Cette thèse s'intéresse au vieillissement des métaux au niveau microstructural. On étudie en particulier les défauts (amas de lacunes, interstitiels ou solutés) via un modèle de dynamique d'amas (DA), qui permet de prédire l'évolution des concentrations de défauts sur des temps longs (plusieurs dizaines d'années). Ce modèle est décrit par un système d'équations différentielles ordinaires (EDOs) de très grande taille, pouvant excéder la centaine de milliards d'équations. Les méthodes numériques classiques de simulation d'EDOs ne sont alors pas efficaces pour de tels systèmes. On montre dans un premier temps que la DA est bien posée et qu'elle vérifie certaines bonnes propriétés physiques comme la conservation de la quantité de matière et la positivité de la solution. On s'intéresse également à une approximation de la DA, qui prend la forme d'une équation aux dérivées partielles, de type Fokker--Planck. On caractérise en particulier l'erreur d'approximation entre la DA et cette approximation. Dans un second temps, on introduit un algorithme de simulation de la DA. Cet algorithme est basé sur un splitting de la dynamique ainsi que sur une interprétation probabiliste des équations de la DA (sous la forme d'un processus de saut) ou de son approximation de Fokker--Planck (sous la forme d'un processus de Langevin). Le but est de réduire le nombre d'équations à résoudre et d'accélérer par conséquent les simulations. On utilise enfin cet algorithme de simulation à différents modèles physiques. On confirme l'intérêt de ce nouvel algorithme pour des modèles complexes. On montre également que cet algorithme permet d'enrichir le modèle de dynamique d'amas à moindre coût / We study ageing of materials at a microstructural level. In particular, defects such as vacancies, interstitials and solute atoms are described by a model called Cluster Dynamics (CD), which characterize the evolution of the concentrations of such defects, on period of times as long as decades. CD is a set of ordinary differential equations (ODEs), which might contain up to hundred of billions of equations. Therefore, classical methods used for solving system of ODEs are not suited in term of efficiency. We first show that CD is well-posed and that physical properties such as the conservation of matter and the preservation of the sign of the solution are verified. We also study an approximation of CD, namely the Fokker--Planck approximation, which is a partial differential equation. We quantify the error between CD and its approximation. We then introduce an algorithm for simulating CD. The algorithm is based on a splitting of the dynamics and couples a deterministic and a stochastic approach of CD. The stochastic approach interprets directly CD as a jump process or its approximation as a Langevin process. The aim is to reduce the number of equations to solve, hence reducing the computation time. We finally apply this algorithm to physical models. The interest of this approach is validated on complex models. Moreover, we show that CD can be efficiently improved thanks to the versatility of the algorithm

The generalized Langevin equation (GLE) has been used to describe the dynamics of particles in a stationary environment. To better understand the dynamics of polymerization, the GLE has been generalized to the irreversible generalized Langevin equation (iGLE) so as to incorporate the non-stationary response of the solvent. This non-stationary response is manifested in the friction kernel and the behavior of the projected (stochastic) force. A particular polymerizing system, such as living polymerization, is specified both through the parameters of the friction kernel and the potential of mean force (PMF). Equilibrium properties such as extent of polymerization have been obtained and are consistent with Flory-Huggin¡¯s theory. In addition, time-dependent non-equilibrium observables such as polymer length, the polymer length distribution, and polydispersity index (PDI) of living polymerization have been obtained. These have been compared to several experiments so as to validate the models, and to provide additional insight into the thermodynamic and kinetic properties of these systems. In addition to the iGLE, a stochastic model has been used to study the effect of nonequilibrium reactivity on living polymerization. This model can be used to determine whether the reaction is controlled by kinetics or diffusion. A combination of the iGLE and stochastic models may help us obtain more information about living polymerization.

