Part I: The Theory of Brownian Vacancy Driven Walk We analyze the lattice walk performed by a tagged member of an infinite 'sea' of particles filling a d-dimensional lattice, in the presence of a single vacancy. The vacancy is allowed to be occupied with probability 1/2d by any of its 2d nearest neighbors, so that it executes a Brownian walk. Particle-particle exchange is forbidden; the only interaction between them being hard core exclusion. Thus, the tagged particle, differing from the others only by its tag, moves only when it exchanges places with the hole. In this sense, it is a random walk "driven" by the Brownian vacancy. The probability distributions for its displacement and for the number of steps taken, after n-steps of the vacancy, are derived. Neither is a Gaussian! We also show that the only nontrivial dimension where the walk is recurrent is d=2. As an application, we compute the expected energy shift caused by a Brownian vacancy in a model for an extreme anisotropic binary alloy. In the last chapter we present a Monte-Carlo study and a mean-field analysis for interface erosion caused by mobile vacancies. Part II: One-Dimensional Periodic Hopping Models with Broken Translational Invariance.Case of a Mobile Directional Impurity We study a random walk on a one-dimensional periodic lattice with arbitrary hopping rates. Further, the lattice contains a single mobile, directional impurity (defect bond), across which the rate is fixed at another arbitrary value. Due to the defect, translational invariance is broken, even if all other rates are identical. The structure of Master equations lead naturally to the introduction of a new entity, associated with the walker-impurity pair which we call the quasi-walker. Analytic solution for the distributions in the steady state limit is obtained. The velocities and diffusion constants for both the random walker and impurity are given, being simply related to that of the quasi-particle through physically meaningful equations. As an application, we extend the Duke-Rubinstein reputation model of gel electrophoresis to include polymers with impurities and give the exact distribution of the steady state. / Ph. D.

We investigate the nonequilibrium steady state of driven magnetic flux lines in type-II superconductors subject to strong point or columnar pinning centers and the aging dynamics of nonequilibrium relaxation process in the presence of weak point pinning centers. We employ a three-dimensional elastic line model and Metropolis Monte Carlo simulations. For the first part, we characterize the system by means of the force-velocity / current-voltage curve, static structure factor, mean vortex radius of gyration, number of double-kink and half-loop excitations, and velocity / voltage noise features. We compare the results for the above quantities for randomly distributed point and columnar defects. Most of both numerical works have been done in two-dimensional systems such as thin film in which the structure of flux lines is treated as a point-like particle. Our main point of investigation in this paper is to demonstrate that the vortex structure and its other transport properties may exhibit a remarkable variety of complex phenomena in three-dimensional or bulk superconductors. The second part devotes to the study of aging phenomena in the absence of a driving force in disordered superconductors with much weaker point disorder. By investigating the density autocorrelation function, we observe all three crucial properties of the aging phenomena; slow power-law relaxation, breaking of time-translation invariance, and the presence of the dynamical scaling. We measure the dynamical exponents b and lambda_c/z and compare to other work. We find exponent values increase for increasing pinning strength, smaller interaction range, lower temperature, and denser defect density while the exponents measured in other approach tend to decrease. / Ph. D.

We explore steady-state properties of a driven lattice gas, which is a simple model of interacting many-particle systems, driven far from equilibrium by an external field. First, we study a system on a square lattice with periodic boundary conditions (PBC) along both principal lattice axes, while the drive acts along only one of these axes. For such systems, we analyze the full distribution of structure factors. Next, we investigate the effects of imposing other boundary conditions on the system. In particular, we focus on models with shifted periodic boundary conditions (SPBC) along one axis and open boundary conditions (OBC) along the other axis. The OBC allow us to have a steady flux of particles through the system while the SPBC permits us to drive the system in a range of possibilities. Using Monte Carlo simulation techniques, we discover a rich variety of phenomena, especially at low temperatures. A continuum theory for the densities, based on Langevin equations, is formulated and its predictions compared to simulation data. Many large scale properties are described successfully. / Ph. D.

