Cela fait environ soixante ans que l'on s'intéresse à la compréhension et à la modélisation du comportement Elastohydrodynamique (EHD) des joints à lèvres. Cependant, on peut considérer que, jusqu'à présent, leur modélisation n'a pas été totalement et rigoureusement traitée. En effet, même si de nombreuses études ont été consacrées à cette modélisation, plusieurs questions ont été soulevées et font toujours l'objet de controverses entre les chercheurs, à savoir l'impact sur les performances des joints à lèvre de l'effet des surfaces texturées de l'arbre, de la loi adoptée pour le comportement mécanique des joints à lèvre, de la démarche utilisée pour l'élaboration de la matrice de compliance (matrice de souplesse), de l'importance de supposer l'arbre lisse ou rugueux, ainsi que la valeur du rapport entre la largeur du contact et la longueur d'onde du défaut suivant la direction circonférentielle de la lèvre.Dans cette thèse, nous avons tenté d'apporter de façon rigoureuse des réponses claires et précises à toutes ces questions en élaborant et en validant un outil de simulation EHD complet pour les joints à lèvre qui tienne compte de presque tous les paramètres, à savoir une loi de comportement du matériau du joint précise, une matrice de souplesse rigoureusement validée et un arbre qui peut être lisse, rugueux et/ou texturé. De plus, un second modèle analytique est proposé. Il traite le comportement vibratoire du "squeeze film", en tenant compte de la non linéarité des caractéristiques intrinsèques du joint et du film. / It's about sixty years that we are interested in understanding and modeling the Elastohydrodynamic behavior (EHD) of rotary lip seals. However, we can consider that, until now, their modeling has not been accurately treated. Even though many studies have been devoted to this model, several questions have been raised and are still the subject of controversy among researchers, namely the parameters influencing on the rotary lip seals performance, such as: the shaft surface textured, the law adopted for the mechanical behavior of lip seals, the approach used to develop the matrix of compliance, the importance of assuming the smooth or rough shaft, and finally the ratio between the width of contact and the wavelength according the circumferential direction of the lip roughness.The main goal of this thesis is to answer rigorously these questions by developing and validating a numerical tool for EHD rotary lip seals modeling, that takes into account: the lip law behavior, the compliance matrix rigorously validated by assuming smooth shaft case, or rough and textured shaft case. In addition, an analytical approach is proposed, models the vibratory behavior of the "squeeze film". This implies a nonlinear comportment that is taken into account.

[pt] A simulação da circulação interna-interna de veículos de carga foi um estudo inédito e inovador para a revisão do Plano Diretor de Transporte Urbano da Região Metropolitana de Rio de Janeiro (PDTU-RMRJ/2011), no qual se faz uma estimação de vetores de produção e atração (P/A) de viagens de caminhões para 730 zonas de tráfego, de matrizes origem-destino (OD) e a alocação de viagens de veículos de carga para três períodos (pico da manhã, pico da tarde e entre picos). A metodologia e modelo utilizados foram baseados em uma aplicação realizada na cidade de Sevilla (Espanha). Para o caso da RMRJ foram estimados vetores de viagens de dois tipos, um com relação às entregas do tipo Empresa a Empresa (Business to Business, B2B) e outro do tipo Empresa a Domicilio (Business to Housing, B2H). Como resultados ilustrativos são mostrados os vetores (P/A) de viagens diárias de caminhões agregados por município, uma matriz OD de caminhões no período entre picos agregada por município e a alocação dessas viagens na rede de simulação do PDTU para o período entre picos. Desses resultados, destaca-se que os municípios com maior quantidade (somam mais de 80 por cento) das viagens produzidas e atraídas dentro da RMRJ são apenas cinco: Rio de Janeiro, Duque de Caxias, Niterói, São Gonçalo e Nova Iguaçu; e que as vias mais utilizadas para o tráfego de caminhões são a BR-101, BR-116 e a BR-040. / [en] Within the framework of the Revision of the Urban Transportation Master Plan for the Rio de Janeiro Metropolitan Region (PDTU-2011) an innovative model was developed – first of its kind in Brazilian cities – for the estimation of truck flows within the study area. Productions and attractions vectors (P/A) of truck trip ends, as well as origin/destination (O/D) matrices for the 730 traffic analysis zones were estimated, and truck assignments for three daily periods (morning peak, afternoon peak, and inter-peaks) were conducted. Model methodology was based in another study conducted for the city of Seville (Spain). Two sets of P/A vectors were estimated, one for business-to-business deliveries (B2B) and another for household deliveries (B2H). Daily truck trip ends P/A vectors aggregated by city are presented, as well as a city level O/D inter-peak truck matrix and the results of its assignment to the PDTU-2011 simulation network. From those illustrative results, it is shown that only five cities (Rio de Janeiro, Duque de Caxias, Niterói, São Gonçalo e Nova Iguaçu) account for more than 80 per cent of truck trips produced and attracted within the Metropolitan Region, and that the most heavily used truck routes are comprised of BR-101, BR-116 and BR-040 expressways.

