Le travail présenté dans ce mémoire est une contribution au domaine de l'analyse et de l'identification du comportement dynamique des structures non linéaires. Le premier objectif est la mise au point et la comparaison de quatre techniques de calcul des Modes Normaux Non linéaires (MNNs) : l'approche de Shaw et Pierre, l'approche de Bellizzi et Bouc, l'équilibrage harmonique et la méthode de tir. La combinaison des trois dernières méthodes avec la méthode de continuation permet de détecter les points de bifurcation et de trouver les nouvelles branches de solutions. Le deuxième objectif est l'identification des paramètres caractérisant le comportement dynamique des systèmes linéaires et non linéaires à partir des réponses libres ou des réponses au bruit ambiant. Les outils présentés sur le traitement du signal réel modulé en amplitude et en fréquence par la transformation en ondelettes continue permettent d'atteindre cet objectif. Le dernier objectif est l'extension de la méthode de sous-structuration linéaire de Craig-Bampton au cas non linéaire. Lorsque l'hypothèse de couplage faible entre les sous-structures est faite, le modèle réduit de la structure globale est obtenu par assemblage de modèles réduits de sous-structures avec interfaces de couplage fixe. Ces modèles réduits sont calculés en utilisant l'approche des MNNs de Shaw et Pierre. La robustesse et l'efficacité des méthodes présentées sont étudiées au travers d'exemples numériques ainsi que de tests réels.

Nous présentons ici l'étude d'un problème de mécanique spatiale, le transfert en temps minimal vers une orbite géostationnaire. Plus précisément, nous nous intéressons à un cas particulier : le transfert mono-entrée. Reprenant les méthodes et les résultats des études précédentes, le transfert mono-entrée optimal est calculé et montre des performances excellentes compte tenu des contraintes supplémentaires introduites sur la direction de la poussée. Le contrôle optimal étant discontinu, nous introduisons deux approximations lisses. Nous considérons tout d'abord une approximation Riemanienne avec la moyennation du transfert en minimum d'énergie avec relaxation de la contrainte sur le contrôle : l'étude de la métrique Riemannienne associée montre que, dans des coordonnées adaptées, les trajectoires optimales sont des droites. Nous relions ensuite le transfert mono-entrée à des transferts bi-entrée contraints mais lisses et utilisons les conditions lisses du deuxième ordre sur ces approximations : cette procédure nous permet notamment de valider l'efficacité de la méthode de tir simple sur le transfert mono-entrée.

The Mohorovičič discontinuity (Moho), which is the surface separating the Earth’s crust from the mantle, is of great interest among geoscientists. The Moho depth can be determined by seismic and gravimetric methods. The seismic methods are expensive, time-consuming and suffer from lack of global coverage of data, while the gravimetric methods use inexpensive and mostly already available global and regional data based on an isostatic model. The main reasons for studying an isostatic model are on one hand the gaps and uncertainties of the seismic models, and, on the other hand, the generous availability of gravity data from global models for the gravimetric-isostatic model. In this study, we present a new gravimetric-isostatic Moho model, called the Vening Meinesz-Moritz (VMM) model. Also, a combined Moho model based on seismic and gravimetric models is presented. Classical isostatic hypotheses assume that the topographic potential is fully compensated at all wavelengths, while is not the case in reality. We found that the maximum degree of compensation for the topographic potential based on the new Moho model is 60, corresponding to the resolution of about 330 km. Other (dynamic) isostatic effects (such as temporal compensation, plate tectonics, post-glacial rebound, etc) should be considered as well, which are disregarded in this thesis. Numerical results imply that the dynamic phenomena affect mostly the long-wavelengths. The VMM model is applied for different purposes. The Moho density contrast is an important parameter for estimating the Moho depth, and we present a technique to simultaneously estimate Moho depth and density contrast by the VMM and seismic models. Another application is the recovery of gravity anomaly from Satellite Gravity Gradiometry (SGG) data by a smoothing technique, and we show that the VMM model performs better than the Airy-Heiskanen isostatic model. We achieved an rms difference of 4 mGal for the gravity anomaly estimated from simulated GOCE data in comparison with EGM08, and this result is better than direct downward continuation of the data without smoothing. We also present a direct method to recover Moho depth from the SGG mission, and we show that the recovered Moho is more or less of the same quality as that obtained from terrestrial gravimetric data (with an rms error of 2 km). Moreover, a strategy is developed for creating substitutes for missing GOCE data in Antarctica, where there is a polar gap of such data. The VMM model is further used for constructing a Synthetic Earth Gravity Model (SEGM). The topographic-isostatic potential is simple to apply for the SEGM, and the latter can be an excellent tool to fill data gaps, extending the EGMs to higher degrees and validating a recovery technique of the gravity field from a satellite mission. Regional and global tests of the SEGM yield a relative error of less than 3 % vs. EGM08 to degree 2160. / QC 20110405