We explore the nature of driven stochastic lattice systems with non-periodic boundary conditions. The systems consist of particle and holes which move by exchanges of nearest neighbor particle-hole pairs. These exchanges are controlled by the energetics associated with an internal Hamiltonian, an external drive and a stochastic coupling to a heat reservoir. The effect of the drive is to bias particle-hole exchanges along the field in such a way that a particle current can be established. Hard-core volume constraints limit the occupation of only one particle (hole) per lattice site. For certain regimes of the overall particle density and temperature, a system displays a homogeneous disordered phase. We investigate cooperative behavior in this phase by using two-point spatial correlation functions and structure factors. By varying the particle density and the temperature, the system orders into a phase separated state, consisting of particle-rich and particle-poor regions. The temperature and density for the co-existence state depend on the boundary conditions. By using Monte Carlo simulations, we establish co-existence curves for systems with shifted periodic boundary conditions. / Ph. D.

Esta tese identificou vários aspectos importantes da estrutura trófica e dinâmica de nutrientes em ecossistemas aquáticos sujeitos a perturbações externas, tais como mudanças no nível da água, aumento de carga de nutrientes e matéria orgânica, biomanipulação e clima. Para descrever tais efeitos sobre a estrutura trófica, um complexo modelo ecológico, com base em processos físicos, químicos e biológicos, foi desenvolvido e aplicado em ecossistemas aquáticos tropicais, subtropicais e temperados. Em tais aplicações, uma análise integrada foi empregada considerando a transferência de impactos da bacia para o ecossistema, com a finalidade de entender a real dinâmica dos ecossistemas aquáticos. As simulações revelaram importantes aspectos sobre a estrutura e funcionalidade dos ecossistemas frente as pertubações. Por exemplo, a lagoa Mangueira, um lago raso subtropical no sul do Brasil, pode oscilar entre dois estados alternativos estáveis (alta e baixa transparência da água), dependendo da concentração de ortofosfato e da túrbidez. Foi sugerido também que podem ocorrer profundas alterações na composição do fitoplâncton com a aumento sistemático da concentração de ortofosfato. Foram constatados significativos gradientes horizontais e verticais na estrutura trófica da lagoa Mangueira, indicando a importância de considerar a heterogeneidade espacial em grandes lagos para melhorar a compreensão dos processos ecológicos e padrões. Cenários críticos de simulação indicaram que o aumento da carga de nutrientes afeta negativamente a transparência da água, diferentemente do efeito de mudanças climáticas. Pequenas alterações na estrutura trófica causadas por esses fatores indicam uma forte resistência da lagoa Mangueira. O modelo ecológico também foi útil para descrever a dinâmica do ecossistema, antes e depois da biomanipulação do lago Engelsholm localizado na Dinamarca. Nesse caso, o modelo conseguiu razoavelmente prever a mudança para um estado de alta transparência da após a biomanipulação, entretanto a mudança na composição do fitoplâncton foi muito mais difícil de representar. Além disso, aplicações mais simples também auxiliaram o processo de tomada de decisão e planejamento. A modelagem ecológica aplicada em ecossistemas aquáticos mostrou ser uma alternativa promissora para a gestão integrada dos recursos naturais. / This thesis identified several important features of the trophic structure and dynamics of nutrients in ecosystems subjected to external disturbances such as changes in the water level, nutrient and organic matter loading, fish communities and climate. To describe such effects on trophic structure, a complex ecological model, based on physical, chemical and biological processes has been developed and applied in tropical, subtropical and temperate aquatic ecosystems. In such applications, an integrated analysis was employed considering the transfer of impacts from the watershed to the ecosystem, in order to bring closer the understading of the ecosystem dynamics. Simulations revealed important features about system structure and functionality in front of disturbances. For instance, lake Mangueira a subtropical lake in Southern Brazil can oscilate between two alternative steady stables (clear or turbid water), depending orthophosphate concentration and water transparency. It was also suggested that can occurs profound changes in phytoplankton composition from increase of orthophosphate concentration. Horizontal and vertical gradients in the trophic structure are notable in lake Mangueira, indicating the importance to consider spatial heterogeneity in large lakes to improve understanding of ecological processes and patterns. Simulation scenarios indicated that increased nutrient loading negatively affects water transparency, differently from climate changes. Slight changes in trophic structure caused by those factors indicate a strong resistence of the lake Mangueira. The ecological model also was useful to describe the ecosystem dynamics before and after biomanipulation of lake Engelsholm located in Denmark. In that case, the model could reasonably well predict a shift to a clear water state, but the changed composition of phytoplankton functional groups was much more hard to represent. Furthermore, simpler applications also provided support for decision making and planning in the ecosystem. Ecological modeling applied in aquatic ecosystems showed be a promising alternative towards the integrated management of natural resources.

