We present an extension of the pair approximation to model reaction networks whose rate constants are heterogeneous. Taking a pair of impurity sites, we reconstruct the probable nearest neighbor interactions based on the pairwise correlation. Comparison with kinetic Monte Carlo and the mean field approximation reveals that explicit treatment of impurity pairs recovers the effects of dynamic correlation in addition to the effects of static disorder. Moreover, implicit treatment of static disorder in the second impurity site leads to considerable reduction of computational costs without loss of accuracy. The heterogeneous pair approximation is an inexpensive method to obtain qualitative improvements when the mean field counterpart exhibits discrepancies with kinetic Monte Carlo.

Pair approximation of heterogeneous reaction networks

2019 Fall National Meeting

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