Made available in DSpace on 2014-06-11T19:25:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-17Bitstream added on 2014-06-13T20:14:03Z : No. of bitstreams: 1 bauke_fc_me_rcla.pdf: 1413465 bytes, checksum: 5695187aaf8a438767e3a8684e26c073 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Neste trabalho estudamos o modelo do movimento Browniano de uma partícula carregada sob a ação de campos elétrico e magnético, externos e homogêneos, no formalismo de Langevin. Calculamos a energia cinética média através do teorema da flutuação-dissipação e obtivemos uma expressão para a temperatura efetiva das partículas Brownianas em função da temperatura do reservatório e dos campos externos. Esta temperatura efetiva mostrou-se sempre maior que a temperatura do reservatório, o que explica a expressão “portadores quentes”. Estudamos essa temperatura efetiva no regime assintótico, ou seja, no estado estacionário atingido em tempos muito longos (quando comparado com o tempo de colisão) e a utilizamos para escrever as equações de transporte em semicondutores, denominadas equações de Shockley generalizadas sendo que incluem nesse caso também a ação do campo magnético. Uma aplicação direta e relevante foi a modelagem para o já conhecido efeito Gunn para portadores assumidos como Brownianos. A temperatura efetiva calculada por nós no regime transiente permitiu estudar também os efeitos do reservatório na relaxação da temperatura efetiva à temperatura terminal (de não equilíbrio e estacionária). Nossos resultados no que diz respeito ao efeito Gunn, embora seja o modelo mais simples de um portador Browniano, mostrou uma surpreendente concordância com resultados experimentais, sugerindo que modelos mais sofisticados devam incluir os elementos apresentados neste estudo / We present a Brownian model for a charged particle in a field of forces, in particular, electric and magnetic external homogeneous fields, within the Langevin formalism. We compute the average kinetic energy via the fluctuation dissipation and obtain an expression for the Brownian particle´s effective temperature. The latter is a function of the heat bath temperature and both external fields. This effective temperature is always greater than the heat bath temperature, therefore the expression “hot carriers”. This effective temperature, in the asymptotic regime, the stationary state at long times (greater than the collision time), is used to write down the transport equations for semiconductors, namely the generalized Shockley equations, now incorporating the magnetic field effect. A direct and relevant application follows: a model for the well known Gunn effect, assuming a Brownian scheme. In the transient regime the computed effective temperature also allow us to probe some features of the heat bath, as the effective temperature relaxes to its terminal stationary value. As for our results in the Gunn effect model, the simplest of all in a Brownian scheme, we obtain a surprisingly good agreement with experimental data, suggesting that more involved models should include our minimal assumptions

Orientador: René Alfonso Nome Silva / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Química / Made available in DSpace on 2018-08-26T04:23:53Z (GMT). No. of bitstreams: 1 Zornio_BrunoFedosse_M.pdf: 1493558 bytes, checksum: 07565e7077eefa5f9f91f03dc9cc90d4 (MD5) Previous issue date: 2014 / Resumo: No final do século XIX Van¿tHoff empiricamente estabeleceu que a constante de velocidade de uma reação química é função exponencial da razão entre energia de ativação da reação pela energia térmica do ambiente (e portanto função da temperatura). Há uma variada ordem nas escalas de tempos reacionais, em especial, a constante de velocidade de reações lentas (por exemplo, reações bioquímicas não catalisadas) é difícil de determinar. Uma partícula difundindo em um meio viscoso que apresenta movimento aleatório ¿ com posição média (em um intervalo de tempo suficientemente grande) nula, e a variância da posição linearmente dependente em função do tempo ¿ é dita browniana, e quando submetida a um potencial bi quadrático é um bom modelo para descrição de reações químicas. A partir da dinâmica de Langevin (que serve para descrever a dinâmica de uma partícula browniana) é derivada a teoria de Kramers para meio viscosos - que relaciona o formato da curva potencial com a constante de taxa de reações químicas -. Experimentalmente pode-se recriar esse modelo utilizando pinças ópticas. Pinças ópticas são capazes de aprisionar partículas da ordem micrométricas em suspensão, pode-se recriar um potencial bi estávelutilizando uma pinça óptica dupla (com dois pontos de aprisionamento). Este estudo tem como objetivo avaliar a constante de taxa de um processo de transição entre poços de potencial de partículas brownianas teoricamente utilizando uma simulação de dinâmica de Langevin para sistemas em equilíbrio tanto quanto para sistemas antes de atingir o equilíbrio, assim como determinar experimentalmente utilizando microscopia ocoeficiente de difusão a partir da trajetória temporal de uma única partícula. Os resultados teóricos obtidos são bastante condizentes com os resultados experimentais descritos na literatura, assim como as predições da constante de taxa para tempos antes do equilíbrio apresentam correlação com o sistema em equilíbrio. Com relação à estimativa do coeficiente de difusão apresenta um erro sistemático associado ao tamanho da trajetória temporal de uma única partícula / Abstract: By the end of the XIX century, Van¿t¿ Hoff has empirically established that the rate constant of some chemical reaction is exponentially dependent by the ratio between the reaction activation energy and the environment thermal energy (and so on function of temperature). There is a wide variety in the reaction time scales, in particular, the rate constant of slow reactions (such as uncatalysed biochemical reactions) is difficult to determine. A diffusing particle in a viscous media which exhibit random motion ¿ with mean position (in a sufficiently large time series) is zero, and the position variance is linearly time dependent ¿ is called Brownian, and when is submitted in a biquadratic potential it¿s a good model to describe chemical reactions. By the Langevin dynamics (which serves to describe the Brownian particle motion) the Kramers theory for viscous media is derived ¿ that theory connects the potential energy shape with the chemical rate constant -. Experimentally it is possible to create this model using optical tweezes. Optical tweezers where capable to trap micrometrical beads in suspension, it can generate a bi-stable using a double optical tweezers (that is with two trapping points). The main objective of this essay is evaluate the rate constant a Brownian particles jumping between potential wells theoretically using Langevin dynamics simulations for the system at equilibrium and before reach the equilibrium, as determinate experimentally the diffusion coefficient of single particle time path using microscopy. The theoretical results is very consistent with experimental results described in literature, as well as the prediction of the rate constant for the system before reaches equilibrium are correlated with the rate constant for the system at equilibrium. For the diffusion coefficient estimative it was observed that there is a systematical source of errors, and its is related with the length of the time series of the single particle path / Mestrado / Físico-Química / Mestre em Química

