Defect-driven transport of impurities plays a key role in the microstructure evolution of alloys, and has a great impact on the mechanical properties at the macroscopic scale. This phenomenon is greatly enhanced in irradiated materials because of the large amount of radiation-induced crystal defects (vacancies and interstitials). For instance, the formation of nanosized solute clusters in neutron-irradiated reactor pressure vessel (RPV) ferritic steels has been shown to hinder dislocation motion and induce hardening and embrittlement. In Swedish RPV steels, this mechanical-property degradation is enhanced by the high content of manganese and nickel impurities. It has been suggested that the formation of Mn-Ni-rich clusters (which contain also Cu, Si, and P) might be the outcome of a dynamic process, where crystal defects act both as nucleation sites and solute carriers. Solute transport by point defects is therefore a crucial mechanism to understand the origin and the dynamics of the clustering process. The first part of this work aims at modeling solute transport by point defects in dilute iron alloys, to identify the intrinsic diffusion mechanisms for a wide range of impurities. Transport and diffusion coefficients are obtained by combining accurate ab initio calculations of defect transition rates with an exact mean-field model. The results show that solute drag by single vacancies is a common phenomenon occurring at RPV temperature (about 300 °C) for all impurities found in the solute clusters, and that transport of phosphorus and manganese atoms is dominated by interstitial-type defects. These transport tendencies confirm that point defects can indeed carry impurities towards nucleated solute clusters. Moreover, the obtained flux-coupling tendencies can also explain the observed radiation-induced solute enrichment on grain boundaries and dislocations. In the second part of this work, the acquired knowledge about solute-transport mechanisms is transferred to kinetic Monte Carlo (KMC) models, with the aim of simulating the RPV microstructure evolution. Firstly, the needed parameters in terms of solute-defect cluster stability and mobility are calculated by means of dedicated KMC simulations. Secondly, an innovative approach to the prediction of transition rates in complex multicomponent alloys is introduced. This approach relies on a neural network based on ab initio-computed migration barriers. Finally, the evolution of the Swedish RPV steels is simulated in a "gray-alloy" fashion, where impurities are introduced indirectly as a modification of the defect-cluster mobilities. The latter simulations are compared to the experimental characterization of the Swedish RPV surveillance samples, and confirm the possibility that solute clusters might form on small interstitial clusters. In conclusion, this work identifies from a solid theoretical perspective the atomic-transport phenomena underlying the formation of embrittling nanofeatures in RPV steels. In addition, it prepares the ground for the development of predictive KMC tools that can simulate the microstructure evolution of a wide variety of irradiated alloys. This is of great interest not only for reactor pressure vessels, but also for many other materials in extreme environments. / <p>QC 20151123</p>

No description available.

In this thesis morphologies, coarsening mechanisms and kinetics are examined in a systematic way, when phase separation and subsequent microstructural coarsening is modelled using deterministic mean field and stochastic Monte Carlo methods. For the mean field approach a microscopic diffusion equation due to Khachaturyan is employed, and a variation of it with an environment dependent mobility. Monte Carlo simulations are carried out with vacancy and Kawasaki dynamics, and a residence time algorithm is applied in the vacancy case. In mean field models microstructural evolution results from a direct minimization of a free energy functional, and the mechanism of atomic diffusion does not appear explicitly. In Monte Carlo models, changes in site occupancies are effected by direct exchanges of neighbouring atoms (Kawasaki dynamics), or through vacancy motion. In this thesis the correspondence between mean field and Monte Carlo models in describing phase transformations in binary alloys is examined. Several examples of cases in which these differences between deterministic and stochastic models affect the phase transformation are given, and the underlying differences are analyzed. It is also investigated how the choice of diffusion mechanism in the Monte Carlo model affects the microstructural evolution. Most Monte Carlo studies have been carried out with Kawasaki dynamics, although in real metals such direct exchanges are very unlikely to occur. It will be shown how the vacancy diffusion mechanism produces a variety of coarsening mechanisms over a range of temperatures, which the Kawasaki dynamics fails to capture. Consequently, kinetics and resulting morphologies, especially at low temperatures, are affected. Finally, the question of physicality of time scales in mean field and Monte Carlo models is addressed. Often a linear dependence between Monte Carlo time and real physical time is assumed, although there is no rigorous justifcation for this. In mean field models, time is defined through the atomic mobility. By examining the effect of a realistic diffusion mechanism in systems undergoing phase transformation, a critical discussion of time scales in microscopic mean field models and a Monte Carlo model with Kawasaki dynamics is presented.

