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O autômato celular Game of LIFE (GL) exibe comportamento coletivo não-trivial (Classe IV de Wolfram) a partir de regras locais simples. Na década de 1990, conjecturou-se que o autômato seria um exemplo de sistema não-conservativo com criticalidade auto-organizada. Nesse trabalho refutamos essa conjectura verificando que o regime transiente para estados absorventes não escala de forma correta para redes grandes. Usando uma aproximação de campo médio com considerações sobre interfaces para a rede quadrada, definimos um parâmetro de controle sigma0 relacionado com a razão de ramificação da interface da fase absorvente. A partir da análise de um grande número de autômatos celulares (6144), encontramos uma transição de fase descontínua no espaço de regras dos autômatos celulares totalistas. Também encontramos que o GL é um autômato celular quasi-crítico, com sigma0=1.006, ou seja, o GL equivale a um processo de nucleação quasi-crítico. Mostramos que essa quasi-criticalidade é resultado da coexistência e competição entre a fase viva e a fase morta: embora o LIFE esteja destinado à extinção (ao estado absorvente morto), o decaimento é adiado devido a um forte ralentamento crítico. / The cellular automaton Game of LIFE exhibits non-trivial collective behavior (Wolfram Class IV) from local simple rules. In the 1990s, it was conjectured that the automaton would be an example of self-organized criticality in non-conservative systems. In this work we refute this conjecture by verifying that the transient regime to absorbing states does not scale for large lattice sizes. By using a mean-field approximation with considerations about interfaces in square lattices, we define a control parameter sigma0 related to the interfacial absorbing phase branching rate. From the analysis of a large number of cellular automata (6144), we find a discontinuous phase transition in the cellular automata rule space. We also find that LIFE is a quasi-critical cellular automaton, with sigma0=1.006, that is, LIFE is a quasi-critical nucleation process. It is shown that this quasi-criticality is a result of coexistence and competition between the living and dead phases: although LIFE is destined to extinction (to the dead absorbing state), this decay is delayed due to a strong critical slowing down.

Estudos sobre a manutenção da diversidade cultural sugerem que o mecanismo de interação social, normalmente considerado como responsável pela homogeneização cultural, também pode gerar diversidade. Com o intuito de estudar esse fenômeno, o cientista político Robert Axelrod propôs um modelo baseado em agentes que exibe estados absorventes multiculturais a partir de uma interação homofílica homogeneizadora entre os agentes. Nesse modelo, a diversidade (ou desordem) cultural é produzida pela escolha dos fatores culturais iniciais dos agentes e a interação homofílica age apenas no sentido de reduzir a desordem inicial. Em virtude de sua simplicidade, várias releituras e variações do modelo de Axelrod são encontradas na literatura: introdução de uma mídia externa, alterações da conectividade dos agentes, inserção de perturbações aleatórias, etc. Entretanto, essas propostas carecem de uma análise sistemática do comportamento do modelo no limite termodinâmico, ou seja, no limite em que o número de agentes tende a infinito. Essa tese foca primariamente nesse tipo de análise nos casos em que os agentes estão fixos nos sítios de uma rede quadrada ou nos sítios de uma cadeia unidimensional. Em particular, quando os fatores culturais iniciais dos agentes são gerados por uma distribuição de Poisson, caracterizamos, através de simulações de Monte Carlo, a transição entre a fase ordenada (pelo menos um domínio cultural ´e macroscópico) e a fase desordenada (todos os domínios culturais são microscópicos) na rede quadrada. Entretanto, não encontramos evidência de uma fase ordenada na cadeia unidimensional. Já para fatores culturais iniciais gerados por uma distribuição uniforme, observamos a transição de fase tanto na rede unidimensional como na bidimensional. Por fim, mostramos que a introdução de um campo externo espacialmente uniforme, cuja interpretação é a de uma mídia global influenciando a opinião dos agentes, elimina o regime monocultural do modelo de Axelrod no limite termodinâmico. / Studies on the maintenance of cultural diversity suggest that the mechanism of social interaction, generally regarded as responsible for cultural homogenization, may also generate diversity. In order to study this phenomenon, the political scientist Robert Axelrod proposed an agent-based model that exhibits multicultural absorbing states, despite the homophilic and homogenizing character of the interaction between agents. In this model the cultural diversity (or disorder) is produced by the choice of the initial cultural traits of the agents, and the homphilic interaction acts towards the reduction of the initial disorder. Due to its simplicity, several re-examinations and variants of Axelrods model are found in the literature: