Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-11-08
Phys. Rev. E 85, 011142 (2012)
Physics
Condensed Matter
Statistical Mechanics
12 pages, 8 figures
Scientific paper
10.1103/PhysRevE.85.011142
We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths, 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 non-trivial effects on the phase behavior of individual lattices. For a system with non-identical 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.
Allen Rosalind J.
Ciandrini Luca
Greulich Philip
Romano Carmen M.
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