Shock formation in an exclusion process with creation and annihilation

MR Evans*, R Juhasz, L Santen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate shock formation in an asymmetric exclusion process with creation and annihilation of particles in the bulk. We show how the continuum mean-field equations can be studied analytically and hence derive the phase diagrams of the model. In the large system-size limit direct simulations of the model show that the stationary state is correctly described by the mean-field equations, thus the predicted mean-field phase diagrams are expected to be exact. The emergence of shocks and the structure of the phase diagram are discussed. We also analyze the fluctuations of the shock position by using a phenomenological random walk picture of the shock dynamics. The stationary distribution of shock positions is calculated, by virtue of which the numerically determined finite-size scaling behavior of the shock width is explained.

Original languageEnglish
Article number026117
Number of pages8
JournalPhysical Review E - Statistical, Nonlinear and Soft Matter Physics
Volume68
Issue number2
DOIs
Publication statusPublished - Aug 2003

Keywords

  • OPEN BOUNDARIES
  • PHASE-TRANSITIONS
  • MOLECULAR MOTORS
  • MODEL
  • DYNAMICS
  • SYSTEMS

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