Esta tese identificou vários aspectos importantes da estrutura trófica e dinâmica de nutrientes em ecossistemas aquáticos sujeitos a perturbações externas, tais como mudanças no nível da água, aumento de carga de nutrientes e matéria orgânica, biomanipulação e clima. Para descrever tais efeitos sobre a estrutura trófica, um complexo modelo ecológico, com base em processos físicos, químicos e biológicos, foi desenvolvido e aplicado em ecossistemas aquáticos tropicais, subtropicais e temperados. Em tais aplicações, uma análise integrada foi empregada considerando a transferência de impactos da bacia para o ecossistema, com a finalidade de entender a real dinâmica dos ecossistemas aquáticos. As simulações revelaram importantes aspectos sobre a estrutura e funcionalidade dos ecossistemas frente as pertubações. Por exemplo, a lagoa Mangueira, um lago raso subtropical no sul do Brasil, pode oscilar entre dois estados alternativos estáveis (alta e baixa transparência da água), dependendo da concentração de ortofosfato e da túrbidez. Foi sugerido também que podem ocorrer profundas alterações na composição do fitoplâncton com a aumento sistemático da concentração de ortofosfato. Foram constatados significativos gradientes horizontais e verticais na estrutura trófica da lagoa Mangueira, indicando a importância de considerar a heterogeneidade espacial em grandes lagos para melhorar a compreensão dos processos ecológicos e padrões. Cenários críticos de simulação indicaram que o aumento da carga de nutrientes afeta negativamente a transparência da água, diferentemente do efeito de mudanças climáticas. Pequenas alterações na estrutura trófica causadas por esses fatores indicam uma forte resistência da lagoa Mangueira. O modelo ecológico também foi útil para descrever a dinâmica do ecossistema, antes e depois da biomanipulação do lago Engelsholm localizado na Dinamarca. Nesse caso, o modelo conseguiu razoavelmente prever a mudança para um estado de alta transparência da após a biomanipulação, entretanto a mudança na composição do fitoplâncton foi muito mais difícil de representar. Além disso, aplicações mais simples também auxiliaram o processo de tomada de decisão e planejamento. A modelagem ecológica aplicada em ecossistemas aquáticos mostrou ser uma alternativa promissora para a gestão integrada dos recursos naturais. / This thesis identified several important features of the trophic structure and dynamics of nutrients in ecosystems subjected to external disturbances such as changes in the water level, nutrient and organic matter loading, fish communities and climate. To describe such effects on trophic structure, a complex ecological model, based on physical, chemical and biological processes has been developed and applied in tropical, subtropical and temperate aquatic ecosystems. In such applications, an integrated analysis was employed considering the transfer of impacts from the watershed to the ecosystem, in order to bring closer the understading of the ecosystem dynamics. Simulations revealed important features about system structure and functionality in front of disturbances. For instance, lake Mangueira a subtropical lake in Southern Brazil can oscilate between two alternative steady stables (clear or turbid water), depending orthophosphate concentration and water transparency. It was also suggested that can occurs profound changes in phytoplankton composition from increase of orthophosphate concentration. Horizontal and vertical gradients in the trophic structure are notable in lake Mangueira, indicating the importance to consider spatial heterogeneity in large lakes to improve understanding of ecological processes and patterns. Simulation scenarios indicated that increased nutrient loading negatively affects water transparency, differently from climate changes. Slight changes in trophic structure caused by those factors indicate a strong resistence of the lake Mangueira. The ecological model also was useful to describe the ecosystem dynamics before and after biomanipulation of lake Engelsholm located in Denmark. In that case, the model could reasonably well predict a shift to a clear water state, but the changed composition of phytoplankton functional groups was much more hard to represent. Furthermore, simpler applications also provided support for decision making and planning in the ecosystem. Ecological modeling applied in aquatic ecosystems showed be a promising alternative towards the integrated management of natural resources.