La synchronisation temporelle des systèmes MIMO a été abondamment étudiée dans les quinze dernières années, mais la plupart des techniques existantes supposent que le bruit est blanc temporellement et spatialement, ce qui ne permet pas de modéliser la présence d'interférence. Nous considérons donc le cas de bruits blancs temporellement mais pas spatialement, dont la matrice de covariance spatiale est inconnue. En formulant le problème de l'estimation de l'instant de synchronisation comme un test d'hypothèses, nous aboutissons au test du rapport de vraisemblance généralisé (GLRT) qui donne lieu à la comparaison avec un seuil d'une statistique de test eta_GLRT. Cependant, pour des raisons de complexité, l'utilisation de cette statistique n'est pas toujours considérée comme réaliste. La première partie de ce travail a donc été consacrée à mettre en évidence des tests alternatifs moins complexes à mettre en œuvre, tout en ayant des performances similaires. Une analyse comparative exhaustive, prenant en considération le bruit et l'interférence, le type de canal, le nombre d'antennes en émission et en réception, et l'orthogonalité de la séquence de synchronisation est réalisée. Enfin, nous étudions le problème de l'optimisation du nombre d'antennes en émission K pour la synchronisation temporelle, montrant que pour un RSB élevé, les performances augmentent avec K dès que le produit de K avec le nombre d'antennes de réception M n'est pas supérieur à 8.Le deuxième aspect de ce travail est une analyse statistique de eta_GLRT dans le cas où la taille de la séquence d'apprentissage N est du même ordre de grandeur que M, ce qui conduit naturellement à étudier le comportement de eta_GLRT dans le régime asymptotique des grands systèmes M tend vers l'infini, N tend l'infini de telle sorte que M/N tende vers une constante non nulle. Nous considérons le cadre applicatif d'un système muni d'une unique antenne d'émission et d'un canal à trajets multiples, qui est formellement identique à celui d'un système MIMO dont le nombre d'antennes d'émissions correspondrait au nombre de trajets. Lorsque le nombre de trajets L est beaucoup plus faible que N et M, nous établissons que eta_GLRT a un comportement gaussien avec l'espérance asymptotique L log (1 / (1-M/N)) et la variance (L/N)*(M/N)/(1-M/N). Ceci est en contraste avec le régime asymptotique standard quand N tend vers l'infini et M et L fixe où eta_GLRT a un comportement chi2. Sous l'hypothèse H_1, eta_GLRT a aussi un comportement gaussien. Nous considérons également le cas où le nombre de trajets L tend vers l'infini à la même vitesse que M et N. Nous utilisons des résultats connus concernant le comportement des statistiques linéaires des valeurs propres des grandes F matrices, et déduisons que dans le régime où L,M,N tendent vers l'infini à la même vitesse, eta_GLRT a encore un comportement gaussien sous H_0, mais avec une espérance et variance différentes. L'analyse de eta_GLRT sous H_1 lorsque L,M,L convergent vers l'infini nécessite l'établissement d'un théorème central limite pour les statistiques linéaires des valeurs propres de matrices F de moyennes non-nulles, une tâche difficile. Motivé par les résultats obtenus dans le cas où L reste fini, nous proposons d'approximer la distribution asymptotique par une distribution gaussienne dont l'espérance et la variance sont la somme de l'espérance et la variance asymptotique sous H_0quand L tend vers l'infini avec l'espérance et la variance asymptotique sous H_1 dans le régime classique N tend vers l'infini et M fixé. Des simulations numériques permettent de comparer les courbes ROC des différents approximant avec des courbes ROC empiriques. Les résultats montrent que nos approximant de grandes dimensions fournissent de meilleurs résultats quand M/N augmente, tout en permettant de capturer la performance réelle pour les petites valeurs de M/N / Time synchronization of MIMO systems have been strongly studied in the last fifteen years, but most of the existing techniques assume a spatially and temporally white noise, which does not allow modeling the presence of interference. We