Coarsening and clustering in run-and-tumble dynamics with short-range exclusion

TL;DR

This paper investigates how clustering and coarsening phenomena emerge in a one-dimensional lattice model of run-and-tumble particles with short-range exclusion, revealing phase transitions and the effects of maximum site occupancy.

Contribution

It extends the persistent exclusion process to allow variable site occupancy and analyzes the resulting phase transitions and crossover behaviors in clustering dynamics.

Findings

Three distinct phases identified: gas, coarsening, and crossover.

The transition from cluster gas to coarsening is continuous with growing cluster mass.

The transition from coarsening to gas can be continuous or discontinuous, with a critical point.

Abstract

The emergence of clustering and coarsening in crowded ensembles of self-propelled agents is studied using a lattice model in one-dimension. The persistent exclusion process, where particles move at directions that change randomly at a low tumble rate $\alpha$, is extended allowing sites to be occupied by more than one particle, with a maximum $n_\text{max}$ per site. Three phases are distinguished. For $n_\text{max}=1$ a gas of clusters form, with sizes distributed exponentially and no coarsening takes place. For $n_\text{max}\geq 3$ and small values of $\alpha$, coarsening takes place and few large clusters appear, with a large fraction of the total number of particles in them. In the same range of $n_\text{max}$ but for larger values of $\alpha$, a gas phase where a negligible fraction of particles takes part of clusters. Finally, $n_\text{max}=2$ corresponds to a crossover phase. The character of the transitions between phases is studied extending the model to allow $n_\text{max}$ to take real values and jumps to an occupied site are probabilistic. The transition from the gas of clusters to the coarsening phase is continuous and the mass of the large clusters grows continuously when varying the maximum occupancy, and the crossover found corresponds to values close to the transition. The second transition, from the coarsening to the gaseous phase can be either continuous or discontinuous depending on the parameters, with a critical point separating both cases.