the introduction of an external media, changes in the connectivity of the agents, introduction of random perturbations, etc. However, these proposals lack a systematic analysis of the behavior of the model in the thermodynamic limit, i.e., in the limit that the number of agents tends to infinity. This thesis focuses mainly on that type of analysis in the cases the agents are fixed in the sites of a square lattice or in the sites of a chain. In particular, when the initial cultural traits of the agents are generated by a Poisson distribution we characterize, through Monte Carlo simulations, the transition between the ordered phase (at least one macroscopic cultural domain) and the disordered phase (only microscopic domains) in the square lattice. However, we found no evidence of an ordered phase in the one-dimensional lattice (chain). For initial cultural traits generated by a uniform distribution, we find a phase transition in both the one and two-dimensional lattices. Finally, we show that the introduction of a spatially uniform external field, which can be interpreted as a global media influencing the opinion of the agents, eliminates the monocultural regime of Axelrods model in the thermodynamic limit.

Nesta presente tese, abordaremos três problemas sobre processos estocásticos unidimensionais governados pela equação mestra. Através do Ansatz do Produto Matricial (MPA) determinaremos as condições suficientes para garantir a integrabilidade de um novo processo de difusão num meio com impurezas. Investigando o espectro de tal modelo, computaremos o expoente crítico z que determina como os observáveis atingem o estado estacionário. Em seguida, estudaremos o clássico modelo de 6-vértices bidimensional definido na matriz de transferência diagonal-diagonal, como um modelo de trafego unidimensional com dinâmica síncrona e assíncrona. E para concluir nosso trabalho, investigaremos alguns modelos de processos de contato com difusão, utilizando a teoria de Campo Médio em Cluster. / In this thesis, we discuss three problems on dimensional stochastic processes governed by master equation. By Product Matrix Ansatz (MPA) we determine the conditions sufficient to ensure integrability of a new process of diffusion in a medium with impurities. Investigating the spectrum of this model, we compute the critical exponent z that determines how the observable flow to stationary state. In the folowing, we study the classical 6-vertex model defined in two-dimensional diagonal-diagonal matrix transfer as a unidimensional model of traffic with synchronous and asynchronous dinamics. And to finish our work, we study models of diffusion processes of contact, using the theory of Cluster Mean-Field

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / No presente trabalho investigamos os efeitos da mudança das constantes de acoplamento entre os híperons (D; L; S e X) e os mésons (s; w e r) tendo em vista sua aplicacação na estrutura de estrelas de nêutron. Para tanto, adotamos o modelo de Walecka não-linear numa aproximacão de campo médio. / In the present work we investigated the effects of changing of the coupling constants between the hyperons (D; L; S and X) and mesons (s; w and r) regarding its application in the structure of neutron stars. To this end, we adopted the non-linear Walecka model in the mean field approximation.

Uma técnica de projeção é usada para tratar o problema de condição inicial na teoria quântica de campos. Neste formalismo, equações de movimento do tipo cinético são deduzidas para o conjunto de variáveis dinâmicas de um corpo. Estas equações são submetidas a uma expansão não perturbativa. Tratamos esta expansão em ordem mais baixa, correspondente a aproximacão de campo médio, para um sistema uniforme de muitos fermions fora do equilíbrio descrito pelo modelo fermiônico quiral de gross-neveu. Nesta aproximação recuperamos os resultados existentes na literatura, tais como, geração dinâmica de massa, liberdade assintótica e o fenômeno de transmutação dimensional. Estudando ainda nesta aproximção o regime de pequenas oscilações em torno do equilíbrio, obtemos soluções analíticas para a evolução dinâmica de nossas variáveis. Verificamos também as condições para existencias de estados ligados neste regime. / A time-dependent projection technique is used to treat the initial value problem in Quantum Field Theory. On the basis of the general dynamics of the fields, we derive equations of kinetic type for the set of one-body dynamics variables. A non-perturbative expansion can be written for these equations. We treat this expansion in lowest order, which corresponds to the Mean-Field Approximation, for a non-equilibrium uniform many-fermions system described by Chiral Gross-Neveu Model. Several literature results are obtained such as dynamical mass generation, dimensional transmutation and asymptotic freedom. In this approximation we study the small oscillations regime obtaining analytical solution for one-body dynamical variables. We have also examined the condition for the existence of bound-state in this case.

