[pt] Nesta dissertação, estratégias de modelagem são apresentadas envolvendo modelos de séries temporais lineares e não lineares para modelar a série do preço spot no mercado elétrico brasileiro. Foram usados, dentre os lineares, os modelos ARIMA(p,d,q) proposto por Box, Jenkins e Reinsel (1994) e os modelos de regressão dinâmica. Dentre os não lineares, o modelo escolhido foi o STAR desenvolvido, inicialmente, por Chan e Tong (1986) e, posteriormente, por Teräsvista (1994). Para este modelo, testes do tipo Multiplicador de Lagrange foram usados para testar linearidade, bem como para avaliar os modelos estimados. Além disso, foi também utilizada uma proposta para os valores iniciais do algoritmo de otimização, desenvolvido por Franses e Dijk (2000). Estimativas do filtro de Kalman suavizado foram usadas para substituir os valores da série de preço durante o racionamento de energia ocorrido no Brasil. / [en] In this dissertation, modeling strategies are presented involving linear and non-linear time series models to model the spot price of Brazil s electrical energy market. It has been used, among the linear models, the modeling approach of Box, Jenkins and Reinsel (1994) i.e., ARIMA(p,d,q) models, and dynamic regression. Among the non-linear ones, the chosen model was the STAR developed, initially, by Chan and Tong (1986) and, later, by Teräsvirta (1994). For this model, the Lagrange Multipliers test, to measure the degree of non linearity of the series , as well as to evaluate the estimated model was used. Moreover, it was also used a proposal for the initial values of the optimization algorithm, developed by Franses and Dijk (2000). The smoothed Kalman filter estimates were used in order to provide values for the spot price series during the energy shortage period.

Made available in DSpace on 2016-08-31T13:33:46Z (GMT). No. of bitstreams: 1 TayaraCPB_Dissert.pdf: 1984521 bytes, checksum: 5a46c1781124a49b404a083b87b969bd (MD5) Previous issue date: 2015-08-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / With advances in technology and the popularization of the use of Unmanned Aerial Vehicles (UAV's) so does the need to use more robust and more effective control techniques. Among the various types of unmanned aerial vehicles, this paper will focus on quadrotor model, which has a mechanical structure in the form of x, whose ends have an engine and propeller assembly, where the rotation of this group is responsible for the lift and the movements developed by quadrotor. This feeling, aiming to apply drivers that provide stability to the dynamic system. This study aims to conduct mathematical modeling using the Euler-Lagrange. With this, it is proposed a PID controller (Proportional Integral Derivative) to maintain stable the three orientation angles and height to a desired value. The development of the proposed controller will be validated via simulation confirming the application feasibility of the technique presented stability / Com o avanço tecnológico e a popularização do uso dos Veículos Aéreos Não Tripulados (VANT s) cresce também a necessidade do uso de técnicas de controle mais robustas e mais eficazes. Dentre os mais diversos tipos de veículos aéreos não tripulados, este trabalho irá focar no modelo do quadrotor, que possui uma estrutura mecânica em forma de cruz, cujas extremidades têm um conjunto de motor e hélice, onde a rotação desse conjunto é responsável pela força de sustentação e pelos movimentos desenvolvidos pelo mesmo. Objetivando aplicar controladores que proporcione estabilidade ao sistema dinâmico deste veiculo aéreo. O presente trabalho tem como objetivo realizar a modelagem matemática deste sistema usando as equações de Euler-Lagrange. Tendo isso, é proposto um controlador PID (Proporcional Integral Derivativo) para manter os três ângulos de orientação estáveis e a altura em um valor desejado. O desenvolvimento do controlador proposto será validado via simulação confirmando a viabilidade da aplicação da técnica de estabilidade apresentada

