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Coarse-grained Simulations of Chemical Oscillation in a Lattice Brusselator System

Accelerated coarse-graining (CG) algorithms for simulating heterogeneous chemical reactions on surface systems have recently gained much attention. In the present paper, we consider such an issue by investigating the oscillation behavior of a two-dimension (2D) lattice-gas Brusselator model. We have adopted a coarse-grained Kinetic Monte Carlo (CG-KMC) procedure, where $m \times m$ microscopic lattice sites are grouped together to form a CG cell, upon which CG processes take place with well-defined CG rates. We find that, however, 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 resulted from the trimolecular reaction in this nonlinear system. By properly incorporating such boundary effects, we 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, we find that 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.