Si le noyau atomique peut sembler aujourd'hui un système bien connu, sa description microscopique théorique comporte toujours des lacunes : décrire la structure nucléaire des noyaux tout le long de la charte des noyaux de manière satisfaisante par une seule interaction s'avère encore compliqué aujourd'hui.Les interactions les plus performantes et les plus utilisées pour atteindre ce but sont les interactions effectives. On peut généralement classer celles-ci en deux catégories: celles de portée finie et celles de portée nulle. L'interaction de Skyrme, dont il est principalement question dans ce manuscrit, appartient à la deuxième catégorie. Apparue dans les années 50 comme un développement en gradients à l'ordre 2, sa simplicité en a longtemps fait une interaction de choix. Une collaboration internationale, UNEDF, a toutefois montré que l'interaction en l'état était trop limitée pour reproduire correctement les données expérimentales actuelles et qu'il était nécessaire d'y trouver des extensions. Ce manuscrit propose une telle extension, décrivant le processus aboutissant à l'utilisation d'un développement en gradients jusqu'à l'ordre 6.Après avoir présenté les principales forces effectives utilisées dans le cadre de la structure nucléaire, nous montrerons le comportement de cette nouvelle interaction dans le modèle idéal de la matière infinie et son application dans la description des étoiles à neutrons. Nous verrons ainsi que les performances de notre interaction se sont avérées prometteuses. La comparaison des mêmes propriétés pour des potentiels de portée finie a validé ce constat. Notre extension à l'interaction de Skyrme offre à minima des performances comparables dans ce modèle.En conséquence, nous détaillerons également dans la suite du manuscrit la manière dont nous avons poursuivi le développement de notre nouvelle interaction en l'adaptant pour la description de noyaux sphériques. La dernière partie présente le processus d'ajustement de notre interaction, visant à une description des noyaux le long de la charte nucléaire. Une paramétrisation issue d'un tel ajustement sera enfin proposée / The nucleus may seem well known, but its microscopic description still isn't perfect. Describing accurately the nuclei along the nuclear chart remain complicated.Nowadays, the effective interactions are the best choice to achieve such a goal, and can be sorted in two categories: finite-range and zero-range. Skyrme interaction, the main subject of this report, belongs to the latter. Used since the 50s because of its simplicity, it is an expansion of gradients up to the 2th order. However, an international collaboration, UNEDF, showed recently that this interaction was too limited to describe all the nuclear constraints given by experimental datas. The conclusion was the necessity of Skyrme interaction extensions.This thesis is describing the process from the design of the interaction to its use in nuclei and in fitting procedures.First, we review the requirements and the construction of a general nuclear interactions, and the main interactions used in nuclear structure, both finite and zero range.We then show the behaviour of these interactions in a perfect model: the infinite nuclear matter. This is considered a preliminary test for every interaction aiming to describe nuclei, and the performances of our interactions are discussed, along the performances of the other models.The last part of the thesis is the adaptation of our extension for calculations of nuclei. Furthermore, the fitting procedure of our extended Skyrme interaction on both infinite nuclear matter and nuclei quantities is detailed. A resulting parametrisation is presented at the end of the thesis, aiming to describe more accurately the nuclear chart and the additional physic provided by the new terms

