Mean Field Theory of the Morphology Transition in Stochastic Diffusion Limited Growth

Details Mean Field Theory of the Morphology Transition in Stochastic Diffusion Limited Growth Mean Field Theory of the Morphology Transition in Stochastic Diffusion Limited Growth

1995-05-09

arxiv.org/abs/patt-sol/9505001v1

Nonlinear Sciences

Pattern Formation and Solitons

16 pages, 5 figures

Scientific paper

10.1103/PhysRevE.52.5134

We propose a mean-field model for describing the averaged properties of a class of stochastic diffusion-limited growth systems. We then show that this model exhibits a morphology transition from a dense-branching structure with a convex envelope to a dendritic one with an overall concave morphology. We have also constructed an order parameter which describes the transition quantitatively. The transition is shown to be continuous, which can be verified by noting the non-existence of any hysteresis.

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