This dissertation presents the development of numerical models based on lattice Boltzmann (LB) and cellular automaton (CA) methods for solving phase change and microstructural evolution problems. First, a new variation of the LB method is discussed for solving the heat conduction problem with phase change. In contrast to previous explicit algorithms, the latent heat source term is treated implicitly in the energy equation, avoiding iteration steps and improving the formulation stability and efficiency. The results showed that the model can deal with phase change problems more accurately and efficiently than explicit LB models. Furthermore, a new numerical technique is introduced for simulating dendrite growth in three dimensions. The LB method is used to calculate the transport phenomena and the CA is employed to capture the solid/liquid interface. It is assumed that the dendritic growth is driven by the difference between the local actual and local equilibrium composition of the liquid in the interface. The evolution of a threedimensional (3D) dendrite is discussed. In addition, the effect of undercooling and degree of anisotropy on the kinetics of dendrite growth is studied. Moreover, effect of melt convection on dendritic solidification is investigated using 3D simulations. It is shown that convection can change the kinetics of growth by affecting the solute distribution around the dendrite. The growth features of twodimensional (2D) and 3D dendrites are compared. Furthermore, the change in growth kinetics and morphology of Al-Cu dendrites is studied by altering melt undercooling, alloy composition and inlet flow velocity. The local-type nature of LB and CA methods enables efficient scaling of the model in petaflops supercomputers, allowing the simulation of large domains in 3D. The model capabilities with large scale simulations of dendritic solidification are discussed and the parallel performance of the algorithm is assessed. Excellent strong scaling up to thousands of computing cores is obtained across the nodes of a computer cluster, along with near-perfect weak scaling. Considering the advantages offered by the presented model, it can be used as a new tool for simulating 3D dendritic solidification under convection.

Orientador: Edson Denis Leonel / Resumo: Nesse trabalho, utilizaremos um autômato celular para investigar o problema de roubos e furtos residenciais. A partir de regras e critérios pré-estabelecidos, definimos o comportamento da difusão da criminalidade em uma cidade como função do tempo e dos seus parâmetros de controle. Utilizando um tratamento estatístico da criminalidade, nossos resultados indicam uma possível transição entre fase endêmica, onde o crime existe porém em baixa ocorrência, e uma fase epidêmica, onde o crime é desenfreado. / Abstract: In this work, we will use a cellular automata to investigate the problem of residential robberies. Starting from a set of rules and criteria, the diffusion of the crime is investigated either as a function of time as well function of the control parameters. Using a statistical treatment our results indicate a possible phase transition between endemic, where crime exists but in low occurrence, and epidemic where crime is rampant. / Mestre

In this work Voronoi diagrams which are drawn by the cellular automaton are discussed. The square and hexagon cellular automata were created and used for drawing Voronoi diagrams. As a result of using the created programs Voronoi diagrams, which are obtained in case of two and more dots, are observed. The following results of the research were achieved: § Voronoi diagram can be obtained by the cellular automaton. § Voronoi diagrams, which were obtained, are not precise due to different speed of movement in different directions. § In square - cell case the obtained diagrams depend on the chosen situation of the neighbors. § In hexagon - cell case the obtained Voronoi diagrams are more but not completely precise. The mathematic calculations are not being made while creating Voronoi diagrams by the cellular automaton.. The diagrams are obtained in short period of time. It is possible to watch the process of the diagram creation. A lot of computer's operation time is lost not during the calculation but for re-drawing the obtained image. This is the reason why it is necessary to optimize the image creating algorithm.

Dendrite growth is the primary form of crystal growth observed in laser deposition process of most commercial metallic alloys. The properties of metallic alloys strongly depend on their microstructure; that is the shape, size, orientation and composition of the dendrite matrix formed during solidification. Understanding and controlling the dendrite growth is vital in order to predict and achieve the desired microstructure and hence properties of the laser deposition metals. A two dimensional (2D) model combining the finite element method (FE) and the cellular automaton technique (CA) was developed to simulate the dendrite growth both for cubic and for hexagonal close-packed (HCP) crystal structure material. The application of this model to dendrite growth occurring in the molten pool during the Laser Engineered Net Shaping (LENS®) process was discussed. Based on the simulation results and the previously published experimental data, the expressions describing the relationship between the cooling rate and the dendrite arm spacing (DAS), were proposed. In addition, the influence of LENS process parameters, such as the moving speed of the laser beam and the layer thickness, on the DAS was also discussed. Different dendrite morphologies calculated at different locations were explained based on local solidification conditions. And the influence of convection on dendrite growth was discussed. The simulation results showed a good agreement with previously published experiments. This work contributes to the understanding of microstructure formation and resulting mechanical properties of LENS-built parts as well as provides a fundamental basis for optimization of the LENS process.

