Este trabalho apresenta uma abordagem do método da função barreira logarítmica (MFBL) para a resolução do problema de fluxo de potência ótimo (FPO). A pesquisa fundamenta-se metodologicamente na função barreira logarítmica e nas condições de primeira ordem de Karush-Kuhn-Tucker (KKT). Para a solução do sistema de equações resultantes das condições de estacionaridade, da função Lagrangiana, utiliza-se o método de Newton. Na implementação computacional utiliza-se técnicas de esparsidade. Através dos resultados numéricos dos testes realizados em 5 sistemas (3, 8, 14, 30 e 118 barras) evidencia-se o potencial desta metodologia na solução do problema de FPO. / This work describes an approach on logarithmic barrier function method to solving the optimal power flow (OPF) problem. Search was based on the logarithmic barrier function and first order conditions of Karush-Kuhn-Tucker (KKT). To solve the equation system, obtained from the stationary conditions of the Lagrangian function, is used the Newton method. Implementation is performed using sparsity techniques. The numerical results, carried out in five systems (3, 8, 14, 30 and 118 bus), demonstrate the reliability of this approach in the solution OPF problem.

Submitted by Marina Teixeira Costa null (marinateixeiracosta@gmail.com) on 2017-02-14T14:27:15Z No. of bitstreams: 1 Dissertação MARINA 12.pdf: 1807218 bytes, checksum: 95bc28b832360cf51847512b47b234d8 (MD5) / Approved for entry into archive by LUIZA DE MENEZES ROMANETTO (luizamenezes@reitoria.unesp.br) on 2017-02-14T15:29:56Z (GMT) No. of bitstreams: 1 costa_mt_me_bauru.pdf: 1807218 bytes, checksum: 95bc28b832360cf51847512b47b234d8 (MD5) / Made available in DSpace on 2017-02-14T15:29:56Z (GMT). No. of bitstreams: 1 costa_mt_me_bauru.pdf: 1807218 bytes, checksum: 95bc28b832360cf51847512b47b234d8 (MD5) Previous issue date: 2016-12-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O problema de Fluxo de Potência Ótimo determina a melhor condição de operação de um sistema elétrico de potência. Há diferentes classes de problemas de Fluxo de Potência Ótimo de acordo com os tipos de funções a serem otimizadas, e os conjuntos de controles e de restrições utilizados. Dentre elas, dá-se destaque ao problema de Fluxo de Potência Ótimo com Restrição de Segurança, o qual é uma importante ferramenta para os Operadores dos Sistemas de Transmissão, tanto para o planejamento operacional, quanto para a precificação da energia. Seu objetivo é minimizar os custos operacionais de geração de energia levando em consideração as restrições decorrentes da operação do sistema sob um conjunto de contingências. Ele é formulado como um problema de otimização não linear, não-convexo de grande porte, com variáveis contínuas e discretas. Neste trabalho investiga-se este problema em relação à sua formulação, dificuldades computacionais e método de solução. Para um tratamento do problema mais próximo à realidade adotam-se alguns controles como variáveis discretas, ou seja, os taps dos transformadores. Estes são tratados através de um método que penaliza a função objetivo quando as variáveis discretas assumem valores não discretos. Desta forma, o problema não linear discreto é transformado em um problema contínuo e o método Primal-Dual Barreira Logarítmica é utilizado em sua resolução. Testes computacionais são apresentados com o problema de Fluxo de Potência Ótimo com Restrição de Segurança associado ao sistema teste IEEE 14 barras em três etapas de teste. Os resultados obtidos e as comparações realizadas comprovam a eficiência do método de resolução escolhido / The Optimum Power Flow problem determines the best operating condition of an electric power system. There are different classes of Optimal Power Flow problems according to the types of functions to be optimized, and the sets of controls and constraints used. Among them, the problem of Optimal Power Flow with Security Constraint is highlighted, which is an important tool for the Transmission System operators, both for operational planning and for energy pricing. Its objective is to minimize the operational costs of power generation taking into account the constraints arising from the operation of the system under a set of contingencies. It is formulated as a nonlinear, nonconvex large optimization problem, of continuous and discrete variables. In this work, the problem in relation to its formulation, computational difficulties and solution method is investigated. For a treatment of the problem closest to the reality, some controls such as discrete variables, i.e. the taps of the transformers, are used. These are treated by a method that penalizes the objective function when the discrete variables assume non-discrete values. Thus, the discrete nonlinear problem is transformed into a continuous problem and the Primal-Dual Logarithmic Barrier method is used in its resolution. Computational tests are performed with the optimal power flow problem with security constraint associated with the test system of IEEE 14 bars in three test stages. The obtained results and the realized comparisons prove the efficiency of the chosen resolution method.