Dans cette thèse, nous étudions les effets cohérents associés à la propagation d’ondes dans les milieux diffusants, en particulier les ondes électromagnétiques.En milieux faiblement désordonnés, l'intensité lumineuse fluctue spatialement sur de grandes distances. Ce phénomène est le résultat d'effets cohérents mésoscopiques complexes, qui se produisent à une échelle microscopique. Nous montrons que ces fluctuations mésoscopiques cohérentes de la lumière induisent des forces de rayonnement d'un nouveau genre. L'amplitude de ces forces fluctuantes est déterminée par un paramètre unique et facilement réglable, la conductance adimensionnée, qui dépend à la fois de la géométrie et des propriétés de diffusion du milieu. Notre découverte devrait donc avoir des applications intéressantes, telles que de nouveaux capteurs pour la matière molle ou la biophysique.Du point de vue méthodologique, nous utilisons une approche à la Langevin pour décrire les fluctuations lumineuses cohérentes, où un bruit précisément calculé rend compte des effets cohérents mésoscopiques. Nous montrons comment inclure systématiquement les corrections cohérentes dans le terme de bruit, afin de reproduire les fluctuations d'intensité. Cette description permet de comprendre les fluctuations cohérentes comme résultant d’un flux lumineux hors équilibre, caractérisé par deux paramètres seulement, le coefficient de diffusion et la mobilité, qui sont par ailleurs liés par une relation d’Einstein. Un avantage évident de cette méthode est sa dépendance à deux paramètres seulement, ce qui fournit une description à la fois compacte et précise des riches effets cohérents sous-jacents. De plus, la correspondance que nous présentons entre la lumière cohérente et l'hydrodynamique hors d'équilibre est facilement généralisable à une large classe de problèmes d'ondes quantiques ou classiques.Pour les perspectives futures, cette connexion entre les effets cohérents mésoscopiques et les processus stochastiques hors équilibre devraient intéresser les communautés de la mésoscopie et de la mécanique statistique. Pour les premiers, le lien avec l'hydrodynamique hors équilibre fournit un nouvel éclairage sur la physique mésoscopique, ainsi que des outils utiles pour étudier les quantités jusqu'ici difficiles d'accès, telles que les fonctions de corrélation d'intensité d'ordres supérieurs. Pour les seconds, ces travaux devraient motiver une étude plus approfondie des processus indépendants du temps inspirés de la mésoscopie. / In this work, we study coherent effects associated to wave propagation in scattering media, in particular electromagnetic waves.In weakly disordered media, light intensity fluctuates spatially over large distances. This phenomenon is the result of complex mesoscopic coherent effects, which occur at a microscopic scale. We show that these mesoscopic coherent fluctuations of light induce radiation forces of a new kind. The strength of these fluctuating forces is determined by a single and easily tunable parameter, the dimensionless conductance, which depends on both the geometry and the scattering properties of the medium. Our findings should therefore have interesting applications such as new sensors in soft condensed matter or biophysics.On the methodological viewpoint, we use a hydrodynamic Langevin approach to describe the coherent light fluctuations, where a properly tailored noise accounts for mesoscopic coherent effects. We show how to systematically include the coherent corrections in the noise term, in order to reproduce the intensity fluctuations. This description allows to understand coherent light fluctuations as resulting from a non equilibrium light flow, characterized by two parameters only, the diffusion coefficient and the mobility, otherwise related by an Einstein relation. A clear asset of this method is its dependence upon two parameters only, which provides a compact yet accurate description of the rich underlying coherent effects. Moreover, the mapping we present between coherent light and out of equilibrium hydrodynamics is easily generalizable to a large class of quantum or classical wave problems.For future perspectives, this connection between coherent effects in mesoscopics and non equilibrium stochastic processes should be of interest in both the mesoscopics and statistical mechanics communities. For the former, the mapping to non equilibrium hydrodynamics provides a new insight to mesoscopic physics as well as useful tools to study quantities so far difficult to access, such as higher orders intensity correlation functions. For the latter, this work should motivate further study of time independent processes inspired from mesoscopics.

