Abstract : This thesis tackles the problem of the possible phase transitions in the presence of a magnetic field, and of the transport properties of quasi-one-dimensional (quasi-1D) superconductors like Bechgaard salts. In the framework of the quasi-1D electron-gas model, the renormalization group (RG) method is used for studying the effect of Zeeman coupling to a magnetic field on the structure of the phase diagram of the quasi-1D electron gas model. For the transport theory, a combination of linearized Boltzmann equation and renormalization group method is used to investigate the electrical resistivity and the Seebeck coefficient of quasi-1D correlated organic metals like the Bechgaard salts near their quantum critical point that joins antiferromagnetism and superconductivity. The thesis is organized in four chapters. In the first chapter, an introduction to the Bechgaard and Fabre salts is given and properties of their generic temperature-pressure phase diagram are explained. These compounds are considered as the reference systems for the comparison between theory and experiments on the nature and symmetry of the superconducting phase in a magnetic field and the anomalous transport properties in the normal phase. The problem of the observed anomalously high value of the upper critical field of Bechgaard salts is the main issue of chapter two. We approach this problem with the aid of the weak coupling renormalization group technique in the presence of Zeeman coupling, for an extended quasi-1D electron-gas model, which includes inter-chain hopping, nesting deviations along with both intrachain and inter-chain repulsive interactions. This allows us to study the efect of quasi-1D spin fluctuations originating from constructive interference between unconventional superconductivity (SC) and density-wave instabilities on the magnetic field vs temperature phase diagram of these quasi-1D superconductors. Our results support the existence of a crossover from d-wave to an inhomogeneous d-wave FFLO superconducting state under field. In the third chapter, we introduce the semi-classical Boltzmann equation for transport in its linearized form. The Boltzmann theory is coupled to the RG method for the calculation of the renormalized umklapp scattering amplitude for the anisotropic scattering time. We then study the temperature and pressure variation of the electrical resistivity and the Seebeck coefficient of the Bechgaard salts quasi-one-dimensional organic superconductors in the quantum critical domain of their normal phase. We demonstrate that momentum and temperature dependence of umklapp scattering strongly affects the temperature behavior of transport in the metallic state, as a function of nesting deviations that simulate the influence of pressure in the actual phase diagram. This defines a characteristic quantum critical region where significant deviations from the Fermi-liquid behavior are seen, either as an anomalous power law of electrical resistivity or sign reversal of the Seebeck coefficient. / Cette thèse aborde le problème des transitions de phase possibles, en présence d'un champ magnétique, et des propriétés de transport dans des supraconducteurs quasi-unidimensionnels (quasi-1D) comme les sels de Bechgaard. Dans le cadre du modèle d'un gaz d'électrons quasi-1D, on utilise la méthode du groupe de renormalisation (GR) pour étudier l'effet du couplage Zeeman sur le diagramme de phase ce système. Pour la théorie du transport, une combinaison de l'équation de Boltzmann linéarisée et de la méthode de groupe de renormalisation est utilisée pour étudier la résistivité électrique et le coefficient de Seebeck de métaux organiques comme les sels de Bechgaard au voisinage de leur point critique quantique joignant l'antiferromagnétisme et la supraconductivité. La thèse est organisée en quatre chapitres. Dans le chapitre un, une introduction aux sels de Bechgaard et de Fabre est donnée et les propriétés de leur diagramme de phase générique en température-pression sont expliquées. Ces composés sont considérés comme des systèmes de référence pour la comparaison entre la théorie et les expériences sur la nature et la symétrie de la phase supraconductrice sous un champ magnétique et les propriétés anormales de transport dans la phase normale. Le problème de la valeur anormalement élevée du champ critique supérieur observée dans les sels de Bechgaard est la question principale traitée au chapitre deux. Nous abordons ce problème à l'aide de la technique de couplage faible du groupe de renormalisation, pour le modèle du gaz d'électrons quasi-1D étendu, qui contient le saut inter-chaînes, les déviations par rapport à l'emboitement parfait, ainsi que les interactions intra-chaînes et inter-chaînes répulsives. Ceci nous permet d'étudier l'effet des fluctuations de spin quasi-1D provenant d'une interférence constructive entre la supraconductivité non conventionnelle (SC) et les instabilités d'onde de densité sur le diagramme de phase en champ magnétique et en température de ces supraconducteurs quasi-1D. Grâce à notre approche, nous examinons les instabilités possibles dans la partie basse température/champ élevé du diagramme de phase. Dans le troisième chapitre, nous introduisons l'équation semi-classique de Boltzmann pour le transport dans sa forme linéarisée. La théorie de Boltzmann est couplée à la méthode du GR pour le calcul de l'amplitude de diffusion umklapp renormalisée entrant dans l'évaluation du temps de diffusion anisotrope. Nous étudions ensuite la variation en température et en pression de la résistivité électrique et le coefficient de Seebeck pour les supraconducteurs organiques quasi-1D, les sels de Bechgaard, dans le domaine critique quantique de leur phase métallique. Nous démontrons que la variation en quantité du mouvement et en température de la diffusion umklapp sur la surface de Fermi affecte fortement le comportement thermique du transport dans l'état métallique, en fonction des déviations à l'emboîtement parfait. Dans notre modèle, ces déviations simulent l'influence de la pression dans le diagramme de phase réel. Ceci définit une région critique quantique caractéristique où des écarts significatifs par rapport au comportement du liquide de Fermi sont observés, soit comme une loi de puissance anormale de la résistivité électrique, soit comme un changement de signe du coefficient de Seebeck.