Esta tese identificou vários aspectos importantes da estrutura trófica e dinâmica de nutrientes em ecossistemas aquáticos sujeitos a perturbações externas, tais como mudanças no nível da água, aumento de carga de nutrientes e matéria orgânica, biomanipulação e clima. Para descrever tais efeitos sobre a estrutura trófica, um complexo modelo ecológico, com base em processos físicos, químicos e biológicos, foi desenvolvido e aplicado em ecossistemas aquáticos tropicais, subtropicais e temperados. Em tais aplicações, uma análise integrada foi empregada considerando a transferência de impactos da bacia para o ecossistema, com a finalidade de entender a real dinâmica dos ecossistemas aquáticos. As simulações revelaram importantes aspectos sobre a estrutura e funcionalidade dos ecossistemas frente as pertubações. Por exemplo, a lagoa Mangueira, um lago raso subtropical no sul do Brasil, pode oscilar entre dois estados alternativos estáveis (alta e baixa transparência da água), dependendo da concentração de ortofosfato e da túrbidez. Foi sugerido também que podem ocorrer profundas alterações na composição do fitoplâncton com a aumento sistemático da concentração de ortofosfato. Foram constatados significativos gradientes horizontais e verticais na estrutura trófica da lagoa Mangueira, indicando a importância de considerar a heterogeneidade espacial em grandes lagos para melhorar a compreensão dos processos ecológicos e padrões. Cenários críticos de simulação indicaram que o aumento da carga de nutrientes afeta negativamente a transparência da água, diferentemente do efeito de mudanças climáticas. Pequenas alterações na estrutura trófica causadas por esses fatores indicam uma forte resistência da lagoa Mangueira. O modelo ecológico também foi útil para descrever a dinâmica do ecossistema, antes e depois da biomanipulação do lago Engelsholm localizado na Dinamarca. Nesse caso, o modelo conseguiu razoavelmente prever a mudança para um estado de alta transparência da após a biomanipulação, entretanto a mudança na composição do fitoplâncton foi muito mais difícil de representar. Além disso, aplicações mais simples também auxiliaram o processo de tomada de decisão e planejamento. A modelagem ecológica aplicada em ecossistemas aquáticos mostrou ser uma alternativa promissora para a gestão integrada dos recursos naturais. / This thesis identified several important features of the trophic structure and dynamics of nutrients in ecosystems subjected to external disturbances such as changes in the water level, nutrient and organic matter loading, fish communities and climate. To describe such effects on trophic structure, a complex ecological model, based on physical, chemical and biological processes has been developed and applied in tropical, subtropical and temperate aquatic ecosystems. In such applications, an integrated analysis was employed considering the transfer of impacts from the watershed to the ecosystem, in order to bring closer the understading of the ecosystem dynamics. Simulations revealed important features about system structure and functionality in front of disturbances. For instance, lake Mangueira a subtropical lake in Southern Brazil can oscilate between two alternative steady stables (clear or turbid water), depending orthophosphate concentration and water transparency. It was also suggested that can occurs profound changes in phytoplankton composition from increase of orthophosphate concentration. Horizontal and vertical gradients in the trophic structure are notable in lake Mangueira, indicating the importance to consider spatial heterogeneity in large lakes to improve understanding of ecological processes and patterns. Simulation scenarios indicated that increased nutrient loading negatively affects water transparency, differently from climate changes. Slight changes in trophic structure caused by those factors indicate a strong resistence of the lake Mangueira. The ecological model also was useful to describe the ecosystem dynamics before and after biomanipulation of lake Engelsholm located in Denmark. In that case, the model could reasonably well predict a shift to a clear water state, but the changed composition of phytoplankton functional groups was much more hard to represent. Furthermore, simpler applications also provided support for decision making and planning in the ecosystem. Ecological modeling applied in aquatic ecosystems showed be a promising alternative towards the integrated management of natural resources.

