scholarly journals Short Cyclic Structures in Polymer Model Networks: A Test of Mean Field Approximation by Monte Carlo Simulations

2012 ◽  
Vol 45 (11) ◽  
pp. 4886-4895 ◽  
Author(s):  
M. Lang ◽  
K. Schwenke ◽  
J.-U. Sommer
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Polymer Model ◽  
Model Networks

ASYMMETRIC EXCLUSION PROCESSES ON LATTICES WITH A JUNCTION: THE EFFECT OF UNEQUAL INJECTION RATES

2009 ◽  
Vol 20 (06) ◽  
pp. 967-978 ◽  
Author(s):  
XIONG WANG ◽  
RUI JIANG ◽  
KATSUHIRO NISHINARI ◽  
MAO-BIN HU ◽  
QING-SONG WU
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Exclusion Processes ◽  
Asymmetric Exclusion ◽  
Asymmetric Exclusion Processes ◽  
Injection Rates

Asymmetric exclusion processes (ASEP) on lattices with a junction, in which two or more parallel lattice branches combine into a single one, is important as a model for complex transport phenomena. This paper investigates the effect of unequal injection rates in ASEP with a junction. It is a generalization of the work of Pronina and Kolomeisky [J. Stat. Mech. P07010 (2005)], in which only equal injection rates are considered. It is shown that the unequal rates give rise to new phases and the phase diagram structure is qualitatively changed. The phase diagram and the density profiles are investigated by using Monte Carlo simulations, mean field approximation and domain wall approach. The analytical results are in good agreement with Monte Carlo simulations.

TOTALLY ASYMMETRIC EXCLUSION PROCESSES ON LATTICES WITH A BRANCHING POINT

2009 ◽  
Vol 20 (12) ◽  
pp. 1999-2012 ◽  
Author(s):  
XIONG WANG ◽  
RUI JIANG ◽  
MAO-BIN HU ◽  
KATSUHIRO NISHINARI ◽  
QING-SONG WU
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Exclusion Process ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Single Chain ◽  
Equal Rate ◽  
Branching Point

We study totally asymmetric simple exclusion process (TASEP) where particles move on a single-chain lattice which diverges into two parallel lattice branches. At the branching point, the particles move to one of the two branches with equal rate r/2. The phase diagram and density profiles are investigated by using mean-field approximation and Monte Carlo simulations. It is found that the phase diagram can be classified into three regions at any value of r. However, a threshold [Formula: see text] is identified. In cases of r > rc and r < rc, the phase diagram exhibits qualitatively different phases. The analytical results are in good agreement with the results of Monte Carlo simulations.

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