La régulation des polluants a mené à la création de nouveaux systèmes de combustion. Le carburant étant stocké sous forme liquide, sa transformation jusqu’à sa combustion est complexe. La capacité de la Simulation aux grandes échelles à simuler des écoulements turbulents réactifs a été montrée sur des cas académiques comme sur des configurations industrielles, tout en prenant en compte les phénomènes multiphysiques intervenant dans ces configurations, mais les études sur la structure de flamme diphasique sont encore trop peu nombreuses. La présence de deux solveurs pour la simulation d’une phase liquide étant disponible dans le code AVBP, leur utilisation permet une comparaison et une compréhension des phénomènes en jeu combinant dispersion, évaporation, et combustion. La première partie de l’étude relate la validation du modèle d’injection FIM-UR. Ce modèle est capable de reconstruire les profils de vitesses et de granulométrie à l’injecteur sans avoir à simuler les phénomènes d’atomisation primaire et secondaire. Une validation en régime turbulent avait déjà été réalisée, et on propose ici de valider le modèle dans un cas laminaire. Des comparaisons entre simulations monodisperses et polydisperse et des expériences sont effectuées. La simulation monodisperse Lagrangienne donne une bonne structure globale mais la simulation polydisperse Lagrangienne permet de retrouver le comportement au centre du cône avec la présence des petites gouttes et à la périphérie du cône par la présence des grosses gouttes. De plus, des améliorations sont apportées au modèle pour le formalisme Eulérien et montrent de bons résultats. La partie suivante s’intéresse à caractériser un spray polydisperse par une distribution monodisperse. En effet, au cas où une approche polydisperse n’est pas possible, le choix du diamètre moyen à prendre pour une simulation monodisperse est délicat. On propose donc d’analyser le comportement d’un spray polydisperse en le comparant à ceux de sprays monodisperses. Deux configurations académiques sont choisies : des cas de Turbulence Homogène Isotrope chargée en particules pour étudier la dynamique, et des calculs d’évaporation 0D. Trois paramètres sont étudiés pour la dynamique : la concentration préférentielle (ou ségrégation), la traînée moyenne et la traînée réduite moyenne. Cette dernière et la ségrégation de la distribution polydisperse semblent affectées par les tailles de goutte les plus faibles, et la concentration préférentielle apparait alors comme la moyenne des ségrégations des classes qui la composent pondérées par l’inverse du nombre de Stokes associé à chacune de ces classes. La traînée moyenne de la simulation polydisperse possède un comportement proche des diamètres moyens D10 et D20. Ces analyses nous poussent donc à choisir le D10 pour caractériser la dynamique d’un spray polydisperse. Les calculs d’évaporation 0D ne permettent pas dans un premier temps de caractériser efficacement la masse évaporée d’un spray polydisperse par celle d’un spray monodisperse équivalent, mais la définition de nouveaux diamètres issus de la littérature des lits fluidisés comme le D50% le permet, ce qui le place autour du D32. On propose donc de caractériser l’évaporation d’un spray polydisperse par ce diamètre. Enfin, la dernière partie étudie la structure de flamme diphasique dans la chambre MERCATO, à l’aide du formalisme Lagrangien, monodisperse et polydisperse, mais aussi en utilisant le formalisme Eulérien. La validation du modèle FIM-UR du premier chapitre et ses améliorations sont utilisées pour représenter les conditions d’injection liquide. En plus d’un calcul polydisperse, deux simulations monodisperses Lagrangiennes sont réalisées en prenant les diamètres moyens D10 et D32, suite à la partie précédente. Des comparaisons qualitatives et des validations sont réalisées, en comparant des profils de vitesses gazeuses axiale et fluctuante et vitesse axiale liquide issus de l’expérience. / Regulations on pollutants have led to the creation of new combustion systems. Giving that fuel is stored in a liquid form, its evolution until combustion is complex. The ability of Large Eddy Simulation has been demonstrated on academic cases, as well as on industrial configurations, by taking into account the multi-physics phenomena, but there is a lack of studies about two-phase flow flame structures. Two solvers for the simulation of two-phase flows are available in the AVBP code, hence both simulations are performed to compare and increase understanding of the phenomena involved such as dispersion, evaporation and combustion. The first part of the study focuses on the validation of the FIM-UR injection model. This model is able to build velocity and droplet profiles at the injector, without simulating primary and secondary break up. A validation in a turbulent case has already been done, and this study validates the model in a laminar case. Comparisons between monodisperse and polydisperse simulations, and experiments are performed. The