La théorie des jeux en champ moyen constitue un formalisme puissant introduit récemmentpour étudier des problèmes d’optimisation stochastiques avec un grand nombre d’agents. Aprèsavoir rappelé les principes de base de cette théorie et présenté quelques cas d’applicationtypiques, on étudie en détail un modèle stylisé de séminaire, de type champ moyen. Nousdérivons une équation exacte qui permet de prédire l’heure de commencement du séminaire etanalysons différents régimes limites, dans lesquels on parvient à des expressions approchées de lasolution. Ainsi on obtient un "diagramme de phase" du problème. On aborde ensuite un modèleplus complexe de population avec des effets de groupe attractifs. Grâce à une analogie formelleavec l’équation de Schrödinger non linéaire, on met en évidence des lois d’évolutions généralespour les valeurs moyennes du problème, que le système vérifie certaines lois de conservation etl’ on développe des approximations de type variationnel. Cela nous permet de comprendre lecomportement qualitatif du problème dans le régime de fortes interactions. / Mean Field Games Theory is a theoretical framework developed recently to deal withstochastic optimization problems when the number of agents is large. First the mathematicaltools are introduced heuristically, step by step, and some examples are presented in finance,economy and social problems. I study then thoroughly a seminar toymodel and derive anequation for the starting time of the meeting. The analysis of the limit regimes allows to builda "phase diagram" of the problem. In a second time, a herding problem, where individualshave their own preferences and are attracted by the group, is tackled. Thanks to a formal analogywith the Non Linear Schrödinger equation, some explicit solutions, conservation laws andso-called variational approximations are derived. Finally I use these tools to get a qualitativeunderstanding of the solution’s behaviour in the strong interaction regime.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A presente dissertação estuda com detalhes a evolução temporal fora do equilíbrio de um condensado de Bose-Einstein homogêneo diluído imerso em um reservatório térmico. Nós modelamos o sistema através de um campo de Bose escalar complexo. É apropriado descrever o comportamento microscópico desse sistema por meio da teoria quântica de campos através do formalismo de Schwinger-Keldysh. Usando esse formalismo, de tempo real a dinâmica do condensado é solucionada por um grupo de equações integro-diferencial auto consistente, essas são solucionadas numericamente. Estudamos também o cenário quench, e como a densidade do gás e as interações entre as flutuações tem o efeito de provocar as instabilidades nesse sistema. Aplicamos esse desenvolvimento para estudar o comportamento de duas espécies homogêneas de um gás de Bose diluído imerso em um reservatório térmico. / This Dissertation study the detailed out of equilibrium time evolution of a homogeneous diluted Bose-Einstein condensate in thermal bath. We modeled the system by means of one bosonic complex scalar field. The microscopic behavior of such an environment can be appropriately described by the non-equilibrium Schwinger-Keldysh formalism in a quantum field theory approach. Using this formalism, real-time dynamics of the condensate is encoded in a set of self-consistent integral-differential equations that we solved numerically. We studied, in the quench scenario, how the role of the interactions in the generation of the initial instability and the subsequent time evolution of the condensate. We also applied this technique to the study of a two-species homogeneous diluted Bose gas in a thermal bath.

Cette thèse de doctorat vise l’examen critique de certaines théories de champ moyen nucléaire phénoménologiques, en se focalisant sur la description fiable des niveaux de particules individuelles. L’approche suivie ici est nouvelle en ce sens que elle permet non seulement la prédiction des valeurs numériques obtenues avec ce formalisme, mais également une estimation des distributions de probabilités correspondant aux résultats expérimentaux. Nous introduisons le concept des ≪erreurs théoriques≫, visant estimer, dans un cadre mathématique bien établi, les incertitudes relatives aux modélisations théoriques. Il est également introduit une notion subjective de pouvoir prédictif des Hamiltoniens nucléaires, qui est analysé dans le contexte des spectres énergétiques de particules individuelles. Le concept mathématique du ≪Problème Inverse≫ est appliqué aux Hamiltoniens de champ moyen réalistes. Cette technique permet la prédiction de propriétés du système partir d’un nombre limité de données. Afin d'approfondir notre connaissance des Problèmes Inverses, nous focalisons notre attention sur un problème mathématique simple. Une fonction dépendant de quatre paramètres libres est introduite afin de reproduire des données ≪expérimentales≫. Nous étudions le comportement des paramètres ≪fittés≫, leur corrélation, ainsi que les erreurs associées. Cette étude nous aide comprendre la signification de la formulation correcte du problème en question. Il nous montre également l'importance d'inclure les erreurs expérimentales et théoriques dans la solution. / This thesis is a critical examination of phenomenological nuclear mean field theories, focusing on reliable description of levels of individual particles. The approach presented here is new in the sense that it not only allows to predict the numerical values obtained with this formalism, but also yields an estimate of the probability distributions corresponding to the experimental results. We introduce the concept of ‘theoretical errors’ to estimate uncertainties in theoreticalmodels. We also introduce a subjective notion of ‘Predictive Power’ of nuclear Hamiltonians, which is analyzed in the context of the energy spectra of individual particles. The mathematical concept of ‘Inverse Problem’ is applied to a realistic mean-field Hamiltonian. This technique allows to predict the properties of a system from a limited number of data. To deepen our understanding of Inverse Problems, we focus on a simple mathematical problem. A function dependent on four free parameters is introduced in order to reproduce ‘experimental’ data. We study the behavior of the ‘fitted’ parameters, their correlation and the associated errors. This study helps us understand the importance of the correct formulation of the problem. It also shows the importance of including theoretical and experimental errors in the solution.

