Orientadores: Vera Lucia da Rocha Lopes, Jose Mario Martinez / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-06T05:45:54Z (GMT). No. of bitstreams: 1 Mendonca_LuzianeFerreirade_D.pdf: 3091539 bytes, checksum: 7c40c0932b2056dbe8dfb8e1f7da8401 (MD5) Previous issue date: 2006 / Resumo: Sistemas de Otimalidade (ou Sistemas KKT) são sistemas formados pelas condições primais-duais estacionárias para a solução de problemas de otimização. Sob hipóteses adequadas (condições de qualificação), os minimizadores locais de um problema de minimização satisfarão as equações e inequações KKT; entretanto, infelizmente, muitos outros pontos estacionários (incluindo maximizadores) também são soluções desse sistema não linear. Por essa razão, os métodos destinados à resolução de problemas de programação não-linear fazem uso constante da estrutura de minimização, e o uso simples de métodos destinados à resolução de sistemas não-lineares podem gerar soluções espúrias. Todavia, caso o método destinado à resolução do sistema KKT tenha um ponto inicial situado na região de atração para um minimizador, esse método pode vir a ser muito eficiente. Neste trabalho, os métodos quase-Newton para a resolução de sistemas não-lineares são usados como aceleradores de algoritmos de programação não-linear (Lagrangiano Aumentado) com restrições de igualdade, desigualdade e caixa. Utilizamos como acelerador o método simétrico inverso de correção de posto um (ISR1), o qual realiza reínicios periódicos e faz uso das estruturas esparsas das matrizes para armazenamento. São demonstrados resultados de convergência e são realizados vários experimentos numéricos que comprovam a eficiência desta estratégia para problemas de minimização com restrições de igualdade, e indicam outros caminhos para problemas de minimização com restrições gerais (igualdade, desigualdade e caixa) / Abstract: Optimality (or KKT) systems arise as primal-dual stationarity conditions for constrained optimization problems. Under suitable constraint qualifications, local minimizers satisfy KKT equations but, unfortunately, many other stationary points (including, perhaps, maximizers) may solve these nonlinear systems too. For this reason, nonlinear-programming solvers make strong use of the minimization structure and the naive use of nonlinear-system solvers in optimization may lead to spurious solutions. Nevertheless, in the basin of attraction of a minimizer, nonlinear-system solvers may be quite efficient. In this work quasi-Newton methods for solving nonlinear systems are used as accelerators of nonlinear-programming (augmented Lagrangian) algorithms. A periodically-restarted memoryless symmetric rank-one (SRI) correction method is introduced for that purpose. Convergence results are given. For problems with only equality constraints, numerical experiments that confirm that the acceleration is effective are presented. A bunch of problems with equalities, inequalities and box constraints is tested and several comments and suggestions for further work are presented / Doutorado / Doutor em Matemática Aplicada

Orientador: Jose Mario Martinez Perez / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T12:07:27Z (GMT). No. of bitstreams: 1 Martinez_AndreLuisMachado_D.pdf: 1457053 bytes, checksum: 6d70bba5dd246c0212765142b6451a5d (MD5) Previous issue date: 2009 / Resumo: Quando resolvemos problemas de programação não linear por meio de algoritmos que utilizam o Lagrangiano Aumentado, um fenômeno chamado voracidade pode ocorrer. Quando isto ocorre o método busca pontos muito infactíveis com valores de função muito pequenos, em geral, nas primeiras iterações, assim o parâmetro de penalidade cresce excessivamente, de tal forma que prejudica o condicionamento do problema. Neste trabalho 'e sugerida uma abordagem de regularização para superar esta dificuldade. Um método de Lagrangiano Aumentado é definido, com a adição de um termo regularizador que inibe a possibilidade do iterando se afastar demasiadamente do ponto de referência. Provamos convergência e apresentamos exemplos numéricos. / Abstract: When one solves Nonlinear Programming problems by means of algorithms that use merit criteria combining the objective function and penalty feasibility terms, a phenomenon called greediness may occur. Unconstrained minimizers attract the iterates at early stages of the calculations and, so, the penalty parameter needs to grow excessively, in such a way that ill conditioning harms the overall convergence. In this work a regularization approach is suggested to overcome this dificulty. An Augmented Lagrangian method is defined with the addition of a regularization term that inhibits the possibility that the iterates go far from a reference point. Convergence proofs and numerical examples are given. / Doutorado / Doutor em Matemática Aplicada

