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Chin. Phys. B, 2011, Vol. 20(6): 060509    DOI: 10.1088/1674-1056/20/6/060509
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Effect of unequal injection rates on asymmetric exclusion processes with junction

Xiao Song(肖松)a), Liu Ming-Zhe(刘明哲) b)†, Wang Jian-Jun(王建军)a), and Wang Hua(王华)a)
a Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China;  College of Nuclear Technology and Automation Engineering, Chengdu University of Technology, Chengdu 610059, China
Abstract  In this paper, we investigate the effect of unequal injection rates on totally asymmetric simple exclusion processes (TASEPs) with a 2-input 1-output junction and parallel update. A mean-field approach is developed to deal with the junction that connects two sub-chains and the single main chain. We obtain the stationary particle currents, density profiles and phase diagrams. Interestingly, we find that the number of stationary-state phases is changeable depending on the value of $\alpha_1$ ($\alpha_1$ is the injection rate on the first sub-chain). When $\alpha_1$ > 1/3, there are seven stationary-state phases in the system, however when $\alpha_1$ < 1/3, only six stationary-state phases exist in the system. The theoretical calculations are shown to be in agreement with Monte Carlo simulations.
Keywords:  totally asymmetric simple exclusion process      mean-field approach      Monte Carlo simulations      junction  
Received:  04 March 2010      Revised:  13 December 2010      Accepted manuscript online: 
PACS:  05.70.Ln (Nonequilibrium and irreversible thermodynamics)  
  02.50.Ey (Stochastic processes)  
  05.60.Cd (Classical transport)  
Fund: Project supported by the National Scientiˉc and Technological Support Project of China (Grant No. 2006BAE 03A 00).

Cite this article: 

Xiao Song(肖松), Liu Ming-Zhe(刘明哲), Wang Jian-Jun(王建军), and Wang Hua(王华) Effect of unequal injection rates on asymmetric exclusion processes with junction 2011 Chin. Phys. B 20 060509

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