consider thus a temporally white but spatially colored noise, with an unknown covariance matrix. Formulating the estimation problem as a hypothesis testing problem, we obtain a Generalized likelihood ratio test (GLRT), which gives us a synchronization statistics eta_GLRT. However, for complexity reasons, it is not always considered realistic for practical situations. A part of this work has thus been devoted to showing that there exist non-GLRT statistics that are less complex to implement than theet a_GLRT, while having similar performance. Furthermore, we perform a comparative parameter analysis, taking into consideration the noise type, channel type, the number of transmit and receive antennas, and the orthogonality of the synchronization sequence. Lastly, the problem of optimization of the number of transmit antennas K for time synchronization has been investigated. showing, for high SNR, increasing performance with K as long as the product KM is not larger than 8, where M is the number of receive antennas. The second aspect of MIMO synchronization studied in thesis is asymptotic analysis of the same GLRT, but for large M. In this context, the synchronization sequence length N is the same order of magnitude as M, and this leads us naturally to the study of the the behavior of eta_GLRT in the asymptotic regime where M,N go towards infinity such that M/N go towards a non-zero constant. We consider the case of a single transmit antenna in a multi-path channel, which formally is equivalent to the MIMO system where the transmit antennas correspond to the number of paths. We address the case When the number of paths L does not scale with M and N, we establish that eta_GLRT has a Gaussian behavior with asymptotic mean L log (1/ (1 - M/N))and variance (L/N)*(M/N)/(1-M/N).This is in contrast with the standard asymptotic regime N goes to infinity and M fixed where eta_GLRT has a chi^2 behaviour. Under hypothesis H_1, eta_GLRT still has a Gaussian behaviour. The corresponding asymptotic mean and variance are obtained as the sum of the asymptotic mean and variance in the standard regime N goes to infinity and M fixed, and L log(1/(1-/M/N))L log (1 / (1-M/N)) and (L/N)*(M/N)/(1-M/N)respectively, i.e. the asymptotic mean and variance under H_0.We also consider the case where the number of paths L converges towards infinity at the same rate as M and N. Using known results of concerning the behaviour of linear statistics of the eigenvalues of large F-matrices, we deduce that in the regime where L,M,N converge to infinity at the same rate, eta_GLRT still has a Gaussian behaviour under H_0, but with a different mean and variance. The analysis of eta_GLRT under H_1 whenL,M,N converge to infinity needs to establish a central limit theorem for linear statistics of the eigenvalues of large non zero-mean F-matrices, a difficult ask. Motivated by the results obtained in the case where L remains finite, we propose to approximate the asymptotic distribution of eta_GLRT by a Gaussian distribution whose mean and variance are the sum of the asymptotic mean and variance under H_0when L goes to infinity with the asymptotic mean and variance under H_1 in the standard regime N goes to infinity and M fixed. Numerical simulations allow to compare the ROC curves obtained with the different approximations with the empirical ROC curves. The results show that the large-system approximations provide better results when M/N increases, while also allowing to capture the actual performance for small values of M/N