Sous chargement, les matériaux dits ‘quasi-fragiles’ tels que les bétons et de nombreuses roches présentent souvent une perte de rigidité progressive, ainsi qu’un comportement anisotrope, asymétrique et hystérétique. Il est maintenant largement admis que ce comportement, fortement non linéaire et complexe, est lié principalement à la création, au développement et au jeu d’ouverture et fermeture des réseaux de microfissures accompagnés de glissement et de frottement entre lèvres de microdéfauts en contact.Dans l’optique d’une utilisation industrielle sérieuse, la construction d’un modèle d’endommagement simple, fiable sur le plan mathématique et thermodynamique et offrant une réponse pertinente pour les matériaux quasi-fragiles jusqu’à l’apparition d’une localisation de l’endommagement, constitue à l’heure actuelle un enjeu important. Il représente en effet une étape indispensable avant de pouvoir espérer modéliser de manière satisfaisante le comportement jusqu’à la ruine de nombreux ouvrages du génie civil. L’objectif du travail de thèse est d’améliorer les capacités prédictives d’un modèle simple d’endommagement par microfissuration existant qui prend en compte les effets unilatéraux liés à l’ouverture-fermeture des microfissures. La nouvelle approche proposée est basée sur l’introduction d’un second phénomène dissipatif susceptible d’être induit lors de la fermeture des microdéfauts : le glissement avec frottement des lèvres en contact. La modélisation de ce nouveau mécanisme dissipatif s’effectue à l’échelle macroscopique en ne faisant référence à l’échelle inférieure ou aux résultats de la micromécanique des milieux microfissurés que pour interpréter ou justifier certaines hypothèses. Une attention particulière est accordée à la continue différentiabilité du potentiel thermodynamique proposé. L’étude et la simulation de différents essais permettent d’illustrer la pertinence des choix retenus. / Under loading, materials called 'quasi-brittle' as concrete and many rocks often exhibit progressive loss of stiffness, as well as anisotropic behavior, and asymmetric hysteretic. It is now widely accepted that this behavior highly nonlinear and complex, is mainly related to the creation, development and set of opening and closing of microcracks accompanied networks and sliding friction between the lips of microdefects in contact. In the context of a serious industrial use, the construction of a damage model simple, thermodynamically and mathematically reliable and providing an appropriate response for quasi-brittle materials until the onset of localization damage, is currently an important issue. It is indeed a necessary step before adequately modelling behavior to the ruin of many civil engineering works. The objective of this thesis is to improve the predictive capabilities of an existing simple model of damage by microcracking which takes into account unilateral effects related to the opening and closing of microcracks. The new approach is based on the introduction of a second dissipative phenomenon may be induced when closing microdefects: frictional sliding of the lips of microcracks. Modeling of this new dissipative mechanism occurs at the macroscopic scale by only referring to the lower scale or the results of the micro environments that microcracked to interpret or justify certain assumptions. Particular attention is paid to the continuous differentiability of the thermodynamic potential proposed. The study and simulation of various tests enable to illustrate the relevance of the choices made.

