Cette thèse doctorale aborde divers aspects méthodologiques de l’analyse de levés électromagnétiques aéroportés en domaine temporel (TDEM) pour une interprétation détaillée à finalités géologique et hydrogéologique. Ce travail s’est appuyé sur un levé réalisé dans la région de Courtenay (Nord-Est de la région Centre) caractérisée par un plateau de craie karstifié (karst des Trois Fontaines) recouvert par des argiles d’altération et des alluvions. Tout d’abord, une méthode de filtrage des données TDEM utilisant la Décomposition en Valeurs Singulières (SVD) a été développée. L’adaptation rigoureuse de cette technique aux mesures TDEM a permis de séparer avec succès les bruits, qui ont pu être cartographiés, et le « signal géologique », diminuant grandement le temps nécessaire à leur traitement. De plus, la méthode s’est avérée efficace pour obtenir, rapidement, des informations géologiques préliminaires sur la zone. Ensuite, une analyse croisée entre le modèle de résistivité obtenu en inversant les données filtrées et les forages disponibles a été effectuée. Celle-ci a mené à une amélioration de la connaissance géologique et hydrogéologique de la zone. Une figure d’ondulation, séparant deux dépôts de craie, et le réseau de failles en subsurface ont pu être imagés, apportant un cadre géologique au karst des Trois Fontaines. Enfin, une nouvelle méthode combinant l’information aux forages et les pentes issues du modèle de résistivité EM a permis d’obtenir un modèle d‟une précision inégalée du toit de la craie. L’ensemble de ces travaux fournit un cadre solide pour de futures études géo-environnementales utilisant des données TDEM aéroportées, et ce, même en zone anthropisée. / This PhD thesis addresses various methodological aspects of the analysis of airborne Time Domain ElectroMagnetic (TDEM) surveys for a detailed interpretation in geological and hydrogeological purposes. This work was based on a survey conducted in the region of Courtenay (north-east of the Région Centre, France) characterized by a plateau of karstified chalk (karst des Trois Fontaines) covered by weathering clays and alluvium. First, a TDEM data filtering method using the Singular Value Decomposition (SVD) was developed. The rigorous adaptation of this technique to TDEM data has successfully separated the noise, which was mapped, and the “geological signal”, greatly reducing the time required for processing. Furthermore, the method has proved to be effective to obtain quick preliminary geological information on the area. Then, a cross analysis between the resistivity model obtained by inverting the filtered data and the available boreholes was conducted. This has led to the improvement of the geological and hydrogeological knowledge of the area. An undulating feature, separating two chalk deposits, and a fault network were imaged in subsurface, providing a geological framework for the Trois Fontaines karst. Finally, a new 3D modelling method combining the information at boreholes and the slopes derived from the EM resistivity model yielded an accurate model of the top of the chalk. All of this work provides a solid framework for future geo-environmental studies using airborne TDEM data, even in anthropized area.

This essay tries to find a possible way for us to deal with the questions concerning climate change by looking into an alternative conception of being. One can speak of the ongoing climate change as a crisis that concerns all of human kind and all beings on earth, but how can we fight it together? The situation demands us to re-think how we humans exist together and among other beings. Despite that the situation calls for instant and radical action, we seem unwilling to do enough. We get stuck on questions about who should take action: is it the politicians or each one alone, or is there something in between? By looking more deeply into the concept of Mitsein as Martin Heidegger depicts it in Being and Time, Jean-Luc Nancy brings to light a possible way past the problematic thought of Heidegger. Nancy shows us in Being Singular Plural that Heideggers exposition on Mitsein is a mere sketch when considering the full potential of the concept. By determining Mitsein as being fundamentally-ontologically originary and anterior to the individuation of Dasein, Nancy opens up a whole new field of thought. According to Nancy, the existential analytic has to begin with something like a ”co-existential analytic”, which will draw the lines for how we exist being-with. With a concept like being singular plural and his way of conceptualizing meaning, Nancy might give us some possible tools to cope with our situation today. Nancys actuality is confirmed by the ecological philosopher Mick Smith, who emphasizes the demand for a new approach towards nature and what it means to be. Smith adds to the essay a glimpse of an emerging philosophical discourse about the thought of an ecological community, where the concept of being singular plural could possibly play a central part.

