Recrystallization of an iron single crystal was reported in detail by Vandermeer and Rath (V&R). We present predictions of recrystallization based on cellular automata (CA) simulations, and compare them with the data and analysis from V&R's study. Agreement is found between our CA simulations and V&R's results, provided that the CA simulations were carried out using a sufficient dynamic range for time, precision spatial dimensionalization, and accommodation of grain shape effects inherent in CA techniques.
This paper generalizes previous work of Rios and Villa on spherical growth. The generalized equation applies to nucleation of ellipsoids according to an inhomogeneous Poisson point process. Microstructural evolution in three dimensions of nucleation and growth transformations of ellipsoids is simulated using the causal cone method. In the simulation, nuclei are located in space according to an inhomogeneous Poisson point process. The transformed regions grow with prolate and oblate ellipsoidal shapes. The ellipsoids have their corresponding axes parallel. The simulation and the exact analytical solution are in excellent agreement. Microstructures generated by the computer simulation are displayed. From these generated microstructures one can obtain the contiguity. In the contiguity against volume fraction plot, data from the sphere and all ellipsoids fall on the same curve. The contiguity curve for nucleation according to an inhomogeneous Poisson point process falls above the contiguity curve for nucleation according to a homogeneous Poisson point process. This behavior indicates that nucleation according to an inhomogeneous Poisson point process introduced a nucleus clustering effect.
Cellular automata simulation in three dimensions is carried out to simulate microstrutural evolution for nuclei distribution ranging from a periodic arrangement to clusters of nuclei. The effect of clustering in three dimensions is found to be much more difficult to detect using conventional microstructural path analysis than in two dimensions. Microstructural path equations fit simulated data well, even when the nuclei are non-randomly located. However, the parameters obtained by means of this fitting lead to erroneous time dependent velocities. Therefore, measuring a descriptor that is sensitive to non-randomness such as the contiguity is even more important in three than in two dimensions
Microstructural evolution in three dimensions of nucleation and growth transformations is simulated by means of cellular automata (CA). In the simulation, nuclei are located in space according to a heterogeneous Poisson point processes. The simulation is compared with exact analytical solution recently obtained by Rios and Villa supposing that the intensity is a harmonic function of the spatial coordinate. The simulated data gives very good agreement with the analytical solution provided that the correct shape factor for the growing CA grains is used. This good agreement is auspicious because the analytical expressions were derived and thus are exact only if the shape of the growing regions is spherical.
<p>Gliomas são tumores cerebrais primários agressivos e invasivos, no qual o mais comum e maligno, glioblastoma multiforme, possui uma combinação de rápido crescimento e invasibilidade. Com o avanço na capacidade de processamento e armazenamento de dados, a utilização de métodos estocásticos para a simulação de problemas físicos reais vem se tornando cada vez mais frequentes. O objetivo do trabalho é simular computacionalmente o crescimento do glioma resolvendo uma equação de reação-difusão em 1D, pelo método de Crank-Nicolson e transpor essa solução para uma geometria 3D por meio do método do Cone Causal e de Monte Carlo. Os resultados obtidos fornecem informações da evolução do raio, concentração de células cancerosas, volume e uma visualização em 3D do tumor. Estes resultados encontrados se mostraram satisfatórios quando comparado com trabalhos que estudam o crescimento tumoral.</p><strong>Palavras chave</strong>: Equação de Reação-Difusão, Gliomas, Método do Cone Causal, Método de Monte Carlo, Método de Diferenças Finitas.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.