O paradigma de sistemas de moléculas auto-replicantes é o modelo de quase-espécies, no qual as moléculas são representadas por seqüências binárias de tamanho L e o mecanismo de replicação é suposto imperfeito. Em particular, cada seqüência é gerada corretamente com probabilidade Q = qL, onde q é a probabilidade de cópia exata por dígito. Um dos resultados mais intrigantes no modelo para o relevo de replicação de pico único, no qual há apenas um tipo de molécula com vantagem seletiva a em relação aos outros tipos, é a observação de um limiar de erro a partir do qual toda informação biológica relevante é perdida. A transição de limiar de erro verificada para Qc = l /a pode ser visualizada como uma transição de fase do tipo ordem-desordem. Verificamos que a largura dessa transição decresce com L de acordo com L-1. Concluímos também que as grandezas físicas de interesse são bem descritas por meio de funções de escala. Elaboramos ainda uma versão estocástica (isto é, tamanho de população N finito) para o modelo de quase-espécies, no qual a dinâmica é descrita por uma cadeia de Markov. Mostramos que o tempo característico &#964 para o desaparecimento de seqüências mestras na população obedece uma relação de escala bem definida. A transição em nosso modelo é constatada através da divergência de &#964 em Qc no limite de N &#8594 &#8734 ,sendo que a largura da transição decresce de acordo com N -1/2. Em nossa abordagem não utilizamos nenhuma definição arbitrária para o limiar de erro para população finita. Como solução para o problema da crise de informação associada ao limiar de erro estudamos o modelo de hiperciclos. Neste modelo, as macromoléculas se replicam com o auxílio de outros membros do hiperciclo por meio do mecanismo de catálise. Estudamos analiticamente a propagação de erro no hiperciclo e obtemos os diagramas de fases no espaço de parâmetros para vários tamanhos de hiperciclo n. Esses diagramas descrevem as regiões de estabilidade das diversas soluções de estado estacionário do sistema. Constatamos que para hiperciclos com n &#8804 4 existe um limiar de erro menor que aquele verificado no modelo de quase-espécies. Desde que o suporte catalítico realizado por uma molécula no hiperciclo pode ser considerado de fato um comportamento altruísta, modelos para evolução do altruísmo como, a teoria de seleção de grupos, têm sido utilizados no contexto de evolução pré-biótica. Aqui investigamos a evolução da produção de enzimas e os efeitos de sinergia utilizando esses conceitos. / The quasi-species model is the paradigm of systems composed of self-replicating molecules, which are represented by sequences of fixed length L. The replication machinery is assumed to be imperfect. Particularly, each sequence is copied exactly with probability Q=qL, where q denotes the probability of exact copy per digit. One of the most intriguing results of the model for the single-peak replication landscape, which considers the existence of a master sequence that has a selective advantage a in comparison to the other types, is the occurrence of an error threshold phenomenon beyond the biological information is completely lost. The error threshold transition can be viewed as an order-disorder phase-transition. We investigated the sharpness of the threshold and found that its characteristics persist across a range of Q of order L-1 about Qc. Other physical quantities of interest are also well described by universal functions. We formulate a stochastic version (i.e., finite population size N) for the quasispecies model, in which a Markov chain defines the dynamics. We show that the characteristic time r for the disappearance of master sequences in the population obeys a well defined scaling relation. The transition in this model is signalized by the divergente of t at Qc in the limit N &#8594 &#8734, and the sharpness of the transition decreases like N -1/2. In our approach we do not use any arbitrary definition of the error threshold for finite population. As a solution for the information crisis associated to the error threshold, here we considered the hypercycle model, where the macromolecules self-replicate with the catalytic support of the other members of the hypercycle. We study analytically the error propagation in the hypercycle and obtain the phases diagrams in the space of parameters for several hypercycle sizes n. These diagrams describe the stability regions of the steady state solutions of the system. We find that for hypercicle size n &#8804 4 the error threshold is smaller than that for the quasispecies model. Since the catalytic support developed by a molecule is in fact an altruistic behavior, some models for the evolution of altruism, for instance, the selection group theory, have been investigated in the context of pre-biotic evolution. Specifically, here we analyze the evolution of enzyme production and the effects of synergism.

