Mean-field analysis of Williams-Bjerknes-type growth

被引：3

作者：

Batchelor, MT

Henry, BI ^{[1
]}

Watt, SD

机构：

[1] Australian Natl Univ, Sch Math Sci, Dept Math, Canberra, ACT 0200, Australia

[2] Univ New S Wales, Dept Math Appl, Sydney, NSW 2052, Australia

来源：

PHYSICA A | 1998年 / 256卷 / 3-4期

基金：

澳大利亚研究理事会;

关键词：

stochastic patterns; mean field; tumour growth;

D O I：

10.1016/S0378-4371(98)00228-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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. (C) 1998 Elsevier Science B.V. All rights reserved.

引用

页码：295 / 311

页数：17