado de Geofísica Rasa) installed in the campus of the University of São Paulo, in São Paulo. The targets were chosen aiming to simulate studies of environmental contamination and works of engineering inside the urban context. The metallic drums (empty) were disposed in the vertical and the horizontal position, and the plastic tubes (empty, filled with salty water and cool water) were disposed in the vertical position. 2D GPR numerical simulations were carried through to assist in the choice of the excellent parameters referring to the acquisition of the data, and to verify if the contrasts between the targets (metallic and plastic tubes) and the background could produce significant reflections. The acquisitions were carried through \"before\" and \"after\" the installation of the targets at the SCGR-IAG using 100 MHz, 200 MHz and 500 MHz antennas. After the acquisitions, GPR data were processed and then analyzed to establish typical answers to each target, considering the type of material, its composition and/or fulfilling. The results were compared with the information of the real depths of the buried targets and the numerical simulations, which matched in an excellent agreement. Moreover, the results allowed to identify with clarity all the targets and differentiate them according to the reflection standard. In the plastic drums it was possible to distinguish the ones that were empty and the filled ones with cool water or salty water. These answers gotten in an area of controlled tests can be considered as typical for the targets, being able to be surpassed for areas where no information of the subsurface is had.

No presente trabalho, conceitos de inferência estatística são utilizados para aplicação e comparação de diferentes métodos de análise de sinais de ressonância magnética funcional. A idéia central baseia-se na obtenção da distribuição de probabilidade da variável aleatória de interesse, para cada método estudado e sob diferentes valores da relação sinal-ruído (SNR). Este objetivo é atingido através de simulações numéricas da função resposta hemodinâmica (HRF) acrescida de ruído gaussiano. Tal procedimento nos permite avaliar a sensibilidade e a especificidade dos métodos empregados através da construção das curvas ROC (receiver operating characteristic) para diferentes valores de SNR. Sob específicas condições experimentais, aplicamos métodos clássicos de análise (teste t de Student e correlação), medidas de informação (distância de Kullback-Leibler e sua forma generalizada) e um método Bayesiano (método do pixel independente). Em especial, mostramos que a distância de Kullback-Leibler (D) (ou entropia relativa) e sua forma generalizada são medidas úteis para análise de sinais dentro do cenário de teoria da informação. Estas entropias são usadas como medidas da \"distância\"entre as funções de probabilidade p1 e p2 dos níveis do sinal relacionados a estímulo e repouso. Para prevenir a ocorrência de valores divergentes de D, introduzimos um pequeno parâmetro d nas definições de p1 e p2. Estendemos a análise, apresentando um estudo original da distância de Kullback-Leibler generalizada Dq (q é o parâmetro de Tsallis). Neste caso, a escolha apropriada do intervalo 0 < q < 1 permite assegurar que Dq seja finito. Obtemos as densidades de probabilidade f (D) e f (Dq) das médias amostrais das variáveis D e Dq , respectivamente, calculadas ao longo das N épocas de todo o experimento. Para pequenos valores de N (N < 30), mostramos que f (D) e f (Dq) são muito bem aproximadas por distribuições Gamma (qui^2 < 0,0009). Em seguida, estudamos o método (Bayesiano) do pixel independente, considerando a probabilidade a posteriori como variável aleatória e obtendo sua distribuição para várias SNR\'s e probabilidades a priori. Os resultados das simulações apontam para o fato de que a correlação e o método do pixel independente apresentam melhor desempenho do que os demais métodos empregados (para SNR > -20 dB). Contudo, deve-se ponderar que o teste t e os métodos entrópicos compartilham da vantagem de não se utilizarem de um modelo para HRF na análise de dados reais. Finalmente, para os diferentes métodos, obtemos os mapas funcionais correspondentes a séries de dados reais de um voluntário assintomático submetido a estímulo motor de evento relacionado, os quais demonstram ativação nas áreas cerebrais motoras primária e secundária. Enfatizamos que o procedimento adotado no presente estudo pode, em princípio, ser utilizado em outros métodos e sob diferentes condições experimentais. / In the present work, concepts of statistical inference are used for application and comparison of different methods of signal analysis in functional magnetic resonance imaging. The central idea is based on obtaining the probability distribution of the random variable of interest, for each method studied under different values of signal-to-noise ratio (SNR). This purpose is achieved by means of numerical simulations of the hemodynamic response function (HRF) with gaussian noise. This procedure allows us to assess the sensitivity and specificity of the methods employed by the construction of the ROC curves (receiver operating characteristic) for different values of SNR. Under specific experimental conditions, we apply classical methods of analysis (Student\'s t test and correlation), information measures (distance of Kullback-Leibler and its generalized form) and