2003/03/31 by M. R. Evans, Róbert Juhász, R. Juhasz +2 · 7 citations
Materials Science · Mathematics · Physics and Astronomy · #Annihilation #Diagram #Field (mathematics) #Geometry #Material Dynamics and Properties #Mathematics #Mean field theory #Mechanics #Phase (matter) #Phase diagram #Physics #Pure mathematics #Quantum mechanics #Scaling #Shock (circulatory) #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.68.026117
18 pages, 11 figures, revised version
arxiv created 2003/06/26 · openalex publication_date 2003/08/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.