Ce travail porte principalement sur la dynamique et les méthodes de détection des exoplanètes coorbitales. Nous appelons "coorbitale" toute configuration pour laquelle deux planètes orbitent avec le même moyen mouvement moyen autour d'une même étoile. Dans un premier temps, nous revisitons les résultats du cas coplanaire circulaire. Nous rappelons également que les variétés des coorbitaux circulaires et celle des coorbitaux coplanaires sont toutes deux invariantes par le flot du Hamiltonien moyen. Nous nous intéressons donc à ces deux cas particuliers. L'accent est mis sur le cas coplanaire (excentrique), où nous étudions l'évolution de familles d'orbites quasi-périodiques de dimension non maximale en fonction de l'excentricité des planètes. Nous montrons que la géométrie des ces familles dépend fortement de l'excentricité, ce qui entraine des changements de topologie importants dans l'ensemble de l'espace des phases à mesure que celle-ci augmente. Un chapitre est dédié à la détection des exoplanètes coorbitales. On y rappelle les différentes méthodes de détection adaptées au cas coorbital. On développe particulièrement le cas des vitesses radiales, ainsi que leur combinaison avec des mesures de transit. Enfin, on décrit une méthode permettant d'étudier l'effet de perturbations orbitales sur les résonances spin-orbite d'un corps indéformable. Nous appliquons cette méthode dans deux cas: le cas coorbital excentrique, et le cas circumbinaire. / This work focuses on the dynamics and the detection methods of co-orbital exoplanets. We call "co-orbital" any configuration in which two planets orbit with the same mean mean-motion around the same star. First, we revisit the results of the circular coplanar case. We also recall that the manifold associated to the coplanar case and the manifold corresponding to the circular case are both invariant by the flow of the averaged Hamiltonian. We hence study these two particular cases. We focus mainly on the coplanar case (eccentric), where we study the evolution of families of non-maximal quasi-periodic orbits parametrized by the eccentricity of the planets. We show that the geometry of these families is highly dependent on the eccentricity, which causes significant topology changes across the space of phases as the latter increases. A chapter is dedicated to the detection of co-orbital exoplanets. We recall the different detection methods adapted to the co-orbital case. We focus on the radial velocity technique, and the combination of radial velocity and transit measurements. Finally, we describe a method to study the effect of orbital perturbations on the spin-orbit resonances for a rigid body. We apply this method in two cases: the eccentric co-orbital case and the circumbinary case.

Der Effekt eines externen Magnetfeldes auf die mehrphasige und turbulente Strömung in Stranggußkokillen und deren Wechelspiel führt in den wissenschaftlichen Arbeiten zu widersprüchlichen Aussagen. Die verschiedenen Prozessparameter können innerhalb eines kleinen Varianzbereichs entscheidenden Einfluss auf die Aussage haben, ob ein Magnetfeld begünstigend oder schädigend auf die Qualität des Produkts wirkt. Um wichtige Einflussfaktoren zu identifizieren, werden daher numerische Strömungssimulationen des Prozesses durchgeführt. Dazu wird zunächst ein mehrphasiger und inkompressibler Mehrregionen-CFD-Löser für magnetohydrodynamische Strömungen entwickelt und validiert, um die komplexe Strömung in einer Stranggußkokille mit hoher Genauigkeit simulieren zu können. Darauf aufbauend wird das numerische Setup anhand einer Modellkokille mit aktuellen Messdaten validiert. Durch die neuartige Kombination Lagrange'scher Lösungsmethoden mit angepassten Termen für die Magnetohydrodynamik sowie der skalenaufgelösten magnetohydrodynamischen Turbulenz, können erstmals Aussagen zur optimalen Magnetfeldverteilung im Hinblick auf Strömungsstabilität, Turbulenzmodulation und Blasenverteilung getroffen werden. Mit Hilfe dieses Wissens können neuartige Konzepte elektromagnetischer Bremssysteme für den Stranggußprozess entwickelt werden.

