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

2011 ◽  
Vol 2011 (04) ◽  
pp. P04003 ◽  
Author(s):  
Mina Kim ◽  
Ludger Santen ◽  
Jae Dong Noh
Keyword(s):  
Long Range ◽  
Exclusion Process ◽  
Asymmetric Simple Exclusion Process ◽  
One Dimensional ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

scholarly journals Dynamical Transitions in a One-Dimensional Katz–Lebowitz–Spohn Model

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1028 ◽  
Author(s):  
Alessandro Pelizzola ◽  
Marco Pretti ◽  
Francesco Puccioni
Keyword(s):  
Finite Size ◽  
Exclusion Process ◽  
Asymmetric Simple Exclusion Process ◽  
Pair Approximation ◽  
Fundamental Diagram ◽  
One Dimensional ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
The One

Dynamical transitions, already found in the high- and low-density phases of the Totally Asymmetric Simple Exclusion Process and a couple of its generalizations, are singularities in the rate of relaxation towards the Non-Equilibrium Stationary State (NESS), which do not correspond to any transition in the NESS itself. We investigate dynamical transitions in the one-dimensional Katz–Lebowitz–Spohn model, a further generalization of the Totally Asymmetric Simple Exclusion Process where the hopping rate depends on the occupation state of the 2 nodes adjacent to the nodes affected by the hop. Following previous work, we choose Glauber rates and bulk-adapted boundary conditions. In particular, we consider a value of the repulsion which parameterizes the Glauber rates such that the fundamental diagram of the model exhibits 2 maxima and a minimum, and the NESS phase diagram is especially rich. We provide evidence, based on pair approximation, domain wall theory and exact finite size results, that dynamical transitions also occur in the one-dimensional Katz–Lebowitz–Spohn model, and discuss 2 new phenomena which are peculiar to this model.

THEORETICAL INVESTIGATION OF SYNCHRONOUS TOTALLY ASYMMETRIC SIMPLE EXCLUSION PROCESS WITH DETACHMENT

2011 ◽  
Vol 25 (12) ◽  
pp. 1585-1592
Author(s):  
SONG XIAO ◽  
JIU-JU CAI ◽  
MING-ZHE LIU ◽  
FEI LIU
Keyword(s):  
Stationary Phases ◽  
Mean Field ◽  
Exclusion Process ◽  
Asymmetric Simple Exclusion Process ◽  
Dimensional System ◽  
One Dimensional ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
The Mean ◽  
Simple Exclusion

This paper investigates a synchronous totally asymmetric simple exclusion process (TASEP) with a detachment in a one-dimensional system. In the model, particles can detach irreversibly with probability q from a bulk site which is far away from boundaries. The phase diagram of the model is calculated in the mean-field approach and verified by Monte Carlo simulations. There are five stationary phases in the system. With the increase of q, the regions of the LD/LD and MC/LD phases increase, while the regions of the HD/HD and LD/HD phases decrease. The MC/HD phase corresponds to a critical point.

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