We numerically investigate the long-time behavior of the density-density auto-correlation function in driven lattice gases, with particle exclusion and periodic boundary conditions in one, two, and three dimensions using precise Monte Carlo simulations of larger system sizes than previous studies. In the one-dimensional asymmetric exclusion process on a ring with half the lattice sites occupied, we find that correlations induce extremely slow relaxation to the asymptotic power law decay We compare the crossover functions obtained from our simulations with various analytic results in the literature, and analyze the characteristic oscillations that occur in finite systems away from half-filling. As expected, correlations are weak in three dimensions and consequently the mean-field description is adequate. We also investigate the relaxation towards the non-equilibrium steady state in the two-time density-density auto-correlations, starting from strongly correlated initial conditions. We obtain simple aging scaling behavior in one, two, and three dimensions, with the expected power laws. We numerically investigate the behavior of driven lattice gases with nearest neighbor interactions at half-filling with periodic boundary conditions below and at the critical temperature using Monte Carlo simulations of very large lattices in two dimensions. This work is one of few that explores the relaxation to a non-equilibrium steady state. We obtain data collapse for the finite-size scaling form of density-density auto-correlation function at the critical point. We achieve data collapse using finite-size scaling of the time-dependent order parameter during the transient regime starting from strongly correlated initial conditions. We present simple aging scaling of the density-density auto-correlation function at the critical point starting from strongly correlated initial conditions using Monte Carlo simulations of two different lattice anisotropies. We thus unambiguously confirm the critical exponents determined by renormalization group methods using measurement of dynamic quantities in the transient regime. Measuring these dynamic quantities in the transient regime provides more conclusive measurements of the critical exponents than previous studies measuring static quantities in the stationary state. We provide qualitative arguments that the lattice anisotropy determines the steady-state for sub-critical quenches. / Ph. D.

No description available.

Dans cette thèse, on étudie la stabilité orbitale d’états stationnaires de modèles mathématiques de type "Hamiltonian mean-field", dits modèles HMF. Cette étude est d’abord menée d’un point de vue théorique en utilisant des méthodes variationnelles. Puis, elle est menée d’un point de vue numérique en commençant par l’élaboration de schémas conservant exactement des états stationnaires. Le Chapitre 2 présente une étude théorique de la stabilité orbitale des états stationnaires du modèle HMF Poisson. Plus précisément, on prouve la stabilité orbitale d’une grande classe d’états stationnaires solutions du système HMF avec potentiel de Poisson. Ces états stationnaires sont des minimiseurs d’un problème à une, deux ou une infinité de contraintes d’une certaine fonctionnelle. La preuve s’appuie sur une approche variationnelle. Cependant le caractère borné du domaine empêche l’utilisation des techniques usuelles basées sur des invariances d’échelles. On introduit alors de nouvelles méthodes, spécifiques à ce problème, mais demeurant dans l’esprit des outils de réarrangements introduits pour le système de Vlasov-Poisson. En particulier, ces méthodes permettent de considérer un nombre arbitraire de contraintes et aboutissent à un résultat de stabilité pour une grande classe d’états stationnaires. Dans le Chapitre 3, on construit des schémas numériques conservant exactement des états stationnaires donnés. Ces schémas modélisent mieux la propriété de stabilité orbitale que les schémas classiques. Puis, on propose un schéma plus général en construisant un schéma qui conserve tous les états stationnaires des modèles HMF. Pour finir, à l’aide de ces schémas, est menée une étude numérique de la stabilité des états stationnaires du système de HMF Poisson qui vient compléter l’étude théorique du Chapitre 2. / In this thesis, we study the nonlinear orbital stability of steady states of "Hamiltonian mean-field" models, called HMF models. First, this study is being done theoretically by using variational methods. It is then carried out numerically by building numerical schemes wich exactly preserve steady states. Chapter 2 presents a theoretical study of the orbital stability of steady states which are solutions to the HMF Poisson system. More specifically, the orbital stability of a large class of steady states which are solutions to the HMF system with Poisson potential is proved. These steady states are obtained as minimizers of an energy functional under one, two or infinitely many constraints. The proof relies on a variational approach. However the boundedness of the space domain prevents us from using usal technics based on scale invariance. Therefore, we introduce new methods which, although specific to our context, remain somehow in the same spirit of rearrangements tools introduced for the Vlasov-Poisson system. In particular, these methods allow for the incorporation of an arbitrary number of constraints, and yield a stability result for a large class of steady states. In Chapter 3, numerical schemes exactly preserving given steady states are built. These schemes model the orbital stability property better than the classic ones. Then, a more general scheme is introduced by building a scheme wich preserves all steady states of HMF models. Lastly, by means of these schemes, we conduct a numerical study of stability of steady states solutions to HMF Poisson system. This completes the theoretical study in Chapter 2.