Este trabalho tem como objetivo realizar um estudo de alocação de unidades termoelétricas em sistemas elétricos de potência (SEP). O fluxo de potencia ótimo (FPO) foi utilizado para se obter o ponto ótimo de operação para o sistema e os multiplicadores de Lagrange associados às restrições. Os multiplicadores de Lagrange indicam a sensibilidade entre a função objetivo e a restrição a ele associada. Esta sensibilidade indica, quais as barras do sistema, são candidatas à alocação de novas usinas termoelétricas. Testes nos sistemas de 5 barras, IEEE 14 barras, IEEE 30 barras, equivalente CESP 440 kV de 53 barras e IEEE 118 barras comprovam a eficiência da abordagem, a qual poderá ser utilizada em estudos de planejamento da expansão do sistema. / The aim of this paper is to present a study of thermoelectrical generation allocation in electric power systems. The optimal power flow (OPF) was used to evaluate the optimal operation point for the power system and also Lagrange multipliers associated with the constraints. The Lagrange multipliers are the sensitivity between the objective function and its constraints. This sensitivity is used to verify in a power system where is the best place to incentive the allocation of new thermoelectrical power plants. Tests on the systems: 5 buses, IEEE 14 buses, IEEE 30 buses, equivalent CESP 440kV 53 buses and IEEE 118 buses showed the efficiency of the presented approach. This method of analyzing the system can be used in study of expansion planning system.

Made available in DSpace on 2016-04-27T16:59:00Z (GMT). No. of bitstreams: 1 Patrick Oliveira de Lima.pdf: 8733714 bytes, checksum: ab9aed451f55100434d75510f10d5dba (MD5) Previous issue date: 2009-11-10 / Secretaria da Educação do Estado de São Paulo / This work has as objective, contribute to the reflection about an important moment in the process of curriculum implementation, in other words, the one which is developed inside of the classroom, analyzing how its plan can be done and where is the teacher related to this process. It has as a theoretician recital the Simon s works about hypothetical trajectories of learning (HTL), expression that he uses to refer to the prognostic from teacher to teach and he uses this expression to show the way that will make the learning process possible. It is a research of qualitative features, because the concern with the process is a constant during the research: the main interest of investigation is the one to evidence how is the planning process and the education accomplishment done, in a growing perspective of learning. The research counts on the contribution of two Math teachers of a public school from São Paulo and their performance among 80 students from high school. In this research, we developed a HTL project about logarithmic functions, searching to involve contextualized situations, interdisciplinary situations and made of activities of problems resolution, involving applications on daily situations, in another knowledge areas and main for the mathematics area. With our work, we intend to contribute to the professional development of the teachers in a consistent way that is intended to be practiced in class, by an articulation strategy between theory, teaching practice and research / O presente trabalho tem como objetivo contribuir para a reflexão sobre um momento importante do processo de implementação curricular, ou seja, aquele que se desenvolve em sala de aula, analisando como pode se dar seu planejamento e qual a participação do professor nesse processo. Tem como fundamentação teórica os trabalhos de Simon sobre trajetórias hipotéticas de aprendizagem (THA), expressão que ele utiliza tanto para fazer referência ao prognóstico do professor para ensinar como para o caminho que possibilitará o processamento da aprendizagem. Trata-se de uma pesquisa de natureza qualitativa, pois a preocupação com o processo é uma constante durante a pesquisa: o interesse principal da investigação é o de evidenciar como se dá o processo de planejamento e realização do ensino, numa perspectiva construtivista de aprendizagem. A pesquisa conta com a colaboração de dois professores de Matemática de uma escola pública estadual de São Paulo e sua atuação junto a 80 alunos de ensino médio. Em nossa pesquisa desenvolvemos uma THA sobre funções logarítmicas, buscando envolver situações contextualizadas, interdisciplinares e constituídas por atividades de resolução de problemas, envolvendo aplicações em situações do cotidiano, em outras áreas de conhecimento e internas à própria Matemática. Com nosso trabalho, pretendemos contribuir para o desenvolvimento profissional dos professores de forma coerente com que se pretende que seja sua prática em sala de aula, mediante uma estratégia de articulação entre teoria, prática docente e pesquisa

