2003/07/31 by Meesoon Ha, J. Timonen, Jussi Timonen +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.68.056122
published as PRE v68 056122 (2003) · 11 pages, 13 figures (published version in PRE)
openalex publication_date 2003/11/24 · arxiv created 2003/11/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling properties. Below the transition, the traffic jam is macroscopic in the sense that the length of the queue scales linearly with system size. Above the transition, only a power-law shaped queue remains. Its density profile scales as deltarho approximately x(-nu) with nu=1/3, and x is the distance from the obstacle. We construct a heuristic argument, indicating that the exponent nu=1/3 is universal and independent of the dynamic exponent of the underlying dynamic process. Fast bonds create only power-law shaped depletion queues, and with an exponent that could be equal to nu=2/3, but the numerical results yield consistently somewhat smaller values nu approximately 0.63(3). The implications of these results to faceting of growing interfaces and localization of directed polymers in random media, both in the presence of a columnar defect are pointed out as well.