The idea that we live in a higher-dimensional space was first introduced almost 100 years ago. In the past two decades many extra-dimensional models have been proposed in order to solve fundamental problems of nature such as the hierarchy problem. Most of them need exploration via non-perturbative approaches and Lattice Gauge Theory provides a tool for doing this. In this thesis, we make attempts to find a non-perturbative way to localize gauge fields that arise from five-dimensional SU(2) gauge theories on 3-branes. In 1984, it was proposed that the phase diagram of anisotropic extra-dimensional lattice gauge theories inherits a new phase, called the "layered" phase, where the gauge fields behave as four-dimensional ones. This was shown for the abelian case, but the existence of this new phase for the simplest non-abelian group, SU(2), was still in doubt. We investigated this system in large volumes using Monte Carlo simulations and we could not find a second order phase transition from a five-dimensional to a continuous four-dimensional theory when all directions were kept large. This made the model unattractive for further exploration as nothing suggests that a non-trivial fixed point could exist. The above investigation was done in a flat background metric. We extended the previous work by putting our theory into a slice of AdS5 space, usually called the warped background. The motivation for this is that our SU(2) theory looks like the gauge-sector of the Randall-Sundrum model, which does not have a concrete solution to the problem of localization of the gauge fields on a 3-brane. We carried out our investigation using the Mean-Field Approach and we present novel results for the phase diagram and measurements of important observables. In our implementation we have a finite extent of the extra dimension and one layer (or 3-brane) on each extra-dimensional coordinate. At weak coupling, we observed that each layer decouples one at a time in the transition to the fully layered phase of the system, forming a mixed phase, whereas there is a strong and sharp transition between the fully layered and the strong-coupling phase. Within the mixed phase, close to the transition into the layered phase, we found evidence that the system is four-dimensional acquiring a Yukawa mass and resembling a Higgs-like phase. The mixed phase grows as the curvature increases suggesting that for an infinite extra dimension the entire weak-coupling phase is mixed.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A presente dissertação estuda com detalhes a evolução temporal fora do equilíbrio de um condensado de Bose-Einstein homogêneo diluído imerso em um reservatório térmico. Nós modelamos o sistema através de um campo de Bose escalar complexo. É apropriado descrever o comportamento microscópico desse sistema por meio da teoria quântica de campos através do formalismo de Schwinger-Keldysh. Usando esse formalismo, de tempo real a dinâmica do condensado é solucionada por um grupo de equações integro-diferencial auto consistente, essas são solucionadas numericamente. Estudamos também o cenário quench, e como a densidade do gás e as interações entre as flutuações tem o efeito de provocar as instabilidades nesse sistema. Aplicamos esse desenvolvimento para estudar o comportamento de duas espécies homogêneas de um gás de Bose diluído imerso em um reservatório térmico. / This Dissertation study the detailed out of equilibrium time evolution of a homogeneous diluted Bose-Einstein condensate in thermal bath. We modeled the system by means of one bosonic complex scalar field. The microscopic behavior of such an environment can be appropriately described by the non-equilibrium Schwinger-Keldysh formalism in a quantum field theory approach. Using this formalism, real-time dynamics of the condensate is encoded in a set of self-consistent integral-differential equations that we solved numerically. We studied, in the quench scenario, how the role of the interactions in the generation of the initial instability and the subsequent time evolution of the condensate. We also applied this technique to the study of a two-species homogeneous diluted Bose gas in a thermal bath.