La thèse est consacrée à une étude d'interpolation complexe "semi-libre" dans le sens suivant: étant donné un ensemble "sigma" dans le disque unité D et une fonction f holomorphe dans D appartenant à une certaine classe X, on cherche g dans une autre classe Y (plus petite que X) qui minimise la norme de g dans Y parmi toutes les fonctions g satisfaisant g=f sur l'ensemble "sigma". Plus précisément, nous nous intéressons aux estimations de la constante d'interpolation suivante: c(sigma, X, Y ) = sup{ inf{||g||_Y: g=f sur sigma}: ||f||_X<=1} Dans la thèse, nous étudions le cas où Y = H^infini et où l'espace des contraintes X est choisi parmi les espaces suivants: les espaces de Hardy, les espaces de Bergman pondérés à poids radial ou encore les espaces de fonctions holomorphes ayant leurs coefficients de Taylor dans lp(w) (w étant un poids). La thèse contient également certaines applications aux nombres conditionnés des matrices de Toeplitz. / The thesis is devoted to a "semi-free" interpolation problem in the following way. Let sigma be a finite set of the unit disc D and f an holomorphic function in D which belongs to a certain class X, we search for g in another class Y (smaller than X) which minimize the norm of g in Y among all the functions g such that g=f on the set "sigma". More precisely, we are interested in the following interpolation constant : c(sigma, X, Y ) = sup{ inf{||g||_Y: g=f sur sigma}: ||f||_X<=1}. We study in the thesis the case where Y=H^\infinity and the space of constrains X is chosen among the following spaces: Hardy spaces, weighted Bergman spaces (with radial waights), and holomorphic functions which Taylor coefficients are in lp(w) (w being a weight). The thesis also contains an application to the condition numbers of Toeplitz matrices.

Une interface est une zone de l'espace qui sépare deux régions possédant des propriétés physiques différentes. La plupart des interfaces de la nature résultent d'un processus de croissance, mêlant une composante aléatoire et une dynamique déterministe régie par les symétries du problème. Le résultat du processus de croissance est un objet présentant des corrélations à longue portée. Dans cette thèse, nous nous proposons d'étudier la statistique d'extrême de différents types d'interfaces. Une première motivation est de raffiner la compréhension géométrique de tels objets, via leur maximum. Une seconde motivation s'inscrit dans la démarche plus générale de la statistique d'extrême de variables aléatoires fortement corrélées. A l'aide de méthodes analytiques d'intégrales de chemin nous analysons la distribution du maximum d'interfaces à l'équilibre, dont l'énergie es t purement élastique à courte portée. Nous attaquons ensuite le problème d'interfaces élastiques en milieu désordonné, principalement à l'aide de simulations numériques. Enfin nous étudierons une interface hors-équilibre dans son régime de croissance. L'équivalence de ce type d'interface avec le polymère dirigé en milieu aléatoire, un des paradigmes de la physique statistique des systèmes désordonnés, donne une portée étendue aux résultats concernant la statistique du maximum de l'interface. Nous exposerons les résultats que nous avons obtenus sur un modèle de mouvements browniens qui ne se croisent pas, tout en explicitant le lien entre ce modèle, l'interface en croissance et le polymère dirigé. / An interface is an area of space that separates two regions having different physical properties. Most interfaces in nature are the result of a growth process, mixing a random behavior and a deterministic dynamic derived from the symmetries of the problem. This growth process gives an object with extended correlations. In this thesis, we focus on the study of the extremum of different kinds of interfaces. A first motivation is to refine the geometric properties of such objects, looking at their maximum. A second motivation is to explore the extreme value statistics of strongly correlated random variables. Using path integral techniques we analyse the probability distribution of the maximum of equilibrium interfaces, possessing short range elastic energy. We then extend this to elastic interfaces in random media, with essentially numerical simulations. Finally we study a particular type of out-of-equilibrium interface, in its growing regime. Such interface is equivalent to the directed polymer in random media, a paradigm of the statistical mechanics of disordered systems. This equivalence reinforces the interest in the extreme value statistics of the interface. We will show the exact results we obtained for a non-intersecting Brownian motion model, explaining precisely the link with the growing interface and the directed polymer.