Le lambda calcul avec constructeurs (de Arbiser, Miquel et Rios) est une extension du lambda calcul avec un mécanisme de filtrage. Le filtrage à la ML y est décomposé en deux étapes: une analyse de cas sur des constantes (telle l'instruction "case" de Pascal), et une commutation de l'application avec la construction de filtrage. Cette règle de commutation entre deux constructions de natures différentes induit une géométrie de calcul surprenante, a priori incompatible avec les intuitions habituelles de typage. Cependant il a été montré que ce calcul est confluent, et vérifie la propriété de séparation (à la Böhm). Cette thèse propose un système de types du polymorphique pour ce calcul, et décrit ensuite un modèle de réalisabilité, qui adapte les candidats de réductibilité de Girard au lambda calcul avec constructeurs. La normalisation forte du calcul typé et l'absence d'erreur de filtrage lors de l'évaluation en découlent immédiatement. Nous nous intéressons ensuite à la sémantique du lambda calcul avec constructeurs non typé. Une notion générique de modèle catégorique pour ce calcul est définie, puis un modèle particulier (le modèle syntaxique dans la catégorie des PERs) est construit. Nous en déduisons un résultat de complétude. Enfin, nous proposons une traduction CPS du lambda calcul avec constructeurs dans le lambda calcul simplement typé avec paires. Le lambda calcul avec constructeurs peut ainsi être simulé dans un calcul bien connu, et cette traduction nous permet aussi de transformer tout modèle par continuation en modèle du lambda calcul avec constructeurs. Une équation catégorique caractéristique de ces modèles apparait alors, qui permet de construire des modèles non syntaxiques (dans les domaines) de Scott du lambda calcul avec constructeurs.

In this thesis we will consider and investigate the properties of analytic functions via their behavior near the boundary of the domain on which they are defined. To do that we introduce the notion of the hyperbolic distortion and the hyperbolic derivative. Classical results state that the hyperbolic derivative is bounded from above by 1, and we will consider the case when it is bounded from below by some positive constant. Boundedness from below of the hyperbolic derivative implies some nice properties of the function near the boundary. For instance Krauss & all in 2007 proved that, if the function is defined on a domain bounded by analytic curve, then boundedness from below of the hyperbolic derivative implies that the function has an analytic continuation across the boundary. We extend this result for the domains with slightly more general boundary, namely for smooth Jordan domains, and get that in this case the function and its derivative will have only continuous extensions to the boundary.

In this thesis we will consider and investigate the properties of analytic functions via their behavior near the boundary of the domain on which they are defined. To do that we introduce the notion of the hyperbolic distortion and the hyperbolic derivative. Classical results state that the hyperbolic derivative is bounded from above by 1, and we will consider the case when it is bounded from below by some positive constant. Boundedness from below of the hyperbolic derivative implies some nice properties of the function near the boundary. For instance Krauss & all in 2007 proved that, if the function is defined on a domain bounded by analytic curve, then boundedness from below of the hyperbolic derivative implies that the function has an analytic continuation across the boundary. We extend this result for the domains with slightly more general boundary, namely for smooth Jordan domains, and get that in this case the function and its derivative will have only continuous extensions to the boundary.

Disertacijoje gautas Dirichlė L funkcijų modifikuotosios Melino transformacijos pratęsimas į visą kompleksinę plokštumą. / In the thesis a meremorphic continuation of Dirichlet L- functions to the whole complex plane have been obtained.

In the thesis moromorphic continuation of modified Mellin transforms of Dirichlet L-functions to the whole complex plane have been obtained. / Disertacijoje gauta modifikuotosios Melino transformacijos L- funkcijai meromorfinis pratęsimas į visą kompleksinę plokštumą.

