Mean-field analysis of Williams-Bjerknes-type growth

M. T. Batchelor; B. I. Henry; S. D. Watt

doi:10.1016/S0378-4371(98)00228-3

Mean-field analysis of Williams-Bjerknes-type growth

M. T. Batchelor, B. I. Henry^*, S. D. Watt

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	295-311
Number of pages	17
Journal	Physica A: Statistical Mechanics and its Applications
Volume	256
Issue number	3-4
DOIs	https://doi.org/10.1016/S0378-4371(98)00228-3
Publication status	Published - 1 Aug 1998

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title = "Mean-field analysis of Williams-Bjerknes-type growth",

abstract = "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.",

keywords = "Mean field, Stochastic patterns, Tumour growth",

author = "Batchelor, {M. T.} and Henry, {B. I.} and Watt, {S. D.}",

year = "1998",

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T1 - Mean-field analysis of Williams-Bjerknes-type growth

AU - Batchelor, M. T.

AU - Henry, B. I.

AU - Watt, S. D.

PY - 1998/8/1

Y1 - 1998/8/1

N2 - 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.

AB - 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.

KW - Mean field

KW - Stochastic patterns

KW - Tumour growth

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U2 - 10.1016/S0378-4371(98)00228-3

DO - 10.1016/S0378-4371(98)00228-3

M3 - Article

SN - 0378-4371

VL - 256

SP - 295

EP - 311

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 3-4

ER -

Mean-field analysis of Williams-Bjerknes-type growth

Abstract

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