De nombreux composés bioactifs hydrophobes sont actuellement mis en avant en raison de leurs propriétés nutritionnelles et fonctionnelles. Une attention particulière est, en conséquence, portée à leur incorporation en tant qu'ingrédients dans des aliments fonctionnels. Cependant, la majorité de ces composés bioactifs sont caractérisés par une faible solubilité en milieu aqueux, une dégradation au cours des procédés de transformation ainsi qu'une absorption limitée au niveau du tractus gastro-intestinal. La micelle de caséines, grâce à ses propriétés fonctionnelles uniques, peut être considérée comme un support d’encapsulation naturel pour ces molécules bioactives hydrophobes. En effet, une des originalités de cette suprastructure est sa dynamique dans le lait se caractérisant par des échanges réversibles de protéines et de minéraux entre le sérum et la structure micellaire interne en fonction des conditions physicochimiques, et notamment avec la température. En particulier, un stockage du lait à 4°C permet la dissociation sélective de la caséine β de la phase micellaire vers la phase soluble et un retour à température ambiante permet sa réintégration. L’objectif de cette thèse est de développer une nouvelle stratégie d’encapsulation de molécules bioactives hydrophobes dans les micelles de caséines via cette dynamique de la caséine β. Dans un premier temps, l’optimisation de la dissociation de la caséine β de la micelle de caséines a été réalisée en modifiant la température et le pH, tout en portant une attention particulière au maintien de l’intégrité des micelles déplétées en caséines β. Un procédé de séparation physique de la caséine β solubilisée a été optimisé par microfiltration à l’échelle pilote. Une étude de la concentration micellaire critique de la caséine β a permis de vérifier son état monomérique à l’issue de cette séparation. Une étude de la cinétique d’interaction entre la caséine β monomérique et deux composés bioactifs hydrophobes, la curcumine et la vitamine D3, a ensuite été réalisée par résonance plasmonique de surface et par spectroscopie de fluorescence. La curcumine a été choisie pour la suite de l’étude au vu de sa bonne affinité pour la caséine β. Le complexe caséine β monomérique-curcumine a ensuite été encapsulé dans des micelles de caséines préalablement déplétées en caséines β. Les résultats de ces travaux montrent l’efficacité de cette stratégie d’encapsulation qui peut présenter un intérêt particulier pour la vectorisation de molécules bioactives hydrophobes afin d’assurer leur protection dans des produits laitiers pauvres en matière grasse.De plus, au cours de ce projet, une méthode de caractérisation des propriétés morphologiques et nano-mécaniques des micelles de caséines par microscopie à force atomique en milieu liquide a été développée. Cette méthode représente un outil intéressant de compréhension de la structure micellaire dans son environnement natif et offre la possibilité d’évaluer l’impact de certaines modifications sur les propriétés de la micelle de caséines, comme sa déplétion en caséine β ou sa réticulation. / In the last years, the number of studies highlighting the nutritional and functional properties of several hydrophobic bioactives has markedly increased. Special attention is consequently paid to their addition as ingredients to food. However, most of these hydrophobic compounds display a low aqueous solubility, poor stability during processing and low absorption in the gastrointestinal tract. Casein micelles exhibiting unique set of properties can be considered as a natural nanocarrier for these molecules. Actually, changes in environmental factors namely pH and temperature induce the dissociation of caseins and minerals from the colloidal phase to the soluble phase. Particularly, a selective dissociation of β-casein occurs at low temperatures. This effect is reversed with an increase in temperature, with a transfer of β-casein from the serum to the micelles when equilibrated at room temperature. The aim of this study is to develop a novel encapsulation strategy to incorporate hydrophobic bioactive compounds into casein micelles using the β-casein reversible dissociation. First, the β-casein dissociation from casein micelles was optimized by temperature and pH modifications while preserving the integrity of the β-casein depleted casein micelles. The separation of dissociated β-caseins from casein micelles was carried out by microfiltration at a pilot scale. The β-casein critical micelle concentration was concurrently evaluated to ensure the monomeric state of -casein after separation. Secondly, the binding kinetic between monomeric β-casein and two hydrophobic compounds, curcumin and vitamin D3, was investigated by surface plasmon resonance and fluorescence spectroscopy. Curcumin was then selected thanks to its high affinity to -casein β. The complex monomeric β-casein – curcumin was encapsulated in β-casein depleted casein micelles. The results of this study show the efficiency of this encapsulation strategy of hydrophobic bioactive compounds, which could be used to protect such molecules in low fat dairy products.Besides, during this project, a novel strategy was developed in order to evaluate the casein micelle topography and nanomechanical properties by atomic force microscopy in liquid environment. This method opens a new line of investigation to better understand the casein micelle structure in its native environment but also investigate the impact induced by the modification of physico-chemical conditions on its topography and elastic properties.