In this thesis, we investigate two expressions for symmetric group characters: Kerov?s universal character polynomials and Stanley?s character polynomials. We give a new explicit form for Kerov?s polynomials, which exactly evaluate the characters of the symmetric group scaled by degree and a constant. We use this explicit expression to obtain specific information about Kerov polynomials, including partial answers to positivity questions. We then use the expression obtained for Kerov?s polynomials to obtain results about Stanley?s character polynomials.

La méthode des éléments finis est une méthode de modélisation des systèmes, utilisée dans l’ensemble des domaines de la physique ainsi que dans l’ingénierie. Elle permet d’obtenir des résultats précis. Cependant la nécessité de modéliser des systèmes de plus en plus complexes, avec une précision de plus en plus grande, demande une puissance de calcul qui n’est pas toujours disponible. Il est ainsi nécessaire, afin de résoudre ces problèmes, de trouver des méthodes de calcul permettant de conserver cette précision, mais de réduire le temps de calcul.Une solution pour tenter de palier à ce défaut est de décomposer le problème complexe initial en plusieurs sous-problèmes, maillés indépendamment, et entre lesquels il est nécessaire de coupler les solutions. Quelques méthodes permettant de recoller ces maillages sont étudiées dans ce présent mémoire. Elles sont présentées ainsi que quelques outils liés, tels que des méthodes de résolution, et des fonctions de formes plus adaptées à leur utilisation. Il est montré, à travers ces travaux, qu’il est tout à fait possible de recoller les maillages en électrotechnique, et par là d’obtenir des résultats intéressants en terme de précision, et de qualité de solution. Cependant, les méthodes de résolution utilisées ici n’ont pas permis d’obtenir des temps de calculs satisfaisants pour les cas étudiés. / The finite element method is used to model complex systems in all the physics and engineering. This method has a good accuracy. Because of the complexity of the systems, and the require precision, this method need a very large computing capacity, which is not always available. Consequently it is necessary to find calculation methods which allow preserving the accuracy, and reducing the computation time.One way to solve this situation is to decompose the complex problem in several sub-problems, with non-connecting meshes, and reconnect them. Some methods used to reconnect are developed in this work, with some tools, like resolution methods, and new shape functions necessary for this configuration of non-connecting meshes. This work shows the possibility of those methods: they reconnect the different meshes, conserve the accuracy and the quality of the solution. But the solving methods used here do not reduce consequently the computation time.

A thesis submitted to the faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Doctor of Philosophy, / The inverse problem in the Calculus of Variations involves determining the Lagrangians, if any, associated with a given (system of) differential equation(s). One can classify Lagrangians according to the Lie algebra of symmetries of the Action integral (the Noether algebra). We give a complete classification of first-order Lagrangians defined on the line and produce results pertaining to the dimensionality of the algebra of Noether symmetries and compare and contrast these with similar results on the algebra of Lie symmetries of the corresponding Euler-Lagrange .equations. It is proved that the maximum dimension of the Noether point symmetry algebra of a particle Lagrangian. is five whereas it is known that the maximum dimension Qf the Lie algebra of the corresponding scalar second-order Euler-Lagrange equation is eight. Moreover, we show th'a.t a particle Lagrangian does not admit a maximal four-dimensional Noether point symmeiry algebra and consequently a particle Lagrangian admits the maximal r E {O, 1,2,3, 5}-dimensional Noether point symmetry algebra, It is well .known that an important means of analyzing differential equations lies in the knowledge of the first integrals of the equation. We deliver an algorithm for finding first integrals of partial differential equations and show how some of the symmetry properties of the first integrals help to 'further' reduce the order of the equations and sometimes completely solve the equations. Finally, we discuss some open questions. These include the inverse problem and classification of partial differential equations. ALo, there is the question of the extension of the results to 'higher' dimensions. / Andrew Chakane 2018