La disponibilité de quantités énormes de données a changé le rôle de la physique par rapport aux autres disciplines. Dans cette thèse, je vais explorer les innovations introduites dans la biologie moléculaire grâce à des approches de physique statistique. Au cours des 20 dernières années, la taille des bases de données sur le génome a augmenté de façon exponentielle : l'exploitation des données brutes, dans le champ d'application de l'extraction d'informations, est donc devenu un sujet majeur dans la physique statistique. Après le succès dans la prédiction de la structure des protéines, des résultats étonnamment bons ont été finalement obtenus aussi pour l'ARN. Cependant, des études récentes ont révélé que, même si les bases de données sont de plus en plus grandes, l'inférence est souvent effectuée dans le régime de sous-échantillonnage et de nouveaux systèmes informatiques sont nécessaires afin de surmonter cette limitation intrinsèque des données réelles. Cette thèse va discuter des méthodes d'inférence et leur application à des prédictions de la structure de l'ARN. Nous allons comprendre certaines approches heuristiques qui ont été appliquées avec succès dans les dernières années, même si théoriquement mal comprises. La dernière partie du travail se concentrera sur le développement d'un outil pour l'inférence de modèles génératifs, en espérant qu'il ouvrira la voie à de nouvelles applications. / The availability of huge amounts of data has changed the role of physics with respect to other disciplines. Within this dissertation I will explore the innovations introduced in molecular biology thanks to statistical physics approaches. In the last 20 years the size of genome databases has exponentially increased, therefore the exploitation of raw data, in the scope of extracting information, has become a major topic in statistical physics. After the success in protein structure prediction, surprising results have been finally achieved also in the related field of RNA structure characterisation. However, recent studies have revealed that, even if databases are growing, inference is often performed in the under sampling regime and new computational schemes are needed in order to overcome this intrinsic limitation of real data. This dissertation will discuss inference methods and their application to RNA structure prediction. We will discuss some heuristic approaches that have been successfully applied in the past years, even if poorly theoretically understood. The last part of the work will focus on the development of a tool for the inference of generative models, hoping it will pave the way towards novel applications.

L'Inconel 718 est un superalliage base-nickel très utilisé pour la fabrication de pièces aéronautiques soumises à de fortes contraintes et de hautes températures. La maîtrise de la microstructure finale issue de la mise en forme à chaud est un des éléments clés pour le contrôle des propriétés mécaniques et pour répondre aux exigences strictes du secteur. Dans cette étude, l'évolution de la microstructure de l'Inconel 718 est étudiée au moyen d'essais de torsion suivis d'une trempe à l'eau (pour examiner les évolutions dynamiques) ou d'un maintien à la température de déformation puis d'une trempe à l'eau (pour examiner les évolutions post-dynamiques). Ces essais sont réalisés dans les domaines de température δ-supersolvus et δ-subsolvus et pour des vitesses de déformation de 10-2 à 0.1 s-1. Des analyses microstructurales par microscopie électronique à balayage et cartographie des orientations cristallographiques par EBSD sont réalisées pour suivre l'évolution de la fraction recristallisée, de la taille de grains recristallisés ainsi que de l'état de précipitation lors de la déformation et des maintiens pré- et post-déformation. Sur base de ces observations expérimentales, les principaux mécanismes métallurgiques actifs sont identifiés, puis modélisés : écrouissage, germination de nouveaux grains, migration de joints de grains, et interaction avec les particules de seconde-phases. Un modèle d'évolution microstructurale en champ moyen a été enrichi pour prendre en compte l'ensemble de ces mécanismes élémentaires et leur dépendance aux conditions thermomécaniques. Ce modèle permet de décrire, pour les domaines δ-subsolvus et δ-supersolvus, les cinétiques de recristallisation dynamique et post-dynamique de l'Inconel 718, les cinétiques de précipitation et dissolution de la phase δ, ainsi que l'évolution de la taille de grains. Il prédit également les courbes contrainte-déformation dans le domaine de température δ-supersolvus. / Inconel 718 is nickel-based Superalloy widely used in the aeronautic industry to manufacture aircraft parts subjected to extreme in-service conditions of high stresses at elevated temperatures. Controlling the microstructure after hot forming is a key element to control the mechanical properties of the final products and meet the tight specifications imposed by the aeronautic industry.In this work, the microstructure evolution of Inconel 718 was investigated via isothermal and iso-strain rate torsion tests followed by water quenching (to