Este trabalho descreve uma abordagem do método primal-dual barreira logarítmica (MPDBL) associado ao método de Newton modificado para a resolução do problema de fluxo barreira logarítmica e nas condições de primeira ordem de Karush-Kuhn-Tucker (KKT). O sistema de equações resultantes das condições de estacionaridade, da função Lagrangiana, foi resolvido pelo método de Newton modificado. Na implementação computacional foram usadas as técnicas de esparsidade. Os resultados numéricos dos testes realizados em 5 sistemas (3, 14, 30, 57 e 118 barras) evidenciam o potencial desta metodologia na solução do problema de FPO. / This work describes an approach on primal-dual logarithmic barrier for solving the optimal power flow problem (OPF). The investigation was based on the logarithmic barrier function and Karush-Kuhn-Tucker (KKT) first-order necessary conditions. The equation system, obtained from the stationary conditions of the Lagrangian function, was solved using the Newton\'s modified method. The implementation was performed using sparsity techniques. The numerical results, carried out in five systems (3, 14,30, 57 and 118 bus), demonstrate the reliability of this approach in the solution OPF problem.

Cette thèse est une étude théorique d’un système d’équations de Cahn-Hilliard/Allen-Cahn couplées qui représente un mélange binaire en séparation de phase. Le but principal de l’étude est le comportement asymptotique des solutions en termes d’attracteurs exponentiels/globaux. Pour cette raison, l’existence et l’unicité de la solution sont étudiées tout d’abord. Une des principales applications de ce modèle d’équations est la cristallographie.Dans la première partie de la thèse, on examine le modèle proposé avec des conditions de type Dirichlet sur le bord et une non linéarité régulière de type polynomial : on réussit à trouver un attracteur exponentiel et par conséquence un attracteur global de dimension finie. Une non linéarité singulière de type logarithmique est ensuite prise dans la deuxième partie, cette fonction étant approchée par une suite de fonctions régulières et l’existence d’un attracteur global est démontrée sous des conditions au bord de type Dirichlet.Enfin, dans la dernière partie, le système est couplé avec une équation pour la température: suivant la loi de Fourrier premièrement, puis la loi de type III de la thermo-élasticité. Dans les deux cas, la dynamique de l’équation est étudiée et un attracteur exponentiel est trouvé malgré la difficulté créée par l’équation hyperbolique dans le deuxième cas. / This thesis is a theoretical study of a coupled system of equations of Cahn-Hilliard and Allen-Cahn that represents phase separation of binary alloys. The main goal of this study is to investigate the asymptotic behavior of the solution in terms of exponential/global attractors. For this reason, the existence and unicity of the solution are first studied. One of the most important applications of this proposed model of equations is crystallography. In the first part of the thesis, the system is studied with boundary conditions of Dirichlet type and a regular nonlinearity (a polynomial). There, we prove the existence of an exponential attractor that leads to the existence of a global attractor of finite dimension. Then, a singular nonlinearity (a logarithmic potential) is considered in the second part. This function is approximated by a sequence of regular ones and a global attractor is found.At the end, the system of equations is coupled with temperature: with the Fourrier law in the first case, then with the type III law (in the context of thermoelasticity) in the second case. The dynamics of the equations are studied and the existence of an exponential attractor is obtained.

