This thesis focuses on the development and convergence study of finite element methods for eigenvalue analysis of arbitrarily shaped domains with multi-material and material-void interfaces. Such configurations can be found in problems with evolving discontinuities and interfaces as in fluid-structure interaction or topology optimization problems. The differential equations considered in this thesis include the elliptic operator, Timoshenko beam and Mindlin plate. The compatibility conditions at the interface are weakly imposed using either Nitsche's method or Lagrange multipliers. The variational statements are derived for each case. The analysis results are benchmarked using Galerkin finite element discretization with bodyitted grids. Nitsche's method shows a direct dependence on a penalty term and for Lagrange multipliers method, additional degrees of freedom are added to the solution vector. The convergence rate of the discretized forms is computationally determined and is shown to be optimal for both Timoshenko beams and Mindlin plates.

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Cette étude s'intéresse à une méthode vortex lagrangienne 2-D permettant de simuler des écoulements incompressibles externes autour de multiples corps en mouvement arbitraire. L'implantation initiale de la méthode a été développée à 1' Université Catholique de Louvain puis des modifications ont été apportées en collaboration avec le Laboratoire de Mécanique des Fluides Numérique pour prendre en compte le mouvement et la présence simultanée de plusieurs corps. Cependant, ces modifications n'étaient pas validées et aucune méthode de calcul des forces et du moment sur les corps individuellement n'était disponible. Au sein de cette étude, plusieurs approches de calcul des forces et du moment sont présentées et détaillées, toutes ayant la particularité de ne pas nécessiter la connaissance du champ de pression de l'écoulement. La première approche utilise des surfaces de contrôle englobant chaque corps ainsi que la surface même des corps. La seconde est développée à partir d'une surface de contrôle à l'infini et ne peut fournir que les forces nettes totales sur l'ensemble des corps en présence. La troisième approche ne requiert que de l'information (vitesse et vorticité) à la surface des corps et elle est la seule pour l'instant qui permet de fournir également le moment de force. Toutes ces approches ainsi que les modifications effectuées pour prendre en compte le mouvement sont validées pour des écoulements à bas Reynolds autour de corps en translation et rotation combinés. Les cas d'un cylindre unique, de deux cylindres en tandem et d'une aile oscillante sont étudiés. Les comparaisons sont effectuées à l'aide de résultats produits par le code commercial eulérien de volumes finis Fluent 6.2. Les résultats mettent en évidence l'habilité de la méthode vortex à capturer précisément la dynamique des fluides, ainsi que l'efficacité de chacune des méthodes de calcul des forces et du moment. / This work is about a 2-D lagrangian vortex method allowing simulation of external incompressible flow around arbitrary moving bodies. The initial implementation of the method was developed at Université Catholique de Louvain and adapted for multiple moving bodies in collaboration with Laboratoire de Mécanique des Fluides Numérique. However, these modifications were not validated and no method of force and moment calculation on individual body was available. In this study, several approaches of force and moment calculation are presented and detailed, ail of which do not require information on the pressure field. The first approach uses control surfaces surrounding each body as well as the body surfaces themselves. The second one is developed from a control surface taken at infinity and can only provide total net forces on ail bodies taken together. The third one requires information (velocity and vorticity) only at body surfaces. The latter is the only approach considered up to now that can provide moment of force on the bodies. Ail three methods as well as ail the modifications that were implemented to adapt the solver to moving bodies are validated for low Reynolds number flows around bodies undergoing combined translation and angular motion. Cases of a single cylinder, two cylinders in tandem, and oscillating airfoil are studied. Comparisons are then made with results obtained with the eulerian finite volume commercial code Fluent 6.2. Results show the ability of the vortex method to correctly capture fluid dynamics, as well as the efficiency of each method for the force and moment calculations.

The development of improved numerical methods for computer simulation of high velocity impact dynamics is of importance in a variety of science and engineering fields. The growth of computing capabilities has created a demand for improved parallel algorithms for high velocity impact modeling. In addition, there are selected impact applications where experimentation is very costly, or even impossible (e.g. when certain bioimpact or space debris problems are of interest). This dissertation extends significantly the class of problems where particle-element based impact simulation techniques may be effectively applied in engineering design. This dissertation develops a hybrid particle-finite element method for a general hexahedral mesh. This work included the formulation of a numerical algorithm for the generation of an ellipsoidal particle set for an unstructured hex mesh, and a new interpolation kernel for the density. The discrete model is constructed using thermomechanical Lagrange equations. The formulation is validated via simulation of published impact experiments. / text