monodisperse Lagrangian simulation shows good results but the polydisperse simulation is able to represent profiles in the center of the cone by small droplets and at the peripheral part of the cone, by big ones. Moreover, improvements in the Eulerian model exhibit good results. The next section tries to evaluate the impact of polydispersion. Indeed, when a polydisperse approach is not available, choosing the mean diameter can be tricky. A comparison between the behavior of polydisperse spray and monodisperse sprays ones is realised. Two academic cases are studied: Homogeneous Isotropic Turbulence with particles to analyze the dynamics, and 0D evaporation cases. For the dynamics, preferential concentration, mean drag and reduced mean drag are studied. The latter and preferential concentration are affected by small droplets, and the preferential concentration of a polydisperse spray is equivalent to the average of preferential concentration of classes, extracted from the polydisperse distribution, weighted by the inverse of the Stokes number of each class. The mean drag behaves like the D10 and D20 mean drags. This analysis allows us to choose the D10 to characterize a polydisperse distribution for the dynamics. Zero-D evaporation simulations cannot characterize the polydisperse spray evaporated mass by the evaporated mass of monodisperses sprays. New definitions of diameters from fluidized bed literature enable the use of D50%, which is close to D32. We propose to use this diameter to characterize the evaporation of a polydisperse spray. Finally, the last section studies the structure of two-phase flames in the MERCATO bench, using the Lagrangian formalism, monodisperse and polydisperse but also using the Eulerian formalism. The validation of FIM-UR model and improvements from the first section are used to represent liquid injection conditions. A polydisperse simulation is realized and two monodisperse simulations are computed using mean diameters D10 and D32, thanks to the previous section. Qualitative comparisons and validations are realized, comparing gaseous velocity profiles and liquid velocity profiles. Good agreements are found and the mean diameter D32 seems to be close to the polydisperse spray. A comparison between mean flames is done with an Abel transform of the flame from the experiments. The flame has an "M shape", anchored by small recirculation zones out of the swirler, and by a point at the tip of the central recirculation zone. Then, the impact of droplet distributions is analyzed. Even if few bigger droplets from the polydisperse distribution are convected in the hot gases due to bigger particular time and evaporation time, two-phase flow flame structures are equivalent. Different combustion regimes appeared with premixed flames and pockets of fuel burning in the hot gases.

Made available in DSpace on 2014-12-17T15:05:03Z (GMT). No. of bitstreams: 1 JeffersonLRO_DISSERT.pdf: 1554020 bytes, checksum: 9422a35bb594853d7162e990d1f93feb (MD5) Previous issue date: 2013-07-04 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / De nombreuses ?tudes sur l`utilisation p?dagogique de l`histoire des math?matiques viennent a identifier les arguments qui sous-tiennent ces actions ?ducatives comme une fa?on d`aborder les math?matiques scolaires afin de mener les ?l?ves ? un apprentissage r?flexif et significatif des math?matiques. Cherchant a v?rifier, de mani?re pratique, comment ces relations entre histoire des math?matiques et l`enseignement des math?matiques peuvent se mat?rialiser sous la forme d`activit?s didactiques, nous avons effectu? un sondage sur les oeuvres du math?maticien Joseph Louis Lagrange (1736-1813) et identifi? le potentiel d`exploration ?ducatif, de l`oeuvre Le?ons ?l?mentaires sur les math?matiques donn?es a l`?cole Normale en 1795, de cet math?maticien. L`objectif principal de notre ?tude ?tait de faire des recherches sur le potentiel d`une oeuvre antique d?di? ? l`enseignement des math?matiques et de la consid?rer comme support conceptuel et didactique pour la cr?ation d`un mod?le d`activit?s didactiques pour l`enseignement des math?matiques, dans la formation des enseignants de math?matiques et aussi en ce qui concerne l`apprentissage des math?matiques des ?l?ves de l`?cole primaire. Nous avons fait une lecture, la traduction et l`ajout de notes et commentaires sur le travail et une recherche bibliographique sur la relation entre l`histoire des math?matiques et l`enseignement des math?matiques, de fa?on a