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We analyze the out-of-equilibrium behavior of exclusion processes whereagents interact with their nearest neighbors, and we study the short-rangecorrelations which develop because of the exclusion and other contactinteractions. The form of interactions we focus on, including adhesion andcontact-preserving interactions, is especially relevant for migration processesof living cells. We show the local agent density and nearest-neighbor two-pointcorrelations resulting from simulations on two dimensional lattices in thetransient regime where agents invade an initially empty space from a source andin the stationary regime between a source and a sink. We compare the results ofsimulations with the corresponding quantities derived from the master equationof the exclusion processes, and in both cases, we show that, during theinvasion 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 andthe time dependence of its height may be used to discriminate between differentforms of contact interactions or to quantitatively estimate the intensity ofinteractions. We discuss, in the stationary density profile between a full andan empty reservoir of agents, the presence of a discontinuity close to theempty reservoir. Then, we develop a method for deriving approximatehydrodynamic limits of the processes. From the resulting systems of partialdifferential equations, we recover the self-similar behavior of the agentdensity and correlations during space invasion.

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