Formation of solidification patterns in aggregation models

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Abstract
Generalizations of the diffusion-limited aggregation model are considered in order to simulate pattern formation during solidification. The two-dimensional clusters grown on a seed particle are initially circular but at later stages the process crosses over into dendritic growth. The effects of an anisotropic surface tension are studied by assuming that the sticking probability of the particles depends on the local orientation of the interface. Directional solidification is simulated by the deposition of particles undergoing biased random walks. Linearly stable patterns are generated if the basic features of the directional solidification experiments are taken into account. The resulting patterns are very similar to those observed experimentally.