a Bayesian method (independent pixel method). In particular, we show that the distance of Kullback-Leibler D (or relative entropy) and its generalized form are useful measures for analysis of signals within the information theory scenario. These entropies are used as measures of the \"distance\"between the probability functions p1 and p2 of the signal levels related to stimulus and non-stimulus. In order to avoid undesirable divergences of D, we introduced a small parameter d in the definitions of p1 and p2. We extend such analysis, by presenting an original study of the generalized Kullback-Leibler distance Dq (q is Tsallis parameter). In this case, the appropriate choice of range 0 < q < 1 ensures that Dq is finite. We obtain the probability densities f (D) and f (Dq) of the sample averages of the variables D and Dq, respectively, calculated over the N epochs of the entire experiment. For small values of N (N < 30), we show that f (D) and f (Dq) are well approximated by Gamma distributions (qui^2 < 0.0009). Afterward, we studied the independent pixel bayesian method, considering the probability a posteriori as a random variable, and obtaining its distribution for various SNR\'s and probabilities a priori. The results of simulations point to the fact that the correlation and the independent pixel method have better performance than the other methods used (for SNR> -20 dB). However, one should consider that the Student\'s t test and the entropic methods share the advantage of not using a model for HRF in real data analysis. Finally, we obtain the maps corresponding to real data series from an asymptomatic volunteer submitted to an event-related motor stimulus, which shows brain activation in the primary and secondary motor brain areas. We emphasize that the procedure adopted in this study may, in principle, be used in other methods and under different experimental conditions.

La thèse a pour but de développer une méthodologie de calcul instationnaire permettant une étude qualitative et quantitative de l’aérodynamique externe d’une automobile. La première partie de l’étude est consacrée au développement de la méthodologie numérique sur les différents corps d’Ahmed à 25°, géométries simplifiées d’une automobile réelle, afin de valider les choix stratégiques de maillages et de méthodes numériques ainsi que s’assurer de la bonne résolution de l’écoulement. Les résultats numériques sont comparés aux données expérimentales obtenues au cours d’essais réalisés à la soufflerie La Ferté Vidame lors de travaux de thèse précédents. A l’issue de ce travail, la méthode hybride Delayed Detached Eddy Simulation Shear-Stress Transport (DDES SST) est sélectionnée pour la suite de l’étude au vu des meilleures performances obtenues (torseur aérodynamique, coefficient de pression, topologie d’écoulement) par rapport aux méthodes Reynolds Averaged Navier-Stokes (RANS), Scale Adaptive Simulation (SAS) et Stress-Blended Eddy Simulation (SBES). La seconde phase de l’étude consiste à adapter la méthodologie précédemment développée sur un véhicule réel, la Peugeot 308 SW. Au préalable, une base de données expérimentales conséquente a été réalisée au sein du Groupement d’Intérêt Economique Souffleries Aéroacoustiques Automobiles (GIE S2A) au cours de ces travaux. La géométrie est tout d’abord simplifiée afin de faciliter la mise en place de la méthodologie numérique : entrées d’air fermées, soubassement lissé, roues remplacées par des carénages. Les résultats obtenus sont encourageants et démontrent globalement la supériorité de la DDES par rapport aux méthodes RANS classiques. La topologie d’écoulement est mieux prédite (soubassement et sillage), même si la prédiction du coefficient de portance reste une difficulté majeure pour ce type de méthode hybride. / The main goal of this PhD is to develop an unsteady numerical method to study the external aerodynamic flow around real vehicles. The first part of the study focuses on the flow around simplified geometries, such as 25° Ahmed bodies (with sharp and rounded edges on the back of the body), in order to determine the optimal turbulence model, mesh setup and numerical parameters. Computational Fluid Dynamics (CFD) results are compared to experimental data reported in literature conducted in the La Ferté Vidame wind tunnel. Based on this study, Shear-Stress Transport Delayed Detached Eddy Simulation (SST DDES) demonstrates superiority over Reynolds Averaged Navier-Stokes (RANS), Scale Adaptive Simulation (SAS) and Stress Blended Eddy Simulation (SBES) turbulence models, regarding both drag and lift coefficients predictions, and flow topology.Secondly, the numerical procedure is adapted for a real vehicle, the Peugeot 308 SW estate car. A substantial experimental campaign was carried out in the Groupement d’Intérêt Economique Souffleries Aéroacoustiques Automobiles (GIE S2A) wind tunnel to provide data against which the numerical results are compared. Given the geometric complexity of a real vehicle, the car is simplified for this study as follows: the front air inlets are closed, the underbody is smoothed with additional panels and the wheels are replaced by fairings. DDES computations show encouraging results. A significant improvement of the flow topology is obtained with DDES compared to RANS models. However, the prediction of the lift coefficient remains a major difficulty with these hybrid methods.