2011/11/30 by Philip Greulich, Luca Ciandrini, Rosalind J. Allen +1 · 2 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.85.011142
published as Phys. Rev. E 85, 011142 (2012) · 12 pages, 8 figures
openalex publication_date 2012/01/27 · arxiv created 2012/03/08 · arxiv updated 2012/03/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths and entry and exit rates, competing for a finite reservoir of particles. We present relations for the partitioning of particles between the reservoir and the lattices: These relations allow us to show that competition for particles can have nontrivial effects on the phase behavior of individual lattices. For a system with nonidentical lattices, we find that when a subset of lattices undergoes a phase transition from low to high density, the entire set of lattice currents becomes independent of total particle number. We generalize our approach to systems with a continuous distribution of lattice parameters, for which we demonstrate that measurements of the current carried by a single lattice type can be used to extract the entire distribution of lattice parameters. Our approach applies to populations of TASEPs with any distribution of lattice parameters and could easily be extended beyond the mean-field case.