Este trabalho visou estudar a integração de implantes de colágeno aniônico:elastina obtidos a partir de pericárdio bovino acelularizado e com densidade de carga negativa variável. As cargas negativas foram introduzidas na forma de grupos carboxílicos, por hidrólise seletiva e controlada de grupos carboxamidas de asparagina e glutamina contidos na estrutura primária da proteína. Foram estudados materiais hidrolisados por 24 e 48 horas de tratamento correspondendo, respectivamente, a 46 '+ OU -' e 87 '+ OU -' cargas negativas adicionais em relação ao colágeno nativo. Os implantes foram introduzidos no subcutâneo de rato por tempos de 14, 60, 120 e 180 dias. Os materiais foram caracterizados por análise térmica, microscopia eletrônica de varredura e de transmissão, e os explantes avaliados por microscopia de luz (colorações de Hematoxilina: Eosina, tricrômico de Masson e Verhoeff). O objetivo foi avaliar o uso de matrizes com colágeno modificado para a reconstrução de tecidos moles. Diferentemente do tecido nativo (pericárdio bovino), a resposta biológica de matrizes de colágeno:elastina polianiônica após 14 dias do implante foi caracterizada por uma progressiva redução na fibrose, porém mais importante, não foram observadas células características de resposta inflamatória crônica, particularmente nos materiais tratados quimicamente. Após 180 dias, a maioria dos implantes estavam integrados à região implantada. Tais resultados sugerem que matrizes acelulares de colágeno:elastina preparadas pela desvitalização de tecido natural podem ser suportes bastante úteis para a reconstrução de tecidos moles, devido ao seu elevado grau de biocompatibilidade e integração / This work studied the integration of acellular polyanionic collagen:elastin matrices derived of bovine pericardium (BP) with variable negative charge. Negative charges were introduced in the material by selective hydrolisis of carboxamide side chain groups from Asn and Gln present in the primary structure of the protein. Hydrolized materials after 24 and 48 hours of treatment, respectively with 46 '+ OU -' and 87 '+ OU -' extra negative charges, were studied. Implants were placed in the subcutaneous of rats for periods of 14, 60, 120 and 180 days. Materials were characterized by differential scanning calorimetry, SEM and TEM, and explants analysed by optical microscopy (H.E., Masson tricromic and Verhoeff stains). The purpose of this work was to evaluate the use of modified collagen matrices for soft tissue reconstruction. Differently from native tissue (BP), the biological response of polyanionic collagen:elastin matrices after 14 days from implantation was characterized by a progressive decrease in fibrosis, but most important, no characteristic cells of a chronic inflammatory response were observed. After 180 days, most of the implants were integrated to the implant region. The results suggest that acellular collagen:elastin matrices prepared by devitalization of natural tissue due to their high degree of biocompatibility and integration may be potentially useful as a scaffold for soft tissue reconstruction

A pesquisa relatada nesta dissertação procura demonstrar como um modelo microscópico de simulação pode ser usado para produzir dados para a quantificação de medidas de desempenho relacionadas ao transporte sustentável, de tal forma que seja possível incorporar a contribuição individual de cada veículo que viaja pela rede em cada medida de desempenho utilizada. Para tanto, é apresentado um estudo de caso no corredor Anhangüera-Bandeirantes, entre São Paulo e Jundiaí, onde foram propostas quatro estratégias operacionais hipotéticas para ilustrar como o índice de sustentabilidade pode ser utilizado na tomada de decisões na área de transportes. O modelo de simulação de tráfego utilizado foi o Integration que teve seus parâmetros de entrada recalibrados a partir dos fluxos obtidos dos laços indutivos instalados ao longo do corredor estudado. As matrizes O/D utilizadas nas simulações foram estimadas através do QueensOD e as medidas de desempenho constituintes do índice de sustentabilidade proposto foram : a taxa de viagem, o consumo de combustível e as emissões de HC, CO e \'NO IND. X\'. / The objectives of the research reported in this masters dissertation was to demonstrate how a microsimulation model outputs can be used to quantify performance measures related to sustainable transportation, in a way such