Les simulations en mécanique du solide présentent des difficultés comme le traitement de l'incompressibilité ou les non-linéarités dues aux grandes déformations, aux lois de comportement et de contact. L'objectif principal de ce travail est de proposer des méthodes éléments finis capables de gérer l'incompressibilité en grandes déformations en utilisant des éléments de faible ordre. Parmi les approches de la littérature, les formulations mixtes offrent un cadre théorique intéressant. Dans ce travail, une formulation mixte à trois champs (déplacements, pression, gonflement) est introduite. Dans certains cas, cette formulation peut être condensée en formulation à deux champs. Cependant, il est connu que le problème discret obtenu par une approche éléments finis de type Galerkin n'hérite pas automatiquement de la condition de stabilité “inf-sup” du problème continu : les éléments finis utilisés, et notamment les ordres d'interpolation doivent être choisis de sorte à vérifier cette condition de stabilité. Cependant, il est possible de s'affranchir de cette contrainte en ajoutant des termes de stabilisation à la formulation EF Galerkin. Cette approche permet entre autres d'utiliser des ordres d'interpolation égaux. Dans ce travail, des éléments finis stables de type P2/P1 sont utilisés comme référence, et comparés à une formulation P1/P1, stabilisée soit avec une fonction bulle, soit avec une méthode VMS (Variational Multi-Scale) basée sur un espace sous-grille orthogonal à l'espace EF. Combinées à un modèle grandes déformations basé sur des déformations logarithmiques, ces approches sont d'abord validées sur des cas académiques puis sur des cas industriels. / Simulations in solid mechanics exhibit difficulties as dealing with incompressibility or nonlinearities due to finite strains, constitutive laws and contact. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using low order elements. Among the approaches in the literature, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the “inf-sup” stability condition from the continuous problem: the finite elements used, and in particular the interpolation orders must be chosen so as to satisfy this stability condition. However, it is possible to circumvent it, by adding terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite elements of type P2/P1 are used as reference, and compared to a P1/P1 formulation, stabilized with a bubble function, or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. Combined to a finite strain model based on logarithmic strain, these approaches are first validated on academic cases and then on industrial cases.

Dans cette thèse, d’une part, nous généralisons au cas équivariant un résultat de J. Denef et F. Loeser sur les sommes trigonométriques sur un tore ; d’autre part, nous étudions la stratification de Thom-Boardman associée à la multiplication des sections globales des fibrés en droites sur une courbe. Nous montrons une inégalité subtile sur les dimensions de ces strates. Notre motivation vient du programme de Langlands géométrique. En s’appuyant sur les travaux de W. T. Gan, N. Gurevich, D. Jiang et de S. Lysenko, nous proposons, pour le groupe réductif G de type G2, une construction conjecturale du faisceau automorphe dont le paramètre d’Arthur est unipotent et sous-régulier. En utilisant nos deux résultats ci-dessus, nous déterminons les rangs génériques de toutes les composantes isotypiques d’un faisceau S₃-équivariant qui apparaît dans notre conjecture, ce S₃ étant le centralisateur du SL2 sous-régulier dans le groupe dual de Langlands de G. / In this thesis, on the one hand, we generalise to the equivariant case a result of J. Denef and F. Loeser about trigonometric sums on tori ; on the other hand, we study the Thom-Boardman stratification associated to the multiplication of global sections of line bundles on a curve. We prove a subtle inequaliity about the dimensions of these strata. Our motivation comes from the geometric Langlands program. Based on works of W. T. Gan, N. Gurevich, D. Jiang and S. Lysenko, we propose, for the reductive group G of type G2, a conjectural construction of the automorphic sheaf whose Arthur parameter is unipotent and sub-regular. Using our two results above, we determine the generic ranks of all isotypic components of an S3-equivaraint sheaf which appears in our conjecture, this S3 being the centraliser of the sub-regular SL2 inside the Langlands dual group of G.