Molecular dynamics (MD) computations aim to simulate materials at the atomic level by approximating molecular interactions classically, relying on the Born-Oppenheimer approximation and semi-empirical potential energy functions as an alternative to solving the difficult time-dependent Schrodinger equation. An approximate solution is obtained by discretization in time, with an appropriate algorithm used to advance the state of the system between successive timesteps. Modern MD simulations simulate complex systems with as many as a trillion individual atoms in three spatial dimensions. Many applications use MD to compute ensemble averages of molecular systems at constant temperature. Langevin dynamics approximates the effects of weakly coupling an external energy reservoir to a system of interest, by adding the stochastic Ornstein-Uhlenbeck process to the system momenta, where the resulting trajectories are ergodic with respect to the canonical (Boltzmann-Gibbs) distribution. By solving the resulting stochastic differential equations (SDEs), we can compute trajectories that sample the accessible states of a system at a constant temperature by evolving the dynamics in time. The complexity of the classical potential energy function requires the use of efficient discretization schemes to evolve the dynamics. In this thesis we provide a systematic evaluation of splitting-based methods for the integration of Langevin dynamics. We focus on the weak properties of methods for confiurational sampling in MD, given as the accuracy of averages computed via numerical discretization. Our emphasis is on the application of discretization algorithms to high performance computing (HPC) simulations of a wide variety of phenomena, where configurational sampling is the goal. Our first contribution is to give a framework for the analysis of stochastic splitting methods in the spirit of backward error analysis, which provides, in certain cases, explicit formulae required to correct the errors in observed averages. A second contribution of this thesis is the investigation of the performance of schemes in the overdamped limit of Langevin dynamics (Brownian or Smoluchowski dynamics), showing the inconsistency of some numerical schemes in this limit. A new method is given that is second-order accurate (in law) but requires only one force evaluation per timestep. Finally we compare the performance of our derived schemes against those in common use in MD codes, by comparing the observed errors introduced by each algorithm when sampling a solvated alanine dipeptide molecule, based on our implementation of the schemes in state-of-the-art molecular simulation software. One scheme is found to give exceptional results for the computed averages of functions purely of position.

Lattice simulations are a popular tool for studying the non-perturbative physics of nonlinear field theories. To perform accurate lattice simulations, a careful account of the discretization error is necessary. Spatial discretization error as a result of lattice spacing dependence in Langevin simulations of anisotropic (2 + 1)-dimensional classical scalar field theories is studied. A transfer integral operator (TIO) method and a one-loop renormalization (1LR) procedure are used to formulate effective potentials. The effective potentials contain counterterms which are intended to suppress the lattice spacing dependence. The two effective potentials were tested numerically in the case of a phi-4 model. A high accuracy modified Euler method was used to evolve a phenomenological Langevin equation. Large scale Langevin simulations were performed in parameter ranges determined to be appropriate. Attempts at extracting correlation lengths as a means of determining effectiveness of each method were not successful. Lattice sizes used in this study were not of a sufficient size to obtain an accurate representation of thermal equilibrium. As an alternative, the initial behaviour of the ensemble field average was observed. Results for the TIO method showed that it was successful at suppressing lattice spacing dependence in a mean field limit. Results for the 1LR method showed that it performed poorly.