On introduit une nouvelle modélisation du décollement de membrane soumise à une force croissante par rapport au temps, basée sur une évolution quasi-statique, s'appuyant sur la notion de mouvement général minimisant introduit par De Giorgi. Notre modèle utilise les quasi-ouverts et/ou les mesures capacitaires pour représenter l'état de la membrane à un instant t. Dans notre cas, l'évolution de la membrane est régie par un principe énergétique développé par Mielke, qui a été aussi utilisé dans la propagation des fissures introduite Francfort et Marigo. On obtient ainsi une évolution quasi-statique de la membrane représentée comme mesure capacitaire qui, sans être en contradiction avec le modèle mécanique de Andrews et Shillor, met en valeur les phénomènes de relaxation. On effectue ensuite des simulations numériques sur ce modèle, faites à la fois sur la représentation du décollement de membrane par des quasi-ouverts mais aussi par des mesures, et à chaque fois, un algorithme de descente local compatible avec le point de vue des mécaniciens, et un algorithme plus global à stratégie évolutionnaire sont implémentés. Ces simulations mettent en valeur les phénomènes de relaxation aperçus dans l'étude théorique. Enfin, la dernière partie s'intéresse aux résultats d'identification de multi-fissures de G. Alessandrini et A. Diaz Valenzuela et aux points conductifs introduits par Z. Belhachmi et D. Bucur. Le but est d'étendre et d'étudier ce concept sur un matériau non homogène, pour un défaut ayant un nombre infini de composantes connexes de diamètre minoré / This thesis introduces a new model for debonding membranes, subject to a debonding force depending on time. We deal with a quasi-static evolution in the framework of the minimizing movement theory introduced by De Giorgi. This new tool is based on the analysis of the evolution of capacitary measures and shapes. In our case, the evolution process is governed by an energy principle developped by Mielke also used in the crack propagation model of Francfort and Marigo. The membrane, represented by a capacitary measure, is subject to a natural relaxation phenomenon during the evolution, being in accordance with the mechanical model of Andrews and Shillor. The second chapter consists on the numerical analysis of this model, from two points of view : representation of the debonding membranes by quasi-open sets and by capacitary measures, respectively. In each case, local algorithms in agreement with mechanical point of view and evolutionary strategy algorithms which allow to escape from local minimizers are implemented. These computations emphasize the relaxation phenomenon in agreement with the theory. The last part deals with the identification of multi-cracks by electrostatic boundary measurements. We extend uniqueness results of G. Alessandrini and A. Diaz Valenzuela relying on the analysis of the conductive points introduced by Z. Belhachmi and D. Bucur. The goal is to deal with a non homogeneous material and to prove uniqueness (for two boundary measurement of defects detection having an infinite number of connected components of minorated diameter

Esta dissertação investiga uma particular deformação do modelo de Bullough-Dodd. Não se sabe se tais deformações são ou não integráveis, ainda que nossas simulações numéricas apresentem soluções solitônicas. Exploramos o conceito de quase-integrabilidade em mais esse contexto e mostramos um argumento analítico para a quase-conservação das cargas (isto é, as cargas variam com o tempo, mas seus valores inicial e final são os mesmos). Mesmo quando o argumento analítico não pode fazer previsões, nossas simulações mostram que as cargas apresentam o mesmo comportamento. Isso sugere que as deformações consideradas são integráveis e ainda há espaço para explorá-las. / This dissertation investigates a particular deformation of the Bullough-Dodd model. It\'s unknown if such deformations are integrable or not, yet they present solitonic solutions which were obtained through numerical simulations. We further explore the concept of quasi-integrability in this context, showing analiticaly that at least for some sets of parameters, the charges are quasi-conserved (i.e. the charges vary over time, but it\'s initial and final values are the same). Even when the analitical argument can\'t predict what happens, our simulations show the same charge behaviour. This suggests that those deformations are integrable and can be further explored.

This thesis describes the work undertaken in producing the passive radio-frequency section of a heterodyne receiver for use on the United Kingdom Infra-Red Telescope at signal frequencies in the 200-300 GHz range. This is a Quasi-Optical system, comprised of a Martin-Puplet polarising interferometer employed as a diplexer and the lenses and feed horns by which the diplexer was coupled to the telescope, local oscillator, and mixer. The Gaussian beam-mode approach was employed to develop a theoretical basis for understanding the operation of such a system upon coherent paraxial beams. Quasi-Optical systems were then designed and their performance predicted by the application of this extension of Gaussian optics. Two such systems were constructed and their performance determined by laboratory measurements to be as predicted. One of these systems was then installed on the telescope where it was shown to function as designed. As part of the calibration and test routine on the telescope a number of astronomical measurements were made, including a determination of the apparent temperatures of the planets Jupiter and Saturn by a method different to that employed for results previously published. The Quasi-Optical receiver was successfully calibrated and commissioned as a common-user instrument. As such it will continue to be used in a variety of astronomical research programs undertaken by various groups.