Made available in DSpace on 2016-03-15T19:38:09Z (GMT). No. of bitstreams: 1 Fernando Faria.pdf: 516281 bytes, checksum: fc784946b9c2438b3c18c34593a182cb (MD5) Previous issue date: 2008-03-11 / Wolfram Research, Inc. / Cellular automata are discrete dynamical systems composed of simple, locally connected structures (the cells), general in terms of their computational power, and that display complex patterns of behaviour. The purpose of this work was to expand previous studies by Zanon (2006), on non-uniform, one-dimensional cellular automata with nonlocal neighbourhood, in order to verify the existence of rules of these kinds of automata to solve the density classification task, that is, the determination of the predominant bit in a binary string. Our concern here was to look for solutions of the problem mainly by evolutionary computation means, to solve it in a non-trivial fashion, i.e., without including in the solution the majority rule over the entire lattice, and, at the same time, with the target of inferring common features for the solutions that would be found. The results achieved led to an expansion in the quantity of perfect solutions available in the literature, but it became clear that all of them have at least one of the rules involved able to account for the entire lattice at once, an evidence that solutions without rules with global action may not exist. Furthermore, the following observations have been made for the type of automata we considered: even distinct automata may have the same temporal evolution; a certain degree of flexibility is allowed in the total balancing of the rules present in a solution of the density classification task; and, in principle, no common patterns seem to exist between solutions for lattices with 3 and 5 cells, thereby suggesting the impossibility of constructing a solution to the problem from another of a smaller lattice. / Autômatos celulares são sistemas dinâmicos discretos, formados por estruturas simples (as células) conectadas localmente entre si, gerais em termos de seu poder computacional, e que apresentam padrões de comportamento bastante complexos. O intuito deste trabalho foi expandir estudos anteriores de Zanon (2006), sobre autômatos celulares unidimensionais não-uniformes, com vizinhança não-local, visando verificar a existência de autômatos desse tipo na resolução da tarefa da classificação de densidade, isto é, a determinação do bit predominante em uma cadeia binária. Interessou-nos aqui descobrir soluções do problema principalmente por meio de buscas evolutivas, resolvê-lo de forma não trivial, isto é, sem a necessidade da regra da maioria sobre todo o reticulado, e objetivando inferir características necessárias para as soluções que viessem a resolver o problema. Os resultados obtidos levaram a uma expansão da quantidade de soluções perfeitas reportadas na literatura, mas observou-se que todas elas contém pelo menos uma das regras envolvidas tomando todo o reticulado como base de ação, uma evidência da impossibilidade de existir soluções sem regras individuais de ação global. Adicionalmente, as seguintes constatações foram feitas para os autômatos celulares do tipo considerado: mesmo autômatos distintos entre si podem ter a mesma evolução temporal; uma flexibilização do balanceamento total das regras na solução do problema da classificação de densidade é conseguida; e, em princípio, não há padrões nas soluções perfeitas para reticulados de 3 e 5 células, sugerindo a impossibilidade de se construir uma solução a partir de outra de menor tamanho de reticulado.

