Diffusion-controlled growth and transport in random composites
In the first part of this thesis we consider three different models of diffusioncontrolled growth; phase-field models, diffusion-limited aggregation, and stochastic non-Laplacian growth models. Singular perturbation theory is employed to derive solutions to a phase-field model of solidification for a variety of far-field boundary conditions. Where possible, computational techniques are used to verify the accuracy of the analytical methods. We consider the ramifications of interpreting the...[Show more]
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