Math @ Duke

Publications [#316989] of Gregory J. Herschlag
Papers Published
 Herschlag, GJ; Mitran, S; Lin, G, A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.,
The Journal of Chemical Physics, vol. 142 no. 23
(June, 2015),
pp. 234703, ISSN 00219606 [repository], [doi]
(last updated on 2018/08/18)
Abstract: We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finiterange spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one and twodimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for onedimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a twodimensional model for the oxidation of CO on RuO2(110), showing that loworder truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.


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