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

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 $n_{\text{max}}\ge 3$ 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.

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Cited by in corpus (22)

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• Wetting Transitions Displayed by Persistent Active Particles
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• Tracer dynamics in one dimensional gases of active or passive particles
• Local time for run and tumble particle
• Universality of active wetting transitions
• Non-Gaussian anomalous dynamics in systems of interacting run-and-tumble particles
• Attractor-driven matter
• Nonexistence of motility induced phase separation transition in one dimension
• Kinetic Monte-Carlo Algorithms for Active-Matter systems
• Modelling persistence of motion in a crowded environment: the diffusive limit of excluding velocity-jump processes
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• Tracer dynamics in the active random average process
• Persistent exclusion process with time-periodic drive