University, Diss., 2001--Osnabrück.

Techn. Universiẗat, Diss., 2002--Dresden.

Universiẗat, Diss., 1999--Stuttgart.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 66). Also available in electronic version.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 152-166).

Universiẗat, Diss., 2004--Heidelberg.

Universiẗat, Diss., 2004--Mainz.

Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered analytically intractable. As such, a variety of Monte Carlo simulation algorithms have been developed to explore model dynamics empirically. Whilst well-known methods, such as the Gillespie Algorithm, can be implemented to investigate a given model, the computational demands of traditional simulation techniques remain a significant barrier to modern research. In order to further develop and explore biologically relevant stochastic models, new and efficient computational methods are required. In this thesis, high-performance simulation algorithms are developed to estimate summary statistics that characterise a chosen reaction network. The algorithms make use of variance reduction techniques, which exploit statistical properties of the model dynamics, so that the statistics can be computed efficiently. The multi-level method is an example of a variance reduction technique. The method estimates summary statistics of well-mixed, spatially homogeneous models by using estimates from multiple ensembles of sample paths of different accuracies. In this thesis, the multi-level method is developed in three directions: firstly, a nuanced implementation framework is described; secondly, a reformulated method is applied to stiff reaction systems; and, finally, different approaches to variance reduction are implemented and compared. The variance reduction methods that underpin the multi-level method are then re-purposed to understand how the dynamics of a spatially-extended Markov model are affected by changes in its input parameters. By exploiting the inherent dynamics of spatially-extended models, an efficient finite difference scheme is used to estimate parametric sensitivities robustly. The new simulation methods are tested for functionality and efficiency with a range of illustrative examples. The thesis concludes with a discussion of our findings, and a number of future research directions are proposed.

Les alliages de zirconium sont utilisés pour fabriquer des gaines de combustible ainsi que des assemblages combustibles des réacteurs nucléaires à eau sous pression. Sous irradiation, ils montrent un changement dimensionnel communément appelé croissance. Des observations expérimentales ont montré qu'au-dessus d'une dose seuil, ces alliages sont sujets à une croissance accélérée appelée "breakaway". Il a été bien établi que la formation sous irradiation de boucles de dislocation ‹a› et ‹c› est directement responsables de la croissance des alliages de zirconium sous irradiation et que l’apparition des boucles ‹c› est corrélée avec cette accélération de croissance. Cependant, les mécanismes de germination des boucles qui semblent influencés par la présence d’éléments d’alliage sont encore mal compris. Afin d'améliorer notre compréhension des mécanismes élémentaires, une approche multi-échelle a été utilisée pour simuler l'évolution de la microstructure du zirconium sous irradiation. Des calculs à l’échelle atomique basés sur la théorie de la fonctionnelle de la densité (DFT) et sur des potentiels empiriques sont utilisés dans un premier temps pour déterminer les propriétés des amas de défauts ponctuels (boucles de dislocation, cavités, pyramides de fautes d’empilement). Les résultats obtenus sont ensuite insérés en tant que paramètres d'entrée dans un code Monte Carlo cinétique d'objet (OKMC) qui nous permet de simuler l’évolution de la microstructure du matériau sous irradiation, et donc de prédire la croissance. Nos résultats montrent qu’il est nécessaire de considérer une migration anisotrope de la lacune pour prédire l’accélération de croissance. / Zirconium alloys are used to manufacture fuel cladding as well as fuel assemblies of pressurized water nuclear reactors. Under irradiation, they show a dimensional change commonly called growth. Experimental observations have shown that above a threshold dose, these alloys are subject to accelerated growth called "breakaway". It has been well established that the irradiation formation of <a> and <c> dislocation loops is directly responsible for the growth of irradiated zirconium alloys and that the appearance of <c> loops is correlated with this growth acceleration. However, the nucleation mechanisms of the loops that seem to be influenced by the presence of alloying elements are still poorly understood. In order to improve our understanding, a multi-scale modelling approach has been used to simulate the evolution of zirconium microstructure under irradiation. Atomic-scale calculations based on the density functional theory (DFT) and empirical potentials are used to determine the properties of clusters of point defects (dislocation loops, cavities, pyramids of stacking faults). The results obtained are then used as input parameters of an object kinetic Monte Carlo (OKMC) code which allows us to simulate the microstructure evolution of the material under irradiation. Our results show that it is necessary to consider an anisotropic migration of the vacancies to predict the growth acceleration.

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-Graduação em Física, Florianópolis, 2017. / Made available in DSpace on 2018-01-16T03:23:10Z (GMT). No. of bitstreams: 1 349287.pdf: 1892073 bytes, checksum: 25285d74574ea25b39a94d6887148251 (MD5) Previous issue date: 2017 / Nesta tese investigamos alguns teoremas de flutuação do trabalho, enfatizando aqueles propostos por Jarzynski e por Crooks. A ideia básica por trás desses teoremas é a relação existente entre a diferença de energia livre entre dois estados termodinâmicos de um sistema e o valor médio do trabalho realizado por um agente externo em processos que evoluem num tempo finito através de rotas de não equilíbrio entre os mesmos estados termodinâmicos. Testamos a validade desses teoremas através de cálculos analíticos da energia livre e simulações computacionais para processos fora do equilíbrio. Particularmente, investigamos o modelo de Ising unidimensional, modelo que possui solução analítica, e comparamos com integrações num ensemble de trajetórias onde o parâmetro de controle externo pode ser uma força externa, ou um campo magnético aplicado ao sistema. Os resultados obtidos corroboram as previsões desses teoremas. Também investigamos transições de fase em modelos magnéticos segundo a perspectiva desses teoremas. Apresentamos resultados para um modelo com interações de troca ferro- e antiferromagnética, o chamado modelo metamagnético. Investigamos o comportamento desses teoremas de flutuação quando cruzamos as fronteiras de fase de primeira e segunda ordem desse modelo no plano campo magnético versus temperatura. / Abstract : In this thesis we investigate some fluctuation theorems, among them those proposed by Jarzynski and Crooks. The basic idea behind these theorems is the relationship between the free energy difference between two thermodynamic states of a system and the average work performed by an external agent in a finite time through non equilibrium paths between the same thermodynamic states. We test the validity of these theorems through free energy analytical calculations and simulations for out-of-equilibrium processes. In particular, we investigate the one-dimensional Ising model, which has an analytical solution, and compare it with integrations in an ensemble of trajectories where the external control parameter can be an external force, or the magnetic field applied to the system. The results are in agreement with the predictions of these theorems. We also investigate phase transitions in magnetic models from the perspective of these theorems. We present results for a model with ferro- and antiferromagnetic exchange interactions, the so-called metamagnetic model. We investigate the behavior of these fluctuation theorems when we cross the first and second order phase boundaries in the magnetic field versus temperature plane.