TY - JOUR

T1 - Asymmetric simple exclusion process in one-dimensional chains with long-range links

AU - Kim, Mina

AU - Santen, Ludger

AU - Noh, Jae Dong

PY - 2011/4

Y1 - 2011/4

N2 - We study the boundary-driven asymmetric simple exclusion process(ASEP) in a one-dimensional chain with long-range links. Shortcuts are added to a chain by connecting pL different pairs of sites selected randomly where L and p denote the chain length and the shortcut density, respectively. Particles flow into a chain at one boundary at a rate α and out of a chain at the other boundary at a rate β, while they hop inside a chain via nearest-neighbor bonds and long-range shortcuts. Without shortcuts, the model reduces to the boundary-driven ASEP in a one-dimensional chain which displays the low-density, high-density and maximal-current phases. Shortcuts lead to a drastic change. Numerical simulation studies suggest that there emerge three phases: an empty phase with ρ = 0, a jammed phase with ρ = 1 and a shock phase with 0 < ρ < 1 where ρ is the mean particle density. The shock phase is characterized with a phase separation between an empty region and a jammed region with a localized shock between them. The mechanism for the shock formation and the nonequilibrium phase transition are explained by an analytical theory based on a mean-field approximation and an annealed approximation.

AB - We study the boundary-driven asymmetric simple exclusion process(ASEP) in a one-dimensional chain with long-range links. Shortcuts are added to a chain by connecting pL different pairs of sites selected randomly where L and p denote the chain length and the shortcut density, respectively. Particles flow into a chain at one boundary at a rate α and out of a chain at the other boundary at a rate β, while they hop inside a chain via nearest-neighbor bonds and long-range shortcuts. Without shortcuts, the model reduces to the boundary-driven ASEP in a one-dimensional chain which displays the low-density, high-density and maximal-current phases. Shortcuts lead to a drastic change. Numerical simulation studies suggest that there emerge three phases: an empty phase with ρ = 0, a jammed phase with ρ = 1 and a shock phase with 0 < ρ < 1 where ρ is the mean particle density. The shock phase is characterized with a phase separation between an empty region and a jammed region with a localized shock between them. The mechanism for the shock formation and the nonequilibrium phase transition are explained by an analytical theory based on a mean-field approximation and an annealed approximation.

KW - Phase diagrams (theory)

KW - driven diffusive systems (theory)

KW - stochastic particle dynamics (theory)

KW - traffic models

UR - http://www.scopus.com/inward/record.url?scp=79955841440&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2011/04/P04003

DO - 10.1088/1742-5468/2011/04/P04003

M3 - Article

AN - SCOPUS:79955841440

SN - 1742-5468

VL - 2011

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 4

M1 - P04003

ER -