comprendre les aspects conceptuels et didactiques pour l`?laboration d`um module activit?s didactiques pour l`enseignement des math?matiques bas?e sur certains chapitres du livre de Lagrange. ? cette fin, l`oeuvre a ?t? utilis? comme source primaire et a ?t? ?tudi? sous un fondement th?orique appuyer sur les travaux des Institut de recherche sur l`enseignement des math?matiques IREM. Dans le module ?labor?, les activit?s apportent les contenus dans une suite integr?e ? une logique de classe, ? partir de la lecture directe des d?coupages du texte original, dispos?s entre les questions et les situations-probl?mes , historiquement mis en contexte avec la p?riode et associ?s ? des contenus sp?cifiques. Comme il s`agit d`une recherche bas?e sur l`exploitation de livres anciens, nous croyons que des modules d`activit?s bas?es sur des source primaires peuvent ?tre utilis?es comme un mat?riel p?dagogique pour la formation des enseignants de math?matiques ainsi que pour les derni?res ann?es de l`?cole ?l?mentaire, reformul?es ou accrues d`autres questions telles l`int?r?t de chaque enseignant qui l`utilise / Muitos estudos sobre o uso pedag?gico da hist?ria da Matem?tica v?m apontando argumentos que fundamentam a??es essas did?ticas como um modo de abordar a matem?tica escolar de modo a conduzir os estudantes a uma aprendizagem matem?tica reflexiva e com significado. Na perspectiva de verificar experimentalmente como essas rela??es entre Hist?ria da Matem?tica e Educa??o Matem?tica podem se materializar na forma de atividades did?ticas fizemos um levantamento acerca da obra do matem?tico Joseph Louis Lagrange (1736-1813) e identificamos o potencial de explora??o pedag?gica da obra Le?ons ?l?mentaires sur les math?matiques donn?es a l`?cole Normale en 1795 (Li??es elementares sobre as matem?ticas dadas ? Escola Normal em 1795), do referido matem?tico. O objetivo central do nosso estudo foi investigar o potencial did?tico de uma obra antiga voltada ao ensino de matem?tica e tom?-la como suporte conceitual e did?tico para a cria??o de um modelo de atividades did?ticas para o ensino de matem?tica, tanto na forma??o de professores de matem?tica como para a aprendizagem matem?tica de estudantes do ensino fundamental. Fizemos uma leitura, a tradu??o e a inclus?o de notas e coment?rios sobre a obra e uma pesquisa bibliogr?fica sobre as rela??es entre Hist?ria da Matem?tica e Educa??o Matem?tica, de modo compreender aspectos conceituais e did?ticos para a elabora??o de um m?dulo de atividades did?ticas para o ensino de matem?tica com base em alguns cap?tulos do livro de Lagrange. Para tanto, a obra foi utilizada como fonte prim?ria e estudada sob uma fundamenta??o te?rica baseada, em trabalhos dos Institutos de Pesquisa sobre Ensino das Matem?ticas IREM franceses. No m?dulo elaborado, as atividades trazem os conte?dos numa sequ?ncia integrada ? l?gica de uma aula, com a leitura direta de recortes do texto original, dispostos entre quest?es de fixa??o e situa??es-problema, contextualizadas historicamente com o per?odo e relacionadas aos conte?dos focados. Como se trata de uma pesquisa pautada na explora??o de livros antigos, consideramos que o m?dulo de atividades baseado em fonte prim?ria pode se utilizado como um material pedag?gico para a forma??o de professores de matem?tica bem como para os anos finais do ensino fundamental e reformulado ou acrescido de outras quest?es conforme o interesse de cada professor que utiliz?-lo

Made available in DSpace on 2015-05-15T11:46:05Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 813665 bytes, checksum: 8aa09df2661d8ea4c0561ebad8cd9584 (MD5) Previous issue date: 2012-07-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The goal of our work is to prove the existence of solutions to a class of semilinear elliptic equations in a bounded domain, involving concave-convex type nonlinearities. We use a variety of methods to and these solutions, such as Mountain Pass Theorem, Ekeland's Variational Principle, Lagrange Multipliers Theorem, Nehari Manifold and sub and supersolution method. / O objetivo da nossa dissertação é provar a existência de soluções para uma classe de equações elípticas semilineares em um domínio limitado, envolvendo não linearidades do tipo côncavo-convexas. Mostraremos alguns casos diferentes e métodos diversificados para encontrar tais soluções, usando o Teorema do Passo da Montanha, o Princípio Variacional de Ekeland, Teorema dos Multiplicadores de Lagrange, a Variedade de Nehari e sub e supersolução.