The purpose of this thesis is to assess the extent to which the singular readings of a manuscript reveal the tendencies of the scribe who wrote its text by examining three related Greek manuscripts from the sixth century. The three manuscripts are all luxury copies of the Gospels' purple codices, so named because they are written in silver and gold ink on parchment that has been dyed purple. The manuscripts, Codex Purpureus Petropolitanus (N 022), Codex Sinopensis (O 023) and Codex Rossanensis (Σ 042), were all copied in the sixth century from a common exemplar. Chapter One introduces the three manuscripts. Chapter Two provides a history of research on scribal habits and singular readings, and it describes the method used in this thesis to determine both the validity of the singular readings method and the actual scribal habits of 022, 023 and 042. Chapter Three provides a preliminary assessment of each scribe by comparing scribal features in the passages extant in all three manuscripts. Chapters Four, Five and Six assess the scribal habits of 022, 023 and 042, respectively. In these chapters, perceived scribal habits are measured by a modified singular readings method to replicate the situation for each manuscript if it had no extant close relatives' the situation for most early manuscripts. Actual scribal habits are then determined by the places the scribe changed the text of the exemplar. Chapter Seven offers some concluding thoughts about the scribes, their exemplar and the use of singular readings to determine scribal habits. Appendix One presents for the first time an edition of the reconstructed text of the exemplar of 022, 023 and 042, where at least two of the three manuscripts are extant. Appendices Two, Three and Four are full transcriptions of the Gospel of Matthew in 022, 023 and 042, respectively. Appendix Five provides information on singular readings and corrections in 042 where it alone is extant of the three manuscripts. Appendix Six describes the codicological structures of the three manuscripts. Appendix Seven is a transcription and brief discussion of 080, a fragmentary of a purple codex dating to the sixth century. Finally, both 022 and 042 contain a series of secondary corrections made against a second exemplar, and Appendix Eight argues that the scribe of 042 was responsible for these corrections in both manuscripts.

Neste trabalho, estudamos diferentes construções e propriedades das classes características de variedades suaves e singulares. Para ilustrar a teoria, calculamos a obstrução de Euler de algumas superfícies singulares no espaço tridimensional e apresentamos uma fórmula do tipo Poincaré-Hopf para variedades singulares / In this work, we study different constructions and properties of the characteristics classes of smooth and singular manifolds. To ilustrate the theory, we compute the Euler obstructions of some singular surfaces in tridimensional space and state a Poincaré-Hopf´s formula for singular varieties

Cette thèse porte sur l'étude de problèmes de contrôle optimal sur des réseaux (c'est-à-dire des ensembles constitués de sous-régions reliées entre elles par des jonctions), pour lesquels on autorise différentes dynamiques et différents coûts instantanés dans chaque sous-région du réseau. Comme dans les cas plus classiques, on aimerait pouvoir caractériser la fonction valeur d'un tel problème de contrôle par le biais d'une équation de Hamilton-Jacobi-Bellman. Cependant, les singularités géométriques du domaine, ainsi que les discontinuités des données ne nous permettent pas d'appliquer la théorie classique des solutions de viscosité. Dans la première partie de cette thèse nous prouvons que les fonctions valeurs de problèmes de contrôle optimal définis sur des réseaux 1-dimensionnel sont caractérisées par de telles équations. Dans la seconde partie les résultats précédents sont étendus au cas de problèmes de contrôle définis sur une jonction 2-dimensionnelle. Enfin, dans une dernière partie, nous utilisons les résultats obtenus précédemment pour traiter un problème de perturbation singulière impliquant des problèmes de contrôle optimal dans le plan pour lesquels les dynamiques et les coûts instantanés peuvent être discontinus à travers une frontière oscillante. / This thesis focuses on the study of optimal control problems defined on networks (i.e. sets consisting of sub-regions connected together through junctions), where different dynamics and different running costs are allowed in each sub-region of the network. As in classical cases, we would like to characterize the value function of such an optimal control problem through an Hamilton-Jacobi-Bellman equation. However, the geometrical singularities of the domain and the data discontinuities do not allow us to apply the classical theory of viscosity solutions. In the first part of this thesis, we prove this kind of characterization for the value functions of optimal control problems defined on 1-dimensional networks. In the second part, the previous results are extended to the case of control problems defined on a 2-dimensional junction. Finally, in the last part, we use the results obtained previously to treat a singular perturbation problem involving optimal control problems in the plane for which the dynamics and running costs can be discontinuous through an oscillating border.

