Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources

Details Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources

2008-11-10

arxiv.org/abs/0811.1543v2

J. Stat. Mech. (2009) P02012

Physics

Condensed Matter

Statistical Mechanics

11 pages, 3 figures, v2: Minor changes

Scientific paper

10.1088/1742-5468/2009/02/P02012

We revisit a totally asymmetric simple exclusion process (TASEP) with open boundaries and a global constraint on the total number of particles [Adams, et. al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles into the lattice depends on the number available in the reservoir. Thus, the total occupation on the lattice feeds back into its filling process. Although a simple domain wall theory provided reasonably good predictions for Monte Carlo simulation results for certain quantities, it did not account for the fluctuations of this feedback. We generalize the previous study and find dramatically improved predictions for, e.g., the density profile on the lattice and provide a better understanding of the phenomenon of "shock localization."

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