La formation de la structure de grains dans les métaux pendant la solidification est déterminante pour les propriétés mécaniques et électroniques des pièces coulées. En plus de la texture donnée au matériau, la germination et la croissance des grains sont liées en particulier avec la formation des phases thermodynamiques et les inhomogénéités en composition d'éléments d'alliage. La structure de grains est rarement modélisée à l'échelle macroscopique, d'autant plus que l'approximation 2D est très souvent injustifiée. Dans ces travaux, la germination et la croissance de chaque grain individuel sont suivies avec un modèle macroscopique 3D CAFE. La microstructure interne des grains n'est pas explicitement résolue. Pour valider les approximations faites sur cette microstructure, une comparaison directe avec un modèle microscopique "champ de phase" a été réalisée. Celle-ci a permis de valider les hypothèses de construction du modèle CAFE, de mettre en avant le lien entre données calculées par les modèles microscopiques et paramètres d'entrée des modèles à plus grande échelle, et les domaines de validité de chaque modèle. Dans un deuxième temps, un couplage avec la ségrégation chimique et les bases de données thermodynamiques a été mise en place et appliquée sur un alliage binaire étain-plomb. Une expérience de macroségrégation par convection naturelle a été simulée. L'accord entre les courbes de température expérimentales et simulées atteint une précision de l'ordre de 1K, et la recalescence est correctement prédite. Les cartes de compositions sont comparables qualitativement, ainsi que la structure de grains. Les avantages du suivi de la structure ont été mis en évidence par rapport à une simulation par éléments finis classique. De plus, il a été montré que le calcul 3D était ici indispensable. Enfin, une implémentation parallèle optimisée du code a permis d'appliquer le modèle CAFE à un lingot de silicium polycristallin industriel de dimensions 0,192 x 0,192 x 2,08m, avec une taille de cellules de 250µm. Au total, 4,9 milliards de cellules sont représentées sur le domaine, et la germination et la croissance de 1,6 million de grains sont suivies. / Grain structure formation during solidification of metal parts has a big impact on the final mechanical and electronic properties. Besides determining the crystallographic texture, the nucleation and growth of grains are linked and interact with the appearance of thermodynamic phases and inhomogeneities in the alloy's chemical elements distribution. Grain structure is very rarely modeled on the macro scale, especially because the 2D approximation is often not justified. In this work, the nucleation and growth of each individual grain is tracked with the 3D CAFE macroscopic model. The internal microscopic structure is not explicitly solved. In order to validate the assumptions concerning this microstructure, a direct comparison has been done with a microscopic "phase field" model. That comparison led to the validation of some of the hypothesis on which the CAFE model is built. Moreover, the various data computed in microscopic models that can be used as input parameters of the macroscopic models have been identified, and the limits of each model clearly shown. Secondly, coupling with macrosegregation and thermodynamic databases was achieved, and applied to a binary tin-lead alloy. An experiment featuring macrosegregation induced by natural convection was modeled. The agreement between the experimental and the predicted cooling curves is within 1K, and the recalescence is found to be correctly predicted. The composition maps and the grain structure agree qualitatively with the experiment. The improvement due to structure tracking was demonstrated, regarding a standard finite elements resolution. It was also shown that the 3D simulation is mandatory to reach a good description. Finally, the model was implemented through an optimized parallel algorithm. This permitted to apply the CAFE model on an industrial scale polycrystalline silicon ingot, which dimensions are 0,192 x 0,192 x 2,08m. The cell size is chosen to be 250µm. In total, 4,9 billions of cells were represented, and the nucleation and growth of 1,6 million of grains were tracked.

Modelar a dinâmica de neurônios é relevante em estudos de neurociências. Neste trabalho, propõe-se um modelo computacional de neurônio baseado no comportamento dos canais iônicos presentes na sua membrana. O modelo combina elementos microscópicos, como o comportamento dos canais individuais, com elementos macroscópicos, como a tensão ao longo de um trecho de membrana. Simulações foram realizadas com o objetivo de reproduzir dados biológicos e resultados obtidos de modelos teóricos clássicos da área. Foi possível reproduzir com boa concordância o potencial de ação, o fenômeno da adaptação, a curva da corrente de entrada versus a frequência de disparos e o potencial excitatório pós-sináptico. / Modelling the dynamics of neurons is relevant in studies on neurosciences. In this work, a computational model of neuron based on the behavior of the ionic channels found in its membrane is proposed. The model comprises microscopic elements, as the behavior of the individual channels, and macroscopic elements, as the tension along a membrane patch. Simulations were performed with the aim of reproducing biological data and results derived from classical theoretical models of the field. It was possible to reproduce with good agreement the action potential, the phenomenon of adaptation, the curve of the input current versus the spike frequency, and the excitatory postsynaptic potential.

Durante a solidificação de ligas metálicas, a decantação de grãos equiaxiais pode causar: macrossegregação, mudança na posição da transição colunar-equiaxial e alteração no tamanho de grão equiaxial. O objetivo do presente trabalho é a implementação e análise de um modelo matemático para simular a solidificação sob efeito da decantação de grãos. Este modelo combina: (a) a técnica do autômato celular bi-dimensional em escala microscópica considerando a decantação de grãos, (b) um submodelo microscópico baseado em equações de conservação para simular os processos internos aos grãos e (c) um submodelo macroscópico também baseado em equações de conservação para simular os processos importantes da escala de tamanho macroscópica. Os submodelos macroscópico e microscópico compartilham informações correspondentes às suas escalas características de tamanho através de um método de acoplamento. O modelo matemático completo foi examinado inicialmente através da simulação de diversas situações idealizadas como: a decantação de uma esfera sólida, a decantação de um conjunto de esferas porosas e a decantação e solidificação simultânea de um grão dendrítico isolado e imerso em um líquido super-resfriado. Posteriormente, compararam-se os resultados do modelo para a solidificação isotérmica e para a solidificação unidirecional com resultados disponíveis na literatura obtidos por outros modelos numéricos e por técnicas experimentais. Os resultados do modelo mostraram que a decantação de grãos resulta nos seguintes efeitos no caso da solidificação unidirecional: variação de tamanho médio de grãos e macrossegregação ao longo do lingote e alteração ou até eliminação na posição da transição colunar-equiaxial. / During solidification of metallic alloys, the settling of equiaxed grains can cause macrosegregation, change the position of the columnar-to-equiaxed transition, and change the grain size of equiaxed grains. The objective of the present work is to implement and analyze a mathematical model to simulate the solidification under the effect of grain settling. The present model combines: (a) the cellular automaton technique in two dimensions applied in the microscopic lengthscale to account for the movement of grains; (b) a microscopic submodel based on conservation equations to simulate important phenomena occurring within the grains, and (c) a macroscopic submodel, also based on conservation equations, to simulate important phenomena of the macroscopic lengthscale. Using a strong coupling scheme, the macroscopic and microscopic submodels share important information specific to their typical lengthscales. The complete mathematical model was initially examined in several idealized conditions: the settling of a single solid sphere; the settling of a group of porous spheres; and the growth of a single dendritic grain settling in an undercooled liquid. The model was also used to simulate the isothermal solidification and the unidirectional solidification. For these cases, the outcome of the model was compared with experimental and calculated results available in the literature. For the unidirectional solidification, the model results showed that the settling of grains can cause a variation in the macrosegregation and grain size along the ingot and can change the position or even eliminate the columnar-to-equiaxed transition region.