Os processos de negócio desempenham um papel muito importante na indústria, principalmente pela evolução das tecnologias da informação. As plataformas de computação em nuvem, por exemplo, com a alocação de recursos computacionais sob demanda, possibilitam a execução de processos altamente requisitados. Para tanto, é necessário definir o ambiente de execução dos processos de tal modo que os recursos sejam utilizados de forma ótima e seja garantida a correta funcionalidade do processo. Nesse contexto, diferentes métodos já foram propostos para modelar os processos de negócio e analisar suas propriedades quantitativas e qualitativas. Há, contudo, vários desafios que podem restringir a aplicação desses métodos, especialmente para processos com alta demanda (como os workflows de numerosas instâncias) e que dependem de recursos limitados. A análise de desempenho de workflows de numerosas instâncias via modelagem analítica é o objeto de estudo deste trabalho. Geralmente, para a realização desse tipo de análise usa-se modelos matemáticos baseados em técnicas Markovianas (sistemas estocásticos), que sofrem do problema da explosão do espaço de estados. Entretanto, a Teoria do Campo Médio indica que o comportamento de um sistema estocástico, sob certas condições, pode ser aproximado por o de um sistema determinístico, evitando a explosão do espaço de estados. Neste trabalho usamos tal estratégia e, com base na definição formal de aproximação determinística e suas condições de existência, elaboramos um método para representar os workflows, e seus recursos, como equações diferenciais ordinárias, que descrevem um sistema determinístico. Uma vez definida a aproximação determinística, realizamos a análise de desempenho no modelo determinístico, verificando que os resultados obtidos são uma boa aproximação para a solução estocástica. / Business processes play a very important role in the industry, especially by the evolution of information technologies. Cloud computing platforms, for example, with the allocation of on-demand computing resources enable the execution of highly requested processes. Therefore, it is necessary to define the execution environment of the processes in such a way that the resources are used optimally and the correct functionality of the process is guaranteed. In this context, different methods have already been proposed to model business processes and analyze their quantitative and qualitative properties. There are, however, a number of challenges that may restrict the application of these methods, especially for high-demanded processes (such as workflows of numerous instances) and that rely on resources that are limited. The analysis of the performance of workflows of numerous instances through analytical modeling is the object of study of this work. Generally, for the accomplishment of this type of analysis, mathematical models based on Markovian techniques (stochastic systems) are used, which suffer the problem of the state space explosion. However, the Mean Field Theory, indicates that the behavior of a stochastic system, under certain conditions, can be approximated by that of a deterministic system, avoiding the explosion of the state space. In this work we use such a strategy, based on the formal definition of deterministic approximation and its conditions of existence, we elaborate a method to represent the workflows, and their resources, as ordinary differential equations, which describe a deterministic system. Once the deterministic approximation has been defined, we perform the performance analysis in the deterministic model, verifying that the obtained results are a good approximation for the stochastic solution.

Dans une série de travaux Zied Ammari et Francis Nier ont développé des méthodes pour étudier la dynamique de champ moyen bosonique pour des états quantiques généraux pouvant présenter des corrélations. Ils ont obtenu des formules pour décrire la dynamique des corrélations, ou plus généralement des matrices densité réduites d'ordre arbitraire. Cette thématique a été largement développée ces dernières années. Norbert Mauser en a été un des contributeurs, ainsi que sur la notion de mesure de Wigner qui est la clé de l'analyse développée par Z. Ammari et F. Nier. En général, il est admis que l'asymptotique de champ moyen est une bonne approximation du problème à N particules quand N dépasse la dizaine. Cela concerne l'asymptotique de la matrice densité réduite à une particule qui ne décrit pas la dynamique des corrélations. Un objectif est de tester la validité de la dynamique de champ moyen pour les matrices densité réduites à 2-particules. Pour des tests numériques, les modèles discrets qui n'ont pas été vraiment traités en détail dans les travaux précédents de Z. Ammari et F. Nier semblent bien adaptés. La thèse comprendra donc plusieurs étapes: adapter les résultats précédents de Z. Ammari et F. Nier à des modèles discrets , développer des méthodes numériques pour des systèmes simples mais pertinents, permettant de valider l'approximation de champ moyen et les formules pour la dynamique des corrélations. Au niveau numérique, on utilise des schémas numériques symplectiques, développés spécifiquement ces dernières années pour la discrétisation des équations hamiltoniennes. Une dernière étape concerne la combinaison des deux asymptotiques, champ moyen et approximation des modèles continus par les modèles discrets. / In a serie of works Z. Ammari and F. Nier developed methods to study the dynamics of bosonic mean field for general quantum states which can present correlations. They obtained formulas to describe the dynamics of the correlations, or more generally reduced density matrices with an arbitrary order. This topic was widely developed these last years. N.J. Mauser was one of contributors, as well as on the notion of Wigner measure which is the key of the analysis developed by Z. Ammari and F. Nier. Generally, the mean field asymptotic is admitted is a good approximation of the N-body problem when N exceed about ten. It concerns the asymptotics of the reduced density matrices for one particle which does not describe the dynamics of the correlations. An objective is to test the validity of the mean field dynamics for reduced density matrices for 2 particles. For numerical tests, the discrete models which were not really handled in detail in the previous works of Z. Ammari and F. Nier seem adapted well. The thesis will thus include several steps: adapt the previous results from Z. Ammari and F. Nier to discrete models , develop numerical methods, for simple but relevant systems, allowing to validate the approximation of mean field and the formulas for the dynamics of the correlations. About numerics, symplectic numerical scheme are used, developed specifically these last years for the discretization of the hamiltonian equations. A last possible step concerns the combination of both asymptotics, that is mean field and approximation of the continuous models by the discrete models.