我們常常希望去估計一個大母體中各種不同領域內的參數值，而在抽樣實驗之前整個 母體無法被分層。當實驗的總預算有限，若選取一組簡單隨機樣本來估計這些母體參 數，可能不是一個佷嚴密的推定量，因此實驗者必須先決定一個有效、可行的抽樣方 法。 在本文中採取雙重抽樣的原理抽取樣本，而想要估計的母體參數是母體第ｊ領域所佔 全母體的成數，並在固定的預算下討論貝氏最佳樣本與子樣本數的選取。 SMITH 及SEDRANSK（１９８２）利用雙重抽樣法研究魚群體的年齡組成，並解決了二 個問題（１）利用貝氏法，估算第ｊ領域年齡的魚群所佔全體魚群的成數。（２）當 總預算固定，並給定第一階段樣本數n'及其分配 ｎ' ＝（ｎ' ，ｎ' ，－－－ｎ' ） 1 2 i 說明如何選取最佳的貝氏子樣本數分配，ｎ*＝ ｎ* ，ｎ* ，－－－ｎ* ） 使得近 1 2 i 似的風險函數ｒ*（ｎ',｛ｎi'｝，｛ｎi｝ 最小，其中 ０≦ｎi≦ｎi'（ｉ＝１，２，－－－Ｉ） 而後JINN, SEDRANSK, SMITH（１９８７） 延續以上結果，利用電腦模擬取樣，在必 然的ｎL'≦ｎ'≦ｎU' 條件下，說明如何取得最佳的n'使得 Ａ（n'）＝Ｅn'ln'｛ｒ*（ｎ'，ｎ'，ｎ。*）｝ 最小． 由於上述方法在一般情況下無法求得A(n') 的明確數學式，因此n'也就無法用式子表 示出來。 本文首先考慮Ｉ＝２的特殊情況，在這情況下舉一些例子說明如何求得A(n') 的明確 數學式，並由此求出最佳的貝氏解n'。其次導出一些充分條件使得在忽略限制條件下 由LAGRANGE乘數法所得的解ｎ＝（ｎ1，ｎ2）分別滿足（１）０≦ｎi≦ｎi'或（２） ｎi≦ｎi'（ｉ＝１，２）． 最後在(1) 或 (2)成立的充分條件下，導出Ａ（n'）的 數學式，進而求得最佳貝氏解n'。

Le problème de satisfaisabilité booléenne 3-SAT est connu pour présenter un phénomène de seuil en fonction du quotient entre le nombre de clauses et le nombre de variables. Nous donnons des estimations de la valeur de ce seuil au moyen de méthodes combinatoires et probabilistes: la méthode du premier moment et la méthode du second moment. Ces méthodes mettent en jeu des problèmes d'optimisation sous contraintes et nous amènent à employer de façon intensive la méthode des multiplicateurs de Lagrange. Nous mettons en œuvre une forme pondérée de la méthode du premier moment sur les affectations partielles valides de Maneva ainsi que des variantes. Cela nous conduit à élaborer une pondération générale pour les problèmes de satisfaction de contraintes qui soit compatible avec la méthode du premier moment. Cette pondération est constituée d'une graine et d'un répartiteur, et nous permet d'obtenir une pondération des affectations partielles valides meilleure que celle de Maneva. Nous comparons aussi dans certains cas les performances de la pondération et de l'orientation de l'espace des solutions des problèmes de satisfaction de contraintes relativement à la méthode du premier moment. Nous développons la première sélection non uniforme de solutions pour majorer le seuil de 3-SAT et nous montrons sa supériorité sur ses prédécesseurs. Nous construisons un cadre général pour appliquer la méthode du second moment à k-SAT et nous discutons des conditions qui la font fonctionner. Nous faisons notamment fonctionner la méthode du second moment sur les solutions booléennes et sur les impliquants. Nous étendons cela au modèle distributionnel de k-SAT.