Analisamos o comportamento assintótico de uma família de equilíbrios de uma equação de reação-difusão com a condição de Neumann homegênea definido num domínio fino bidimensional com termos de reação concentradas em uma vizinhança oscilante da fronteira. Assumimos que o domínio e portanto a vizinhança oscilante se degeneram em um intervalo quando o parâmetro positivo tende a zero. O objetivo principal foi mostrar que essa família de soluções, converge para uma equação limite unidimensional, que captura a geometria e o comportamento assintótico dos conjuntos abertos onde o problema é estabelecido. De fato mostramos a continuidade da família de equilíbrios / In this work we analyze the behavior of a family of stead state solutions of a semilinear reaction-diffusion equation with homogeneous Neumann boundary condition, posed in a two-dimensional thin domain with reaction term concentrated in an narrow oscillating neighborhood. Indeed, we assume that the domain of definition of the solutions degenerates into an interval as a small parameter $\\epsilon$ goes to zero. Our main result is that this family of solutions converge to the solution of a one-dimensional limit equation capturing the geometry and oscillatory behaviour of the open sets where the problem is estabilished.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Neste presente trabalho, faremos o estudo de importantes propriedades geomÃtricas e analÃticas de soluÃÃes de equaÃÃes diferenciais parciais elÃpticas totalmente nÃo-lineares do tipo: singulares e degeneradas. O estudo de processos de combustÃo que se degeneram ao longo do conjunto de anulamento da densidade de um gÃs, um caso particular de problemas do tipo "quenching", apresentam em sua modelagem equaÃÃes singulares que estÃo descritas neste trabalho. Nesta primeira parte iremos obter propriedades de uma soluÃÃo minimal, que vÃo desde o controle completo Ãtimo, atà a obtenÃÃo de estimativas de Hausdorff da fronteira livre singular. Por fim, iremos obter a regularidade Ãtima de soluÃÃes de equaÃÃes em que suas propriedades de difusÃo(elipticidade) se deterioram na ordem de uma potÃncia do seu gradiente ao longo do conjunto em que tal taxa de variaÃÃo se anula. / In this work we study important geometric and analytic properties to solutions of fully nonlinear elliptic partial differential equations, both singular and degenerate types. The study of combustion processes that degenerate along the null-set of the density of a gas, a particular case of quenching problems, present in their modeling, equations described in this work. In this first part we obtain properties of a minimal solution, since the complete optimal control until the Hausdorff estimates of the singular free boundary. Ultimately, we obtain the optimal regularity to equation solutions where their diffusion property (elipticity) deterorate in a power of their gradient along the set where such rate of variation nullifies.

Neste trabalho, estuda-se o problema de estabilidade de tensão do ponto de vista dinâmico, enfocando a análise nas instabilidades originadas por grandes perturbações. A modelagem utilizada nestes estudos envolve dinâmicas que possuem múltiplas escalas de tempo, mas na prática, os problemas de instabilidade de tensão estão geralmente associados às dinâmicas de longo prazo. Nesse sentido, o método de análise QSS fornece muitas vantagens do ponto de vista computacional, reduzindo significativamente o tempo de processamento, mediante a substituição das equações de dinâmica rápida por suas correspondentes equações de equilíbrio. As contribuições deste trabalho são duas: a primeira consiste no estudo da importância da região de estabilidade das dinâmicas lentas do SEP e sua relação com a região de estabilidade do sistema original. A segunda consiste em estudar a aplicação do método QSS no SEP oleando para as condições existentes na literatura e analisando principalmente as desvantagens de sua aplicação. Os sistemas de potência apresentados na literatura são utilizados como exemplos. Com base nestas simulações e na teoria existente da análise QSS, são estudadas algumas condições sob as quais o método QSS é válido. A teoria de região de estabilidade para estes sistemas é explorada para fornecer indicativos de margem de estabilidade e controle preventivo. / In this work, we study the problem of voltage stability of the dynamic point of view, focusing the analysis on the instability caused by large disturbances. The modeling used in these studies involves dynamics that have multiple time scales, but in practice, the problems of voltage instability are generally associated with long-term scale. Thus, the QSS method of analysis provides many advantages in terms of computational resource, significantly reducing the processing time, by replacing the equations by their corresponding fast dynamic equilibrium equations. The contributions of this work are two: the first is to study the importance of the stability region of the slow dynamics of the power system and its relation to the stability region of the original system. The second is to study the application of the QSS method in power systems considering the current theory in the literature and analyzing the main disadvantages of its application. The power system presented in the literature are used as examples. Based on these simulations and the existing theory of the QSS method, we study some conditions under which this method is valid. The theory of stability region for these systems is exploited to provide indicative of margin stability and preventive control.

