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bioRxiv · 10.1101/2022.09.10.507392

Clustering and finite size effects in a two-species exclusion process

Chacko, J.·Muhuri, S.·Tripathy, G.
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Abstract

We study the cluster size distribution of particles for a two-species exclusion process which involves totally asymmetric transport process of two oppositely directed species with stochastic directional switching of the species on a 1D lattice. As a function of Q - the ratio of the translation rate and directional switching rate of particles, in the limit of Q [->] 0, the probability distribution of the cluster size is an exponentially decaying function of cluster size m and is exactly similar to the cluster size distribution of a TASEP. For Q >> 1, the model can be mapped to persistent exclusion process (PEP) and the average cluster size, [<]m[>] {propto} Q1/2. We obtain an approximate expression for the average cluster size in this limit. For finite system size system of L lattice sites, for a particle number density{rho} , the probability distribution of cluster sizes exhibits a distinct peak which corresponds to the formation of a single cluster of size ms ={rho} L. However this peak vanishes in the thermodynamic limit L [->] {infty}. Interestingly, the probability of this largest size cluster, P(ms), exhibits scaling behaviour such that in terms of scaled variable Q1 {equiv} Q/L2{rho}(1 -{rho} ), data collapse is observed for the probability of this cluster. The statistical features related to clustering observed for this minimal model may also be relevant for understanding clustering characteristics in active particles systems in confined 1D geometry.

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Chacko, J., Muhuri, S., Tripathy, G.. 2022-09-13. Clustering and finite size effects in a two-species exclusion process. https://doi.org/10.1101/2022.09.10.507392

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