that each individual vehicle contribution is accounted for in the calculation of the performance measures. A case study, focusing the São Paulo to Jundiaí segment of the Anhanguera-Bandeirantes highway corridor, was used to demonstrate the application of the proposed approach. Four hypothetical operational strategies were compared to illustrate how the proposed sustainability index might be used in decision making. The Integration model was used to simulate the highway corridor. The microsimulation model was calibrated using data from the inductive loops installed along the studied section and the synthetic O/D matrices were estimated by means of the QueensOD model, from traffic counts. The sustainability index used included the following performance measures : travel rate, fuel consumption and HC, CO e \'NO IND. X\' emissions.

A tese apresenta um método para a solução dos problemas do valor inicial (PVIs) com margens de erro comparáveis às de métodos numéricos consagrados (MN), tanto para a função quanto para suas derivadas. O método é aplicável a equações diferenciais (EDs) lineares ou não, sendo o ferramental desenvolvido até a quarta ordem, que pode ser expandido para ordens superiores. A solução é uma expressão polinomial de alto grau com coeficientes expressos pela razão entre dois inteiros. O método se mostra eficaz mesmo em alguns casos em que os MN não conseguiram dar a partida. As resoluções são obtidas considerando que o espaço de soluções é um espaço de Hilbert, equipado com a base completa dos polinômios de Legendre. Em decorrência do método aqui desenvolvido, os majorantes de erros para a função e derivadas são determinados analiticamente por um cálculo matricial também deduzido nesta tese. Paralelamente a toda fundamentação analítica, foi desenvolvido o software SAM, que automatiza todas as tarefas na busca de soluções dos PVIs. A tese propõe e verifica a validade de um novo critério de erro no qual pesam tanto os erros locais quanto os erros globais, simultaneamente. Como subprodutos dos resultados já descritos, igualmente integrados ao SAM, obtiveram-se também: (1) Um critério objetivo para analisar a qualidade de um MN, sem necessidade do conhecimento de seu algoritmo; (2) Uma ferramenta para aproximações polinomiais de alta precisão para funções de quadrado integrável em determinado intervalo limitado, com um majorante de erro; (3) Um ferramental analítico para transposição genérica (linear ou não) dos PVIs até 4ª ordem, nas mudanças de domínio; (4) As matrizes de integração e diferenciação genéricas para todas as bases polinomiais do espaço de Hilbert. / This thesis shows a new method to get polynomial solutions to the initial value problems (IVP), with an error margin comparable to the consecrate numerical methods (NM), for both the function and its derivatives. The method works with differential equations (DEs) linear or not, beeing the developed tolls available until 4th order, whose can be expanded to higher orders. The solution is a polynomial high degree expression with coefficients expressed by the ratio between two integers. The method behaves efficiently even in some cases that NM cannot get started. The resolutions are gotten considering that, the solution space is a Hilbert space, equipped with a complete set basis of Legendre Polynomials. Due the method here developed, the errors majoratives for the function and its derivatives are found analytically by a matrix calculus, also derived in this thesis. Beside all analytical foundation, a software (SAM) was developed to automate the whole process, joining all the tasks involved in the search for solutions to the IVP. This thesis proposes, verifies and validates a new error criterion, which takes in account simultaneously the local and global errors. As sub-products of the results described before, also integrated to the SAM, the following achievements should be highlighted: (1) An objective criterion to analyze the quality of any NM, despite of the knowledge of its algorithm; (2) A tool for a polynomial approximation, of high precision, for functions whose square is integrable in a given limited domain, with an errors majorative; (3) A tool-kit for a generically transpose (linear or not) of the IVPs domain and form, taking into account its derivatives, until the 4th order; (4) The generic matrices for integration and differentiation for all the polynomial basis of the Hilbert space.