Made available in DSpace on 2014-06-11T19:30:50Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-11-07Bitstream added on 2014-06-13T19:47:13Z : No. of bitstreams: 1 malange_fcv_dr_ilha.pdf: 1077798 bytes, checksum: 6e2455ed107dc7931eb5bc7473ecce8a (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho apresenta uma metodologia alternativa para a melhoria da margem de carregamento e redução da perda total de potência ativa com base no método da continuação. Para atingir esta meta, uma equação de parametrização baseada na perda de potência ativa total e as equações da potência reativa nas barras de geração são acrescentadas às equações de fluxo de carga convencional. As tensões nas barras PV são consideradas como variáveis de controle e um novo parâmetro é escolhido para reduzir as perdas de potência ativa nas linhas de transmissão. Os resultados mostram que este procedimento, em geral, conduz a um aumento no ponto de máximo carregamento e por conseguinte, melhoria na margem estática da estabilidade de tensão. Este procedimento também leva a uma redução nos custos operacionais e, simultaneamente, uma melhoria no perfil da tensão. / This work presents an alternative methodology for loading margin improvement and total real power losses reduction by using a continuation method. In order to attain this goal, a parameterizing equation based on the total real power losses and the equations of the reactive power at the slack and generation buses are added to the conventional Power Flow equations. The voltages at these buses are considered as control variables and a new parameter is chosen with to reduce the real power losses in the transmission lines. The results show that this procedure leads to maximum loading point increase and consequently, in static voltage stability margin improvement. Besides, this procedure also takes to a reduction in the operational costs and, simultaneously, to voltage profile improvement.

Orientador: Dilson Amâncio Alves / Banca: Anna Diva Plasencia Lotufo / Banca: Edmárcio Antonio Belati / Resumo: Este trabalho apresenta o método de Newton desacoplado para o fluxo de carga continuado. O método foi melhorado por uma técnica de parametrização geométrica possibilitando assim o traçado completo das curvas P-V, e o cálculo do ponto de máximo carregamento de sistemas elétricos de potência, sem os problemas de mau condicionamento. O objetivo é o de apresentar de forma didática os passos envolvidos no processo de melhoria do método de Newton Desacoplado a partir da observação das trajetórias de solução do fluxo de carga. A técnica de parametrização geométrica que consiste na adição de uma equação de reta que passa por um ponto no plano formado pelas variáveis: tensão nodal de uma barra k qualquer e o fator de carregamento eliminam os problemas de singularidades das matrizes envolvidas no processo e ampliam o grupo das variáveis de tensão que podem ser usadas como parâmetro da continuação. Os resultados obtidos com a nova metodologia para o sistema teste do IEEE (14, 30, 57, 118 e 300 barras) e também para os sistemas reais de grande porte, o 638 barras do sistema Sul-Sudeste brasileiro e do sistema de 904 barras do sudoeste Americano, mostram que as características do método convencional são melhoradas na região do ponto de máximo carregamento e que a região de convergência ao redor da singularidade é sensivelmente aumentada. São apresentados vários testes com a finalidade de prover um completo entendimento do funcionamento do método proposto e também avaliar seu desempenho / Abstract: This work presents the decoupled Newton method for continuation power flow. The method was improved by using a geometric parameterization technique that allows the complete tracing of P-V curves, and the computation of maximum loading point of a power system, without ill-conditioning problems. The goal is to present in a clear and didactic way the steps involved in the development of the improved decoupled Newton method obtained from the observation of the geometrical behavior of power flow solutions. The geometric parameterization technique that consists of the addition of a line equation, which passes through a point in the plane determined by the bus voltage magnitude and loading factor variables, can eliminate the ill-conditioning problems of matrices used by the method and can enlarge the set of voltage variables that can be used as continuation parameter to P-V curve tracing. The method is applied to the IEEE systems (14, 30, 57, 118 and 300 buses) and two large real systems: the south-southeast Brazilian system (638 buses) and the 904-bus southwestern American system. The results show that the best characteristics of the conventional decoupled Newton's method are improved in the vicinity of the maximum loading point and therefore the region of convergence around it is enlarged. Several tests are presented with the purpose of providing a complete understanding of the behavior of the proposed method and also to evaluate its performance / Mestre