Chu Shun Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 63-65). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Preliminaries --- p.8 / Chapter 2 --- Singular Integrals --- p.15 / Chapter 2.1 --- Marcinkiewicz Integral --- p.15 / Chapter 2.2 --- Decomposition in cubes of open sets in Rn --- p.17 / Chapter 2.3 --- Interpolation Theorem for Lp --- p.18 / Chapter 2.4 --- Singular Integrals on homogeneous of degree 0 --- p.25 / Chapter 3 --- Solutions to the Euler Equations --- p.36 / Chapter 3.1 --- Existence and Uniqueness of smooth solutions for Euler Equations --- p.36 / Chapter 3.2 --- Rate of Convergence and Decay in Time --- p.43 / Chapter 3.2.1 --- Rate of Convergence --- p.43 / Chapter 3.2.2 --- Lp Decay for Solutions of the Navier-Stokes Equations --- p.46 / Chapter 3.3 --- Weak Solution to the Euler Equations --- p.48 / Chapter 3.3.1 --- Weak Solution to the Velocity Formulation --- p.49 / Chapter 3.3.2 --- Weak Solution to the Vorticity Formulation --- p.52 / Bibliography --- p.63

by Ho Wing Kin. / Thesis submitted in: July 1997. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 89-92). / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- The Euler-Lagrange Equation for Capillary Surfaces --- p.6 / Chapter 1.2 --- The Capillary Tube --- p.12 / Chapter 2 --- Comparison Principles --- p.16 / Chapter 2.1 --- The General Comparison Principle --- p.16 / Chapter 2.2 --- Applications --- p.24 / Chapter 3 --- Existence Criteria --- p.30 / Chapter 3.1 --- Necessary Conditions --- p.31 / Chapter 3.2 --- Sufficient Conditions --- p.35 / Chapter 4 --- Uniqueness --- p.53 / Chapter 4.1 --- General Bounded Domains Case --- p.53 / Chapter 4.2 --- Infinite Strip Case --- p.56 / Chapter 5 --- Gradient Estimate of Surfaces of Constant Mean Curvature --- p.66 / Chapter 5.1 --- The Gradient Estimate --- p.67 / Chapter 5.2 --- Behavior as R→ 1 --- p.70 / Chapter 5.3 --- Existence of the Comparison Surfaces --- p.76 / Chapter 5.4 --- Ro is Best Possible --- p.82 / Appendix Mean Curvature --- p.85