Durante a solidificação de ligas metálicas, a decantação de grãos equiaxiais pode causar: macrossegregação, mudança na posição da transição colunar-equiaxial e alteração no tamanho de grão equiaxial. O objetivo do presente trabalho é a implementação e análise de um modelo matemático para simular a solidificação sob efeito da decantação de grãos. Este modelo combina: (a) a técnica do autômato celular bi-dimensional em escala microscópica considerando a decantação de grãos, (b) um submodelo microscópico baseado em equações de conservação para simular os processos internos aos grãos e (c) um submodelo macroscópico também baseado em equações de conservação para simular os processos importantes da escala de tamanho macroscópica. Os submodelos macroscópico e microscópico compartilham informações correspondentes às suas escalas características de tamanho através de um método de acoplamento. O modelo matemático completo foi examinado inicialmente através da simulação de diversas situações idealizadas como: a decantação de uma esfera sólida, a decantação de um conjunto de esferas porosas e a decantação e solidificação simultânea de um grão dendrítico isolado e imerso em um líquido super-resfriado. Posteriormente, compararam-se os resultados do modelo para a solidificação isotérmica e para a solidificação unidirecional com resultados disponíveis na literatura obtidos por outros modelos numéricos e por técnicas experimentais. Os resultados do modelo mostraram que a decantação de grãos resulta nos seguintes efeitos no caso da solidificação unidirecional: variação de tamanho médio de grãos e macrossegregação ao longo do lingote e alteração ou até eliminação na posição da transição colunar-equiaxial. / During solidification of metallic alloys, the settling of equiaxed grains can cause macrosegregation, change the position of the columnar-to-equiaxed transition, and change the grain size of equiaxed grains. The objective of the present work is to implement and analyze a mathematical model to simulate the solidification under the effect of grain settling. The present model combines: (a) the cellular automaton technique in two dimensions applied in the microscopic lengthscale to account for the movement of grains; (b) a microscopic submodel based on conservation equations to simulate important phenomena occurring within the grains, and (c) a macroscopic submodel, also based on conservation equations, to simulate important phenomena of the macroscopic lengthscale. Using a strong coupling scheme, the macroscopic and microscopic submodels share important information specific to their typical lengthscales. The complete mathematical model was initially examined in several idealized conditions: the settling of a single solid sphere; the settling of a group of porous spheres; and the growth of a single dendritic grain settling in an undercooled liquid. The model was also used to simulate the isothermal solidification and the unidirectional solidification. For these cases, the outcome of the model was compared with experimental and calculated results available in the literature. For the unidirectional solidification, the model results showed that the settling of grains can cause a variation in the macrosegregation and grain size along the ingot and can change the position or even eliminate the columnar-to-equiaxed transition region.

Made available in DSpace on 2017-07-21T19:25:58Z (GMT). No. of bitstreams: 1 Caroline Martins.pdf: 2933587 bytes, checksum: 3b47c87334757fd35f267d132590b3b7 (MD5) Previous issue date: 2010-03-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we considered cellular automaton model with time delay. The time delay reflects the delay between the time at which the site is affected and the time at which its variable is updated. We analyzed the effect of the rules on the dynamics through the cluster counting. According to this cluster counting, the dynamics behaviour is investigated. We verified the same periodic oscillations as the delay differential equation. / Nessa dissertação consideramos um modelo de automato celular com um tempo de atraso. O tempo de atraso incluso reflete a diferença existente entre o tempo que o sıtio é afetado e o tempo em que sua variável é afetada. Analizamos o efeito das regras na dinâmica através da contagem de cluster. O procedimento dinamico é investigado de acordo com essa contagem de cluster. Verificamos as mesmas oscilações periódicas das equações diferenciais com atraso.