Ce mémoire de thèse à été réalisée dans le cadre d'une collaboration scientifique avec "La Manufacture Française des Pneumatiques Michelin". Il porte sur l'analyse mathématique et numérique de la convergence et de la stabilité de formulations mixtes ou hybrides de problèmes d'optimisation sous contrainte avec la méthode des multiplicateurs de Lagrange et dans le cadre de la méthode éléments finis étendus (XFEM). Tout d'abord, nous essayons de démontrer la stabilité de la discrétisation X-FEM pour le problème d'élasticité linéaire incompressible en statique. Le deuxième axe, qui représente le contenu principal de la thèse est dédié à l'étude de certaines méthodes de multiplicateur de Lagrange stabilisées. La particularité de ces méthodes est que la stabilité du multiplicateur est assurée par l'ajout de termes supplémentaires dans la formulation faible. Dans ce contexte, nous commençons par l'étude de la méthode de stabilisation de Barbosa-Hughes appliquée au problème de contact unilatéral sans frottement avec XFEM cut-off. Ensuite, nous construisons une nouvelle méthode basée sur des techniques de projections locales pour stabiliser un problème de Dirichlet dans le cadre de X-FEM et une approche de type domaine fictif. Nous faisons aussi une étude comparative entre la stabilisation avec la technique de projection locale et la stabilisation de Barbosa-Hughes. Enfin, nous appliquons cette nouvelle méthode de stabilisation aux problèmes de contact unilatéral en élastostatique avec frottement de Tresca dans le cadre de X-FEM. / This Ph.D. thesis was done in collaboration with "La Manufacture Française des Pneumatiques Michelin". It concerns the mathematical and numerical analysis of convergence and stability of mixed or hybrid formulation of constrained optimization problem with Lagrange multiplier method in the framework of the eXtended Finite Element Method (XFEM). First we try to prove the stability of the X-FEM discretization for incompressible elastostatic problem by ensured a LBB condition. The second axis, which present the main content of the thesis, is dedicated to the use of some stabilized Lagrange multiplier methods. The particularity of these stabilized methods is that the stability of the multiplier is provided by adding supplementary terms in the weak formulation. In this context, we study the Barbosa-Hughes stabilization technique applied to the frictionless unilateral contact problem with XFEM-cut-off. Then we present a new consistent method based on local projections for the stabilization of a Dirichlet condition in the framework of extended finite element method with a fictitious domain approach. Moreover we make comparative study between the local projection stabilization and the Barbosa-Hughes stabilization. Finally we use the local projection stabilization to approximate the two-dimensional linear elastostatics unilateral contact problem with Tresca frictional in the framework of the eXtended Finite Element Method X-FEM.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-11T16:41:11Z No. of bitstreams: 1 cesaraugustoconopoimaperez.pdf: 4395089 bytes, checksum: 9e33b57e376886bbc7ff8300d693cf87 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-22T16:42:49Z (GMT) No. of bitstreams: 1 cesaraugustoconopoimaperez.pdf: 4395089 bytes, checksum: 9e33b57e376886bbc7ff8300d693cf87 (MD5) / Made available in DSpace on 2018-01-22T16:42:49Z (GMT). No. of bitstreams: 1 cesaraugustoconopoimaperez.pdf: 4395089 bytes, checksum: 9e33b57e376886bbc7ff8300d693cf87 (MD5) Previous issue date: 2017-10-25 / A resposta passiva e ativa de uma célula biológica a um campo elétrico é estudada aplicando um Método de Elementos Finitos Mortar MEFM. A resposta de uma célula é um processo com duas escalas temporais, o primeiro na escala de microsegundos para a polarização da célula e o segundo na escala de milisegundos para a resposta ativa devido a dinâmica complexa das correntes nos canais iônicos da membrana celular. O modelo matemático para descrever a dinâmica da resposta celular é baseado na lei de conservação de corrente elétrica em um meio condutor. Introduzindo uma variável adicional conhecida como multiplicador de Lagrange definido na interface da célula, o problema de valor de fronteira associado a conservação de corrente elétrica é desacoplado do problema de valor inicial associado a responta passiva e ativa da célula. O método proposto permite resolver o problema da distribuição de potencial elétrico em um arranjo geométrico arbitrário de células. Com o objetivo de validar a metodologia apresentada, a convergência espacial do método é numericamente investigada e a solução aproxima e exata que descreve a polarização de uma célula, são comparadas. Finalmente, para demonstrar a efetividade do método, a resposta ativa a um campo elétrico aplicado num arranjo de células de geometria arbitraria é investigada. / The response of passive and active biological cell to applied electric field is investigated with a Mortar Finite Element Method MFEM. Cells response is a process with two different time scales, one in microseconds for the cell polarization and the other in milliseconds for the active response of the cell due to the complex dynamics of the ion-channel current on the cell membrane. The mathematical model to describe the dynamics of the cell response is based on the conservation law of electric current in a conductive medium. By introducing an additional variable known as Lagrange multiplier defined on the cell interface, the boundary value problem associated to the conservation of electric current is decoupled from the initial value problem associated to the passive and active response of the cell. The proposed method allows to solve electric potential distribution in arbitrary cell geometry and arrangements. In order to validate the presented methodology, the h-convergence order of the MFEM is numerically investigated. The numerical and exact solutions describing cell polarization are also compared. Finally, to demonstrate the effectiveness of the method, the active response to an applied electric field in cells clusters and cells with arbitrary geometry are investigated.