Neste trabalho, um novo método grafo-algébrico para o projeto de ilhamento intencional é proposto. O ilhamento intencional é um dos últimos recursos utilizados pelos operadores para evitar um colapso total do sistema elétrico. Ele objetiva dividir um sistema elétrico em dois ou mais subsistemas estáveis quando não é possível garantir a estabilidade do sistema interligado. O método desenvolvido é uma extensão de um método grafo-algébrico, baseado na fatoração da matriz incidência ramo-nó e que foi desenvolvido para a identificação de ilhamento não intencional, para o problema de projeto de ilhamento intencional. A aplicação da fatoração da matriz incidência ramo-nó no problema de projeto de ilhamento é contribuição inédita deste trabalho. O método proposto identifica os conjuntos de corte, compostos por linhas de transmissão/transformadores (ramos), aptos a dividir um sistema elétrico de potência conexo em dois ou mais subsistemas (ilhas), sob a condição de um número mínimo, previamente estabelecido, de ramos interrompidos ou uma interrupção mínima de fluxo de potência ativa. A identificação dos conjuntos de cortes é realizada por meio de uma fatoração ordenada da matriz incidência nó-ramo e por um processo de regularização de cortes. O método foi testado com resultados promissores em alguns sistemas elétricos de pequeno e médio porte. Apresentou boas características que sugerem que o mesmo seja adequado para aplicações em tempo real. O método fornece a informação das barras que formam cada ilha, adapta-se facilmente a mudanças na topologia e pode ser facilmente implementado com rotinas já existentes nos programas de computador comumente utilizados para análise de sistemas elétricos de potência. Trabalhos futuros são necessários para testar a metodologia em sistemas de maior porte, para avaliar a eficiência computacional do método e comparar com a eficiência de outros métodos relatados na literatura. / In this work , a new graph-algebraic method for the design of intentional islanding is proposed. Intentional islanding is one of the last resources used by the Power Electrical System Operators to avoid a total collapse of the electrical system. It aims to divide a power system into two or more stable subsystems when it is not possible to guarantee the stability of the interconnected system. The developed method is an extension of a graph-algebraic method, which is based on a factorization of the branch-node incidence matrix and which was developed to identify unintended islanding, to the problem of intended. The unprecedented contribution of this work is the application of the factorization of the incidence branch-node matrix in the design of islanding control. The proposed method identifies the cutsets, composed of transmission lines / transformers (branches) , able to divide a connected Electrical Power System in two or more subsystems (islands), under the constraint of a minimum number of interrupted branches or minimal interruption of power flow. The identification of cutsets are made through an ordered factorization of the incidence branch node matrix and a regularization process of cutsets. The method has been tested with promising results in some electrical systems of small and medium size. It has shown good characteristics which suggests that it is suitable for real-time applications. The method automatically provides the set of buses that form each island, it easily adapts to changes in topology and can be easily implemented with routines that are already developed in existing computer programs commonly used for analysis of electric power systems. Further work is needed to test the methodology in larger systems to evaluate the computational efficiency of the method and compare with the efficiency of other methods reported in the literature.