Mean field analysis of Williams-Bjerknes type growth

Details Mean field analysis of Williams-Bjerknes type growth Mean field analysis of Williams-Bjerknes type growth

1998-03-26

arxiv.org/abs/cond-mat/9803315v1

Physica A 256 (1998) 295-311

Physics

Condensed Matter

Soft Condensed Matter

21 pages, Latex2e, Elsevier style, 5 figures

Scientific paper

We investigate a class of stochastic growth models involving competition between two phases in which one of the phases has a competitive advantage. The equilibrium populations of the competing phases are calculated using a mean field analysis. Regression probabilities for the extinction of the advantaged phase are calculated in a leading order approximation. The results of the calculations are in good agreement with simulations carried out on a square lattice with periodic boundaries. The class of models are variants of the Williams- Bjerknes model for the growth of tumours in the basal layer of an epithelium. In the limit in which only one of the phases is unstable the class of models reduces to the well known variants of the Eden model.

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