When two or more chaotic systems are coupled, they may exhibit synchronized chaotic oscillations. The synchronization of chaos is usually understood as the regime of chaotic oscillations in which the corresponding variables or coupled systems are equal to each other. This kind of synchronized chaos is most frequently observed in systems specifically designed to be able to produce this behaviour. In this thesis, one particular type of synchronization, called impulsive synchronization, is investigated and applied to low dimensional chaotic, hyperchaotic and spatiotemporal chaotic systems. This synchronization technique requires driving one chaotic system, called response system, by samples of the state variables of the other chaotic system, called drive system, at discrete moments. Equi-Lagrange stability and equi-attractivity in the large property of the synchronization error become our major concerns when discussing the dynamics of synchronization to guarantee the convergence of the error dynamics to zero. Sufficient conditions for equi-Lagrange stability and equi-attractivity in the large are obtained for the different types of chaos-generating systems used. The issue of robustness of synchronized chaotic oscillations with respect to parameter variations and time delay, is also addressed and investigated when dealing with impulsive synchronization of low dimensional chaotic and hyperchaotic systems. Due to the fact that it is impossible to design two identical chaotic systems and that transmission and sampling delays in impulsive synchronization are inevitable, robustness becomes a fundamental issue in the models considered. Therefore it is established, in this thesis, that under relatively large parameter perturbations and bounded delay, impulsive synchronization still shows very desired behaviour. In fact, criteria for robustness of this particular type of synchronization are derived for both cases, especially in the case of time delay, where sufficient conditions for the synchronization error to be equi-attractivity in the large, are derived and an upper bound on the delay terms is also obtained in terms of the other parameters of the systems involved. The theoretical results, described above, regarding impulsive synchronization, are reconfirmed numerically. This is done by analyzing the Lyapunov exponents of the error dynamics and by showing the simulations of the different models discussed in each case. The application of the theory of synchronization, in general, and impulsive synchronization, in particular, to communication security, is also presented in this thesis. A new impulsive cryptosystem, called induced-message cryptosystem, is proposed and its properties are investigated. It was established that this cryptosystem does not require the transmission of the encrypted signal but instead the impulses will carry the information needed for synchronization and for retrieving the message signal. Thus the security of transmission is increased and the time-frame congestion problem, discussed in the literature, is also solved. Several other impulsive cryptosystems are also proposed to accommodate more solutions to several security issues and to illustrate the different properties of impulsive synchronization. Finally, extending the applications of impulsive synchronization to employ spatiotemporal chaotic systems, generated by partial differential equations, is addressed. Several possible models implementing this approach are suggested in this thesis and few questions are raised towards possible future research work in this area.

Summary: The thesis comprises from the introduction and five main parts: three of them are published papers, the rest two are manuscripts prepared for submitting to the scientific journals. The first two are published phylogenetic studies of the cichlasomatine cichlids based on (1) molecular characters, and (2) both morphological and molecular data with the description of a new genus Andinoacara. The third (3) is the already published description of the new species Andinoacara stalsbergi from Peru combining both morphological and phylogenetic approaches and including the detailed phylogeny of the genus Andinoacara. The next unpublished manuscript (4) is the more detailed comprehensive phylogeography of the two non-relative genera (including Andinoacaras) of the trans-Andean cichlids. Including all valid species from the majority of their distribution areas it was reconstructed the ancestral area of both genera in the Choco region, Colombia, and revealed the directions of their distribution spreading. The last (5) unpublished manuscript is the phylogeographical study of the cichlid genus Serranochromis from the headwaters of the totally unknown Central Angola. It showed several evidences of the faunal exchange among the adjacent river systems. Lastly, the thesis is supplemented by several appendices...

Este trabalho apresenta a modelagem de um problema representado por um pêndulo elástico com excitação paramétrica vertical do suporte e a análise de estabilidade do sistema pendular que se obtém desconsiderando a elasticidade do pêndulo. A modelagem dos pêndulos e a obtenção das equações do movimento são feitas a partir da equação de Lagrange, utilizando as leis de Newton e para a análise de estabilidade do sistema pendular são apresentados os diagramas de bifurcações, multiplicadores de Floquet, mapas e seções de Poincaré e expoentes de Lyapunov. O comportamento do sistema pendular com excitação paramétrica vertical do suporte é investigado através de simulação computacional e apresentam-se resultados para diferentes faixas de valores da amplitude de excitação externa. / This work presents the modeling of an elastic pendulum with parametric excitation of the support and the analysis of the stability of the pendulum that one obtains disregarding the elasticity of the pendulum. The modeling of the pendulum and the equation of motions are obtained from the Lagrange\'s equations, using Newton\'s law. The concepts of bifurcation, Floquet\'s multipliers, Poincaré maps and sections and Lyapunov exponent are presented for the analysis of stability. The behavior of the pendulum with parametric excitation of the suport is investigated through computational simulation and results for different intervals of values of the external excitation amplitude are presented.

Neste trabalho são estudadas três metodologias de otimização não-linear: o Método da Função Lagrangeana, o Método da Função Penalidade e o Método da Função Lagrangeana Aumentada. Com o estudo da Função Lagrangeana e do Método da Função Penalidade, foi possível alcançar a formulação da Função Lagrangeana Aumentada com o objetivo de resolver problemas de programação não-linear não-convexos. Testes numéricos são apresentados para o problema não-convexo de programação não-linear conhecido como Fluxo de Potência Ótimo. / In this dissertation, three nonlinear optimization methodologies are studied: the Lagrangian Function Method, the Penalty Function Method and Augmented Lagrangian Function Method. Through the studies ofthe Lagrangian Function and the Penalty function Method, it was possible to reach the formulation of the Augmented Lagrangian Function aiming to solve nonlinear nonconvex programming problems. Numerical tests are presented for the nonconvex nonlinear programming problem known as optimal power flow.