Queuing transitions in the asymmetric simple exclusion process.
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.
Ha
Meesoon
M
Department of Physics, University of Washington, P.O. Box 351560, Seattle, WA 98195-1560, USA.
Timonen
Jussi
J
den Nijs
Marcel
M