<p>Cells express a variety of proteins on their surface that allows them to sample the world. These proteins are embedded in the plasma membrane, a bilayer of lipids that surrounds the cell. Since the lipid and protein dimensions are in the nanometer range, they are subject to thermal agitation by water molecules and show characteristic diffusive motion. The diffusive movement of these proteins plays a critical role in the cell's ability to react to external signals and regulate its internal environment. </p><p>One prominent application of protein diffusion is in the synaptic connection, where is the highly localized concentration of receptors. The receptive dendrite membrane contains many types of receptors that are accumulated to form functional microdomains opposite the presynaptic terminal buttons that release neurotransmitters. Experiments reveal that receptors move from extrasynaptic locations to synaptic locations by lateral diffusion, thereby concentrating receptors at synapses. Two key processes that control synaptic AMPAR numbers are receptor diffusion within the synaptic and extrasynaptic space and interactions between receptors and PSD scaffold proteins. Electron microscopy images suggest that the PSD is highly crowded potentially limiting the ability of receptors to diffuse and interact with scaffold proteins. However, the contribution of macromolecular crowding to receptor retention remains to be tested systematically. </p><p>Here, we combine experimental and computational approaches to test the effect of synaptic steric hindrance on receptor mobility and enrichment. We first investigate how the diffusion is influenced by membrane geometry. The membrane itself can have three-dimensional structure, which means that the actual path length of diffusion can be different from a projected path length. Here, we use a position Langevin equation for diffusion, which incorporates curvature and gradient effects of surfaces. Numeric simulation of the equation allows for the prediction of effective diffusion coefficients over corrugated surfaces.</p><p>In order to examine the distinct contributions of crowding and receptor-scaffold binding, we developed a computational model for AMPA-receptor diffusion in the synaptic and extrasynaptic space, which contains immobile obstacles, representing scaffolding, receptor and adhesion molecules in the PSD. The spatial distribution of scaffold proteins was determined directly from photo-activated localization microscopy measurements that mapped molecular positions with a resolution of ~20 nm. The AMPAR/scaffold association and dissociation rates were adjusted by computer simulations to fit single-particle tracking and fluorescence recovery after photobleaching measurements. The model predicts the recovery curves are influenced mostly by size changes while variation of kinetic rates did not significantly alter receptor residence time or mobility. We also examined the effect of binding, by adding a single synaptic binding motif to a small transmembrane protein, which slows its diffusion within the synapse. These results suggest that both protein size and binding play important roles in retaining surface-diffusing TM proteins within the excitatory synapse and shed light on the biophysical mechanisms that lead to high density of AMPARs at synapses.</p> / Dissertation

Lattice simulations are a popular tool for studying the non-perturbative physics of nonlinear field theories. To perform accurate lattice simulations, a careful account of the discretization error is necessary. Spatial discretization error as a result of lattice spacing dependence in Langevin simulations of anisotropic (2 + 1)-dimensional classical scalar field theories is studied. A transfer integral operator (TIO) method and a one-loop renormalization (1LR) procedure are used to formulate effective potentials. The effective potentials contain counterterms which are intended to suppress the lattice spacing dependence. The two effective potentials were tested numerically in the case of a phi-4 model. A high accuracy modified Euler method was used to evolve a phenomenological Langevin equation. Large scale Langevin simulations were performed in parameter ranges determined to be appropriate. Attempts at extracting correlation lengths as a means of determining effectiveness of each method were not successful. Lattice sizes used in this study were not of a sufficient size to obtain an accurate representation of thermal equilibrium. As an alternative, the initial behaviour of the ensemble field average was observed. Results for the TIO method showed that it was successful at suppressing lattice spacing dependence in a mean field limit. Results for the 1LR method showed that it performed poorly.

Thesis (Ph.D.)--Tufts University, 2004. / Adviser: Larry H. Ford. Submitted to the Dept. of Physics. Includes bibliographical references (leaves 117-120). Access restricted to members of the Tufts University community. Also available via the World Wide Web;