Although the Maxwell equations govern the propagation of EM waves at all frequencies, the methods required to generate, direct, analyse and detect radiation differ from band to band. This thesis is concerned with the development and demonstration of 'Quasi-optical' techniques for millimetre wavelengths, which involve the propagation of Gaussian profiled beams a few wavelengths across, and the realization of a general circuit approach to mm-wave measurement. Gaussian beam-mode analysis, which is used in later chapters to understand propagation of quasi-optical beams, is reviewed in chapter 1. Chapter 2 outlines the design, manufacture and testing of corrugated feed horns which generate fundamental Gaussian beam-modes. The design and manufacture of lenses which control the spreading of the beams and directional couplers which provide desirable signal processing functions in quasi-optical circuits is discussed in chapter 3. Chapter 4 traces the development of a Faraday isolator which operates in free-space and can suppress unwanted reflections in quasi-optical circuits. Chapter 5 discusses a reusable circuit board upon which systems can be easily and quickly constructed. A null reflectometer built using quasi-optical components is outlined in chapter 6 and reflection measurements from lenses and horns presented. Chapter 7 describes a corrugated feed horn/lens antenna used in a balloon-borne nw-wave cosmic background experiment. Finally, Chapter 8 demonstrates the use of quasi-optical components in a 115 GHz receiver circuit.

"The last fifteen years have seen much success in the analysis of quasi-static evolution for Griffith fracture, which is the mathematically natural starting point for studying fracture. At the same time, attempts have been made to show existence for similar models based on cohesive fracture rather than Griffith. These models are generally viewed as physically more realistic than Griffith, in that they are better models for crack nucleation. These attempts at existence proofs have been unsuccessful without very strong additional assumptions, for example, specifying the crack path a priori. The main purpose of this thesis is to characterize as well as possible the mathematical difficulties in cohesive fracture, and to make progress toward an existence result without the prescribed crack path assumption. So far, the most powerful method for existence proofs is to build a sequence of approximate solutions, based on time discretization, and take the limit as the time steps go to zero. We show that there are mainly two complications on the cracks of these approximate solutions that we need to rule out in order to show existence. The first one is due to the potential oscillation of the crack path. The second is due to the potential splitting of a crack into two or more nearby cracks, with the same total jump in displacement. We begin by first constructing an example illustrating how oscillations described above can affect the minimality of the limit. Then we prove that the splitting described above can be ruled out for any sequence of unilateral minimizers. With this result, we show how exactly oscillation affect the minimality on the limit of the sequence. We then move to the evolution problem and show the convergence of energy for almost every t. Based on this result we develop a method that allows us to analyze the problem using only a finite set of times. An application of this method is a proof of absolute continuity. Future work will be aimed at using the tools we developed to rule out oscillation and finally to prove existence results under more general assumptions."

Let (M,g) be a quasi-Sasaki manifold with Reeb vector field xi. Our goal is to understand the structure of M when g is an Einstein metric. Assuming that the S^1 action induced by xi is locally free or assuming a certain non-negativity condition on the transverse curvature, we prove some rigidity results on the structure of (M,g). Naturally associated to a quasi-Sasaki metric g is a transverse Kahler metric g^T. The transverse Kahler-Ricci flow of g^T is the normalized Ricci flow of the transverse metric. Exploiting the transverse Kahler geometry of (M,g), we can extend results in Kahler-Ricci flow to our transverse version. In particular, we show that a deep and beautiful theorem due to Perleman has its counterpart in the quasi-Sasaki setting. We also consider evolving a Sasaki metric g by Ricci flow. Unfortunately, if g(0) is Sasaki then g(t) is not Sasaki for t>0. However, in some instances g(t) is quasi-Sasaki. We examine this and give some qualitative results and examples in the special case that the initial metric is eta-Einstein.

Orientador: Simone Mazzini Bruschi / Banca: Cláudia Buttarello Gentile / Banca: Marta Cilene Gadoti / Resumo: Neste trabalho caracterizamos o conjunto dos pontos de equilíbrio de um problema parabólico quasilinear governado pelo p-Laplaciano, p > 2, e do problema parabólico governado pelo Laplaciano / Abstract: In this work we give a characterization set of the equilibrium points of a parabolic problem quasi-linear governed by the p-Laplacian, p > 2, and the a parabolic problem governed by the Laplacian / Mestre