Made available in DSpace on 2016-08-17T14:52:49Z (GMT). No. of bitstreams: 1 Aniceto_de_Deus_Pereira_Neto.pdf: 1168768 bytes, checksum: adc4488efe00f3201345ff8a783ac6bb (MD5) Previous issue date: 2008-07-25 / The restructuring and deregulation of electricity markets has caused signi¯cant changes in electrical power systems in several countries. This process has result in a market-based competition by creating an open market environment. In this new environment each generation company runs the Unit Commitment to maximize their pro¯ts, and have no obligation to meet the energy and spinning reserve demands, as happened in the past. With this new structure, the Unit Commitment problem has received special attention, since generation companies in actual model always seek the maximum pro¯t without concern to serve all demands. On the other hand, there is the system operator, which always seeks to optimize overall system at the lowest cost. So, there are two di®erent situations into this competitive market environment: generators seeking the maximum bene¯t without concern to the system security operating, and independent system operator seeking always operate the system safely and at less cost. This work presents the mathematical models and the solution Unit Commitment problem, which was implemented considering two view points: the generation companies and the system independent operator views. Moreover, an auction model is extended to PRD in a horizon of 24 hours. This auction model simulates the interaction between generators and system operator to meet demands and security of the system. The idea is to stimulate the players to o®er products to energy (primary) and reserve (Ancilar Service) markets using only prices o®ered by market operator for each product. This iterative process is ¯nalized when generators supply su±cient to meet demand, and not cause any violation on °ow limits in transmission lines. The solution method proposed for Unit Commitment is based on evolution strategies and Lagrange Relaxation, resulting in a robust hybrid algorithm. The method have been validated in a test system composed of 6 buses, 7 transmission lines and 10 generating units. The results showed the e±ciency of the hybrid model proposed, which was able to solve the unit commitment problem in its various models considered here. / A reestruturação dos mercados de energia elétrica provocou mudanças significativas nos sistemas elétricos de potência de diversos países. Neste novo ambiente, cada empresa de geração executa individualmente o Pré-Despacho para maximizar seus benefícios financeiros, e não têm a obrigação em atender suas demandas de potência e reserva girante, como acontecia no modelo tradicional. Por outro lado existe o operador do sistema, o qual sempre busca a otimização global do sistema ao menor custo. Assim, têm-se duas situações distintas neste ambiente competitivo: os geradores buscando o máximo benefício sem preocupação com a segurança operativa do sistema, e o operador independente buscando sempre operar o sistema de forma segura e ao menor custo. Este trabalho apresenta as modelagens matemáticas e a solução do Pré- Despacho executado sob os dois pontos de vista: dos agentes de geração e do operador independente do sistema. Além do mais, um modelo de leilão é estendido para o PRD num horizonte de 24 horas. Este modelo simula a interação entre os agentes de geração e o operador do sistema na busca por uma solução única que concilie o interesse de ambos. A idéia é estimular os agentes geradores a ofertarem os produtos para os mercados de energia (primário) e de reserva (Serviço Ancilar) mediante oferta de preços pelo operador do mercado para os respectivos produtos. Esse procedimento iterativo é finalizado quando a oferta dos geradores for suficiente para atender completamente a demanda e, não provocar violações em nenhum limite de fuxos na malha de transmissão. O método de solução proposto para o Pré-Despacho é baseado em estratégias evolutivas e Relaxação de Lagrange, resultando em um modelo híbrido robusto. Os modelos e técnicas foram validados em um sistema teste composto por 6 barras, 7 linhas de transmissão e 10 unidades geradoras. Os resultados obtidos demonstraram a eficiência do método de solução, o qual se mostrou capaz de resolver o problema de Pré-Despacho nas suas diversas modelagens utilizadas.

