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Dynamic boundaries in asymmetric exclusion processes

Sarah A. Nowak1, Pak-Wing Fok1,2, and Tom Chou1,3

  • 1Department of Biomathematics, UCLA, Los Angeles, California 90095-1766, USA
  • 2Department of Applied and Computational Mathematics, Caltech, Pasadena, California 91125, USA
  • 3Department of Mathematics, UCLA, Los Angeles, California 90095-1555, USA

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Phys. Rev. E 76, 031135 – Published 27 September, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.031135

Abstract

We investigate the dynamics of a one-dimensional asymmetric exclusion process with Langmuir kinetics and a fluctuating wall. At the left-hand boundary, particles are injected onto the lattice; from there, the particles hop to the right. Along the lattice, particles can adsorb or desorb, and the right-hand boundary is defined by a wall particle. The confining wall particle has intrinsic forward and backward hopping, a net leftward drift, and cannot desorb. Performing Monte Carlo simulations and using a moving-frame finite segment approach coupled to mean field theory, we find the parameter regimes in which the wall acquires a steady-state position. In other regimes, the wall will either drift to the left and fall off the lattice at the injection site, or drift indefinitely to the right. Our results are discussed in the context of nonequilibrium phases of the system, fluctuating boundary layers, and particle densities in the laboratory frame versus the frame of the fluctuating wall.

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  32. In [13, 15], an asymmetric exclusion process in a fixed domain with open boundaries and Langmuir kinetics was studied. Regimes arise in which the position of a shock in the particle density becomes insensitive to the ejection rate β on the right-hand side, once β>0.5. Because these observations were made under the assumption k+>k−, and we consider k−>k+, by particle hole symmetry, the ejection rate in these works corresponds to the injection rate α in our problem. While the authors of [13, 15] find a shock position insensitive to boundary conditions, we find an insensitive mean wall position.

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Phys. Rev. E 76, 031135– Published 27 September, 2007
  • Received 3 May 2007

© 2007 American Physical Society

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