Math @ Duke

Publications [#316990] of Gregory J. Herschlag
Papers Published
 Herschlag, G; Mitran, S; Lin, G, A consistent hierarchy of generalized kinetic equation approximations to
the chemical master equation applied to surface catalysis,
J. Chem. Phys., vol. 142
(November, 2014),
pp. 234703 [1411.3696v2]
(last updated on 2018/10/17)
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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