Este trabalho tem como objetivo o desenvolvimento de uma metodologia de monitoramento a partir da alocação de medidores voltada para a estimação de estado harmônico trifásica em sistemas de distribuição de energia elétrica desequilibrados. O algoritmo de estimação de estado harmônico desenvolvido tem como entrada os fasores de tensão e de corrente em pontos pré-definidos de medição sobre os alimentadores em análise. Para a alocação dos medidores, verificou-se a necessidade de a mesma ser realizada e direcionada para este problema, e um algoritmo de otimização em específico foi desenvolvido utilizando algoritmos genéticos. Para a estimação de estado harmônico, a técnica de Decomposição em Valores Singulares foi utilizada, por ser adequada a sistemas não completamente observáveis. Em relação às simulações, cargas não lineares (ou perturbadoras) foram conectadas ao longo dos alimentadores testes do IEEE de 13, 34 e 37 barras, considerando configuração trifásica assimétrica para as linhas e cargas desbalanceadas. Todas as simulações computacionais foram realizadas dispondo do programa DIgSILENT PowerFactory. Os resultados satisfatórios encontrados denotam que o desempenho do estimador desenvolvido é dependente dos pontos de medição pré-definidos a partir da alocação dos medidores realizada. Pela metodologia implementada e aplicada, o algoritmo de estimação de estado harmônico veio a corretamente calcular todas as variáveis de estado e, consequentemente, os sistemas testes em análise tornaram-se completamente observáveis para todas as fases e ordens harmônicas caracterizadas. / This research aims for the development of a monitoring methodology through the allo-cation of meters in order to perform a three-phase harmonic state estimation in unbalanced distribution systems. The harmonic state estimation algorithm developed has voltage and current phasors as inputs at predefined measurement points on the feeders about analysis. For an allocation of the meters, there was a need for it to be performed and directed to this problem, and a specific optimization algorithm was developed using Genetic Algorithms. For a harmonic state estimation, the Singular Value Decomposition technique was made, because it is suitable for systems that are not completely observable. Regarding the simulations, the non-linear (or disturbing) loads were connected along the test feeders of the IEEE of 13, 34 and 37 bus, considering the three-phase asymmetric configuration for lines and loads. All computational simulations were performed in the DIgSILENT PowerFactory software. The satisfactory results found note that the performance of the developed estimator depends on the pre-defined measurement points from the allocation of the realized meters. By the applied methodology, the harmonic state estimation algorithm came to correctly calculate all the state variables and, consequently, the test systems about analysis became fully observable for all phases and harmonic orders characterized.

In this work we study rate of convergence of attractors for parabolic equations. We consider various types of problems where the diffusion coefficient has varied profiles: large diffusion, localized large diffusion and large diffusion except in the neighborhood of a point where it becomes small. In all cases we obtain a singular perturbation where a rate of convergence of attractors is obtained. / Neste trabalho estudamos taxa de convergência de atratores para equações parabólicas. Consideramos vários tipos de problemas onde o coeficiente de difusão apresenta perfís variados: difusão grande, difusão grande localizada e difusão grande exceto na vizinhança de um ponto onde ela torna-se pequena. Em todos os casos consideramos perturbações singulares e uma taxa de convergência para os atratores é obtida.