By numerical methods, two models of anisotropic mixed quantum spin chains, consisting of spins of two different sizes, Sa = 1/2 and Sb = 1 as well as Sb = 3/2, are studied with respect to their critical properties at quantum phase transitions in a selected region of parameter space. The quantum spin chains are made up of basecells of four spins, according to the structure Sa − Sa − Sb − Sb. They are described by the XXZ Hamiltonian, that extends the quantum Heisenberg model by a variable anisotropic exchange interaction. As additional control parameter, an alternating exchange constant between nearest-neighbour spins is introduced. Insight gained by complementary application of exact diagonalization and quantum Monte Carlo simulations, as well as appropriate methods of analysis, is embedded in the broad existing knowledge on homogeneous quantum spin chains. In anisotropic homogeneous quantum spin chains, there exist phase boundaries with continuously varying critical exponents, the Gaussian critical lines, along which, in addition to standard scaling relations, further extended scaling relations hold. Reweighting methods, also applied to improved quantum Monte Carlo estimators, and finite-size scaling analysis of simulation data deliver a wealth of numerical results confirming the existence of a Gaussian critical line also in the mixed spin models considered. Extrapolation of exact data offers, apart from confirmation of simulation data, furthermore, insight into the conformal operator content of the model with Sb = 1. / Mittels numerischer Methoden werden zwei Modelle anisotroper gemischter Quantenspinketten, bestehend aus Spins zweier unterschiedlicher Größen, Sa = 1/2 und Sb = 1 sowie Sb = 3/2, hinsichtlich ihrer kritischen Eigenschaften an Quanten-Phasenübergängen in einem ausgewählten Parameterbereich untersucht. Die Quantenspinketten sind aus Basiszellen zu vier Spins, gemäß der Struktur Sa − Sa − Sb − Sb, aufgebaut. Sie werden durch den XXZ Hamiltonoperator beschrieben, der das isotrope Quanten-Heisenberg Modell um eine variable anistrope Austauschwechselwirkung erweitert. Als zusätzlicher Kontrollparameter wird eine alterniernde Kopplungskonstante zwischen unmittelbar benachbarten Spins eingeführt. Die durch komplementäre Anwendung exakter Diagonalisierung und Quanten-Monte-Carlo Simulationen, sowie entsprechender Analyseverfahren, gewonnenen Erkenntnisse werden in das umfangreiche existierende Wissen über homogene Quantenspinketten eingebettet. Im Speziellen treten in anisotropen homogenen Quantenspinketten Phasengrenzen mit kontinuierlich variierenden kritischen Exponenten auf, die Gaußschen kritischen Linien, auf denen neben den herkömmlichen auch erweiterte Skalenrelationen Gültigkeit besitzen. Umgewichtungsmethoden, speziell auch angewandt auf verbesserte Quanten-Monte-Carlo Schätzer, und Endlichkeitsskalenanalyse von Simulationsdaten liefern eine Fülle von numerischen Ergebnissen, die das Auftreten der Gaußschen kritischen Linie auch in den untersuchten gemischten Quantenspinketten bestätigen. Die Extrapolation exakter Daten bietet, neben der Bestätigung der Simulationsdaten, darüber hinaus Einblick in einen Teil des konformen Operatorinhalts des Modells mit Sb = 1.

The topic of this thesis is a diffusion process on a potential landscape which is given by a smooth Hamiltonian function in the regime of small noise. The work provides a new proof of the Eyring-Kramers formula for the Poincaré inequality of the associated generator of the diffusion. The Poincaré inequality characterizes the spectral gap of the generator and establishes the exponential rate of convergence towards equilibrium in the L²-distance. This result was first obtained by Bovier et. al. in 2004 relying on potential theory. The presented approach in the thesis generalizes to obtain also asymptotic sharp estimates of the constant in the logarithmic Sobolev inequality. The optimal constant in the logarithmic Sobolev inequality characterizes the convergence rate to equilibrium with respect to the relative entropy, which is a stronger distance as the L²-distance and slightly weaker than the L¹-distance. The optimal constant has here no direct spectral representation. The proof makes use of the scale separation present in the dynamics. The Eyring-Kramers formula follows as a simple corollary from the two main results of the work: The first one shows that the associated Gibbs measure restricted to a basin of attraction has a good Poincaré and logarithmic Sobolev constants providing the fast convergence of the diffusion to metastable states. The second main ingredient is a mean-difference estimate. Here a weighted transportation distance is used. It contains the main contribution to the Poincaré and logarithmic Sobolev constant, resulting from exponential long waiting times of jumps between metastable states of the diffusion.