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Inhomogeneous exclusion processes with extended objects: the effect of defect locations.

J J Dong¹, B Schmittmann, R K P Zia

¹Center for Stochastic Processes in Science and Engineering, Department of Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA. jjdong@vt.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 1, 2008

Summary

Local defects in particle transport systems significantly alter flow. Simulations show particle size and defect location critically impact steady-state currents and density profiles.

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Area of Science:

Statistical Mechanics
Condensed Matter Physics
Biophysics

Background:

The totally asymmetric simple exclusion process (TASEP) models particle transport on a line.
Local inhomogeneities, such as slow sites, can disrupt uniform particle flow.
Understanding these effects is crucial for modeling biological transport phenomena.

Purpose of the Study:

To investigate the impact of local inhomogeneities (slow sites) on the TASEP.
To compare the effects of these defects for particles of different sizes (l=1 vs. l>1).
To analyze the influence of defect number and proximity on system dynamics.

Main Methods:

Numerical simulations of the totally asymmetric simple exclusion process.
Analysis of stationary current and density profiles.
Examination of asymptotic behavior as hopping rate approaches zero (q-->0).

Main Results:

Local defects qualitatively affect the steady state similarly for particles of size l=1 and l>1.
A single slow site significantly influences the current based on its position.
Two closely spaced slow sites can cause dramatic decreases in the stationary current.
Asymptotic analysis (q-->0) reveals further details of defect-induced behavior.

Conclusions:

Local inhomogeneities profoundly impact particle transport dynamics in TASEP.
Particle size and defect arrangement are critical factors determining transport efficiency.
Findings provide insights into biological transport mechanisms and potential bottlenecks.