investigate dynamic evolution) or by annealing at deformation temperature then water quenching (to investigate post-dynamic evolution). These tests were conducted in both δ-Supersolvus and δ-Subsolvus temperature domains and for strain rates of 0.01 to 0.1 s-1.Scanning electron microscopy (SEM) and Electron Back Scattered Diffraction (EBSD) were used to characterize the microstructure and follow the evolution of the recrystallized fraction, the recrystallized grain size and the δ-phase precipitation after deformation and during pre-deformation and post-deformation annealing. Based on these experimental observations, the main metallurgical mechanisms have been identified and modelled: hardening, nucleation of new grains, grain boundaries migration and the δ-phase- recrystallization interaction.A two-site mean field approach having a low computational cost was chosen to model the microstructural evolution at different thermomechanical conditions. This model describes the main mechanisms taking place during hot forming of Inconel 718 in both δ-Supersolvus and δ-Subsolvus domains and predicts the recrystallization kinetics in both dynamic and post-dynamic regimes , the δ-phase precipitation and dissolution kinetics and the grain size evolution. The model predicts also the strain-stress curves at high temperatures in the absence of δ-phase particles.

Les propriétés finales des alliages métalliques sont directement liées à la microstructure de fin de mise en forme. Les mécanismes de recristallisation dynamique (DRX) et post-dynamique (PDRX) jouent un rôle important sur les évolutions microstructurales intervenant pendant et après les étapes de déformation à chaud. Dans ce contexte, un défi majeur pour les industriels et les chercheurs est de prédire la microstructure obtenue en fonction des conditions de mise en forme. Cela implique de bien connaître les mécanismes de DRX et PDRX et leur cinétique. Les modèles en champ complet permettent de modéliser explicitement la microstructure des alliages métalliques et ses possibles évolutions à l’échelle du polycristal. Ces modèles sont précis comparativement aux modèles œuvrant aux plus grandes échelles, mais ils sont généralement très couteux en termes de temps de calcul. Les modèles à champ moyen sont quant à eux basés sur une description implicite de la microstructure, conduisant à des temps de calcul considérablement réduits, mais ils reposent sur un grand nombre d’hypothèses, notamment topologiques. Cette thèse propose un nouveau modèle champ complet de DRX/PDRX et croissance de grains, capable de fonctionner en 2D comme en 3D, et une nouvelle approche en champ moyen, s'appuyant sur ces simulations en champ complet. La nouvelle approche champ moyen prend notamment mieux en compte les effets topologiques pour une meilleure prédiction des distributions de tailles de grains. Ce travail inclut une procédure de calibration et une validation des deux modèles s'appuyant sur une campagne d’essais expérimentaux sur un acier austénitique 304L. / Final properties of metal alloys are directly related to their microstructure, inherited from the processing route. Dynamic (DRX) and post-dynamic recrystallization (PDRX) mechanisms play a primordial role in microstructure evolutions occurring during and after hot-deformation. Within this context, predicting microstructures depending on the applied thermomechanical conditions is a major challenge for both industrials and researchers. This requires a good knowledge of recrystallization mechanisms and kinetics. Full field models are based on an explicit description of the microstructure of a metallic alloy, and its possible evolutions at a polycrystalline scale. These models are accurate compared to models operating at larger scales, but they generally lead to prohibitive numerical costs. On the other hand, mean field models are based on an implicit description of the microstructure, leading to considerably reduced numerical costs, but they are based on many assumptions, notably with regards to topology. The outcome of this PhD work is a new full field model of DRX/PDRX and grain growth, working in 3D as well as in 2D, and a new DRX/PDRX mean field approach which better accounts for topological effects, and provides better predictions for grain size distributions. This work also includes a calibration procedure and a validation of these two new models, using experimental data obtained from compression tests performed on the 304L austenitic steel.