Ting Rao, Zhen Zhang, Zhong-huai Hou, Hou-wen Xin. Coarse-grained Simulations of Chemical Oscillation in Lattice Brusselator System[J]. Chinese Journal of Chemical Physics , 2011, 24(4): 425-433. doi: 10.1088/1674-0068/24/04/425-433
Citation: Ting Rao, Zhen Zhang, Zhong-huai Hou, Hou-wen Xin. Coarse-grained Simulations of Chemical Oscillation in Lattice Brusselator System[J]. Chinese Journal of Chemical Physics , 2011, 24(4): 425-433. doi: 10.1088/1674-0068/24/04/425-433

Coarse-grained Simulations of Chemical Oscillation in Lattice Brusselator System

doi: 10.1088/1674-0068/24/04/425-433
Funds:  This work was supported by the National Natu-ral Science Foundation of China (No.20933006 and No.20873130).
  • Received Date: 2011-04-27
  • The oscillation behavior of a two-dimension lattice-gas Brusselator model was investigated. We have adopted a coarse-grained kinetic Monte Carlo (CG-KMC) procedure, where m£m microscopic lattice sites are grouped together to form a CG cell, upon which CG processes take place with well-defined CG rates. Such a CG approach almost fails if the CG rates are obtained by a simple local mean field (s-LMF) approximation, due to the ignorance of correlation among adjcent cells resulting from the trimolecular reaction in this nonlinear system. By proper incorporating such boundary effects, thus introduce the so-called b-LMF CG approach. Extensive numerical simulations demonstrate that the b-LMF method can reproduce the oscillation behavior of the system quite well, given that the diffusion constant is not too small. In addition, the deviation from the KMC results reaches a nearly zero minimum level at an intermediate cell size, which lies in between the effective diffusion length and the minimal size required to sustain a well-defined temporal oscillation.
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Coarse-grained Simulations of Chemical Oscillation in Lattice Brusselator System

doi: 10.1088/1674-0068/24/04/425-433
Funds:  This work was supported by the National Natu-ral Science Foundation of China (No.20933006 and No.20873130).

Abstract: The oscillation behavior of a two-dimension lattice-gas Brusselator model was investigated. We have adopted a coarse-grained kinetic Monte Carlo (CG-KMC) procedure, where m£m microscopic lattice sites are grouped together to form a CG cell, upon which CG processes take place with well-defined CG rates. Such a CG approach almost fails if the CG rates are obtained by a simple local mean field (s-LMF) approximation, due to the ignorance of correlation among adjcent cells resulting from the trimolecular reaction in this nonlinear system. By proper incorporating such boundary effects, thus introduce the so-called b-LMF CG approach. Extensive numerical simulations demonstrate that the b-LMF method can reproduce the oscillation behavior of the system quite well, given that the diffusion constant is not too small. In addition, the deviation from the KMC results reaches a nearly zero minimum level at an intermediate cell size, which lies in between the effective diffusion length and the minimal size required to sustain a well-defined temporal oscillation.

Ting Rao, Zhen Zhang, Zhong-huai Hou, Hou-wen Xin. Coarse-grained Simulations of Chemical Oscillation in Lattice Brusselator System[J]. Chinese Journal of Chemical Physics , 2011, 24(4): 425-433. doi: 10.1088/1674-0068/24/04/425-433
Citation: Ting Rao, Zhen Zhang, Zhong-huai Hou, Hou-wen Xin. Coarse-grained Simulations of Chemical Oscillation in Lattice Brusselator System[J]. Chinese Journal of Chemical Physics , 2011, 24(4): 425-433. doi: 10.1088/1674-0068/24/04/425-433

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