Exclusion processes: Short-range correlations induced by adhesion and contact interactions

被引:9
作者
Ascolani, Gianluca [1 ]
Badoual, Mathilde [2 ]
Deroulers, Christophe [2 ]
机构
[1] Univ Paris 11, Univ Paris Diderot, CNRS, UMR 8165,IMNC, F-91405 Orsay, France
[2] Univ Paris 11, Univ Paris Diderot, CNRS, UMR 8165,Lab IMNC, F-91405 Orsay, France
来源
PHYSICAL REVIEW E | 2013年 / 87卷 / 01期
关键词
STRONG DYNAMIC CORRELATIONS; LATTICE-GAS AUTOMATA; NONLINEAR DIFFUSION; HYDRODYNAMIC LIMIT; TRIANGULAR LATTICE; PAIR APPROXIMATION; CELL-MIGRATION; MODEL; POPULATION; SYSTEM;
D O I
10.1103/PhysRevE.87.012702
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We analyze the out-of-equilibrium behavior of exclusion processes where agents interact with their nearest neighbors, and we study the short-range correlations which develop because of the exclusion and other contact interactions. The form of interactions we focus on, including adhesion and contact-preserving interactions, is especially relevant for migration processes of living cells. We show the local agent density and nearest-neighbor two-point correlations resulting from simulations on two-dimensional lattices in the transient regime where agents invade an initially empty space from a source and in the stationary regime between a source and a sink. We compare the results of simulations with the corresponding quantities derived from the master equation of the exclusion processes, and in both cases, we show that, during the invasion of space by agents, a wave of correlations travels with velocity v(t) similar to t(-1/2). The relative placement of this wave to the agent density front and the time dependence of its height may be used to discriminate between different forms of contact interactions or to quantitatively estimate the intensity of interactions. We discuss, in the stationary density profile between a full and an empty reservoir of agents, the presence of a discontinuity close to the empty reservoir. Then we develop a method for deriving approximate hydrodynamic limits of the processes. From the resulting systems of partial differential equations, we recover the self-similar behavior of the agent density and correlations during space invasion. DOI: 10.1103/PhysRevE.87.012702
引用
收藏
页数:18
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