本論文討論了具有非平凡旋度的穩態亞音速流體的適定性問題。 / 首先，我們研究了通過無限長週期管道的二維亞音速流禮。當管道某一週期位置伯努利函數擾動很小，且質量數介於與適當的範圍時，有且僅有唯一的亞音速流禮。特別地，對於伯努利函數為常值的情形，我們還通過結構緊性的方法證明了亞音速-音速流體的存在性。此時，質量數可以達到一臨界值。謝春景和辛周平在處理二維司壓歐拉方程時曾引入了一個重要的處理方法一一流函數表達式。然而，對於週期流體的問題，伯努利函數和流函數的相互關係是無法事先確定的。為此，我們建立了一個關於流函數的非線性映射。該映射的不動點給出了相應歐拉方程的解。 / 其次，對於二維亞音速流體通過對稱障礙物的問題，當來流的伯努利函數關於y方向對稱，且擾動很小時，我們給出了流体的存在性和唯一性的証明。这里，我們利用歐拉方程的流函數方法，得到了對應于流函數的二階方程的解。能量方法以及動量場與來流動量場之差的L2可積性給出了流函數的漸進行為。這一漸進行為結合障礙物外無駐點的事實說明了流函數表示與原先歐拉方程是相容的。 / 最后，我們研究了當給定管道壁上法向动量時，三維穩態流體通過方體管道的問題。如果入口處伯努利函數的擾動和旋度的法向分量為零，則當邊界的法向動量不超過一臨界值時，無旋的亞音速流體存在。對於一般情形，若伯努利函數的擾動和旋度的法向分量很小時，我們利用將速度均分解均無旋部分和旋度部分的方法給出了流體存在性的證明。這裡，我們通過求解一加權的散旋系統得到了旋度部份的解:而無旋部份則由一擬線性橢圓方程的解給出。 / In this thesis, the wellposedness theory of steady subsonic flows with nontrivial vorticities is studied in various aspects. / First, we study 2-D subsonic flows through infinitely long periodic nozzles. It is showed that when mass flux lies in a suitable regime and the variation of Bernoulli's function at some given section is sufficiently small, there exists a unique global subsonic flow in the periodic nozzle. In particular, if Bernoulli's function is a constant, the existence of subsonic flow is also obtained when mass flux takes the critical number by a compensated compactness framework. One of the main tools to handle 2-D compressible Euler equations is the stream function formulation first established by Xie and Xin. The main difficulty in adapting this formulation in periodic nozzles is that the relation between Bernoulli's function and stream function cannot be fixed. We resolve this difficulty via setting up a nonlinear map from stream function at the given section to itself. The fixed point of this map induces a solution of corresponding Euler equations. / Second, the existence and uniqueness of 2-D subsonic flows past a symmetric body are established under the assumption that Bernoulli's function is given symmetrically in the upstream with small variation. By the stream function formulation for 2-D compressible Euler equations, one obtains the solution of the Euler equations via solving a quasilinear second order equation for stream function. This is achieved with the help of the theory of elliptic equations of two variables. Asymptotic behavior for the stream function is obtained via energy method and L²-integral of the difference between the momentum and its asymptotic behavior in the upstream. The asymptotic behavior, together with the property that stagnation points are absent outside the body, yields that the stream function formulation is consistent with the original Euler system. / Finally, we study the existence of 3-D steady subsonic flows in rectangular nozzles when prescribing the normal component of the momentum on the boundary. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the exit vanish, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. In general, if the normal component of the vorticity and the variation of Bernoulli's function are both sufficiently small, we prove the existence of Euler flows by decomposing the velocity into the vortical part and the potential part. A div-curl system with given weighted function is used to obtain the vortical part and the potential part is induced by the solution to a quasilinear elliptic equation. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chen, Chao. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 111-120). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.12 / Chapter 3 --- 2-D subsonic flows through in finitely long periodic nozzles --- p.23 / Chapter 3.1 --- Introduction and main result --- p.23 / Chapter 3.2 --- Stream function formulation of potential flows --- p.27 / Chapter 3.2.1 --- Bernoulli's law and stream function formulation --- p.27 / Chapter 3.2.2 --- Potential flows and proof of Theorem 3.1.1 --- p.30 / Chapter 3.3 --- Analysis of the well-posedness of Euler flows --- p.32 / Chapter 3.3.1 --- Existence, uniqueness, and periodicity of truncated flows --- p.34 / Chapter 3.3.2 --- Existence and uniqueness of Euler flflows --- p.41 / Chapter 4 --- 2-D subsonic flows past a symmetric body --- p.47 / Chapter 4.1 --- Motivation and mathematical formulation --- p.47 / Chapter 4.2 --- Truncated problem --- p.53 / Chapter 4.3 --- Asymptotic behavior at upstream and downstream --- p.59 / Chapter 4.4 --- Existence and uniqueness of Euler flflows --- p.61 / Chapter 5 --- 3-D subsonic Euler flows through nitely long nozzles --- p.67 / Chapter 5.1 --- Mathematical formulation and main results --- p.67 / Chapter 5.2 --- Some preliminaries --- p.71 / Chapter 5.3 --- 3-D potential flows --- p.76 / Chapter 5.3.1 --- Apriori estimates for truncated potential flows --- p.77 / Chapter 5.3.2 --- Existence and uniqueness of potential flows --- p.91 / Chapter 5.4 --- General 3-D steady Euler systems --- p.94 / Chapter 6 --- Further discussions and future work --- p.109 / Bibliography --- p.111