Exclusion processes: short range correlations induced by adhesion and contact interactions

Abstract

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) ~ 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.

References in corpus (20)

• Traffic and Related Self-Driven Many-Particle Systems
• Statistical Physics of Vehicular Traffic and Some Related Systems
• Glassy dynamics of kinetically constrained models
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Universal cumulants of the current in diffusive systems on a ring
• Lattice Gas Automata for Reactive Systems
• Modeling tumor cell migration: from microscopic to macroscopic
• Heterogeneity and growing lengthscales in the dynamics of kinetically constrained lattice gases in two dimensions
• Classifying the expansion kinetics and critical surface dynamics of growing cell populations
• Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact
• Multiscale dynamics of biological cells with chemotactic interactions: from a discrete stochastic model to a continuous description
• Pair approximation of the stochastic susceptible-infected-recovered-susceptible epidemic model on the hypercubic lattice
• The role of cell-cell adhesion in wound healing
• A multi-lane TASEP model for crossing pedestrian traffic flows
• Field theoretic approach to metastability in the contact process
• Pattern Formation of Glioma Cells: Effects of Adhesion
• Generalized Diffusion
• A microscopic approach to nonlinear Reaction-Diffusion: the case of morphogen gradient formation
• Nonlinear diffusion from Einstein's master equation
• Dynamic propensity in a kinetically constrained lattice gas

Cited by in corpus (3)

• Reactions, Diffusion and Volume Exclusion in a Heterogeneous System of Interacting Particles
• ABM of osteoblast's mechanotransduction pathway: time patterns of critical events
• Restoring detailed balance in non-Hermitian Markov processes