Cette thèse traite de la modélisation et de l'approximation numérique des écoulements liquide-gaz compressibles. La difficulté centrale est la modélisation et l'approximation de l'interface liquide-gaz. Le modèle bifluide est constitué d'un système de lois de conservation fermé par une loi d'état du mélange. La loi d'état conditionne les bonnes propriétés (hyperbolicité, existence d'une entropie de Lax) du système. Les schémas classiques de type Godunov conduisent à des imprécisions les rendant inutilisables en pratique. L'existence de solutions discontinues rend difficile la construction de schémas d'ordre élevé et nécessite des maillages très fins pour une précision acceptable. Il est indispensable de proposer des algorithmes performants pour les calculateurs parallèles les plus récents. Nous aborderons chacune de ces problématiques: construction d'une "bonne" loi de pression, construction de schémas numériques adaptés, programmation sur calculateur massivement multicoeur. / This thesis deals with the modeling and numerical approximation of compressible gas-liquid flows. The main difficulty lies in modeling and approximation of the liquid-gas interface. The two-fluid model is a system of conservation laws closed with a mixture pressure law. The law has to be chosen carefully, it conditions good properties of the system as hyperbolicity or existence of a Lax entropy. Classic conservative Godunov-type schemes lead to inaccuracies that make them unusable inpractice. The existence of discontinuous solutions makes it difficult to build high order schemes and requires very fine meshes to an acceptable accuracy. It is therefore essential to provide efficient algorithms for the High Performance Computing. In this thesis, we will partially treat each of these issues : construction of a "good" pressure law, building adapted numerical schemes, programming on GPU or GPU cluster.

Cette thèse de doctorat composée de trois chapitres contribue au développement de la problématique sur la sélection de modèle de volatilité de type GARCH. Le premier chapitre propose une étude de simulation sur la sélection de modèles dans le cadre spécifique des modèles à changement de régimes. On propose des expériences de simulation permettant de mettre en évidence l'inefficacité des critères de sélection usuels dans des cas particuliers, ce qui peut conduire à des erreurs de spécification lors du choix de modèle. Le deuxième chapitre propose un test du multiplicateur de Lagrange de mauvaise spécification dans les modèles GARCH univariés. L'hypothèse nulle admet que le processus générateur des données est un modèle GARCH linéaire tandis que sous l'hypothèse alternative il correspond à une forme fonctionnelle inconnue qui est linéarisée à l’aide d’un développement de Taylor. On illustre le test dans une application empirique sur les taux de change. Le dernier chapitre étudie l'impact du prix du pétrole sur les spreads de Credit Default Swaps souverains de deux pays exportateurs de pétrole: le Vénézuela et la Russie. Utilisant des données récentes, nous trouvons que les rendements du prix du pétrole impactent les spread de CDS souverains du Vénézuela directement alors que cela passe par le canal du taux de change pour la Russie. Ce chapitre emploie des méthodes statistiques avancées, notamment l'utilisation de modèles à changement de régimes Markoviens. Finalement, l'appendice propose le manuel de la toolbox MSGtool (Matlab) qui propose une collection de fonctions pour l'étude des modèles à changement de régimes Markoviens. La toolbox est très user-friendly. / This Ph.D. thesis composed by three chapters contributes to the development of model selection in GARCH-type models.The first chapter investigates whether the most common selection criteria lead to choose the right specification in a regime switching framework. We propose simulation experiments which reveal the inefficiency of some selection criteria in particular cases which lead to misspecification. Depending on the Data Generating Process used in the experiments, great care is needed when choosing a criterion.In the second chapter, a misspecication test for GARCH-type models is presented. We propose a Lagrange Multiplier type test based on a Taylor expansion to distinguish between (G)ARCH models and unknown nonlinear GARCH-type models. This test can be seen as a general misspecication test. We investigate the size and the power of this test through Monte Carlo experiments. We show the usefulness of our test with an illustrative empirical example based on daily exchange rate returns.In the third chapter, we study the impact of oil price returns on sovereign Credit Default Swaps (CDS) spreads for two major oil producers, Russia and Venezuela. Using daily spreads from 2008 to 2015, we find that crude oil price returns are a critical determinant of Venezuela CDS spreads changes, but does not explain significantly Russian CDS spreads. Indeed, oil prices seem to impact Russian CDS spreads through the exchange rates canal. Finally, we propose as an appendix the manual of the MSGtool, a MATLAB toolbox, which provides a collection of functions for the simulation and estimation of a large variety of Markov Switching GARCH (MSG) models.