A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.
Abstract
We develop a hierarchy of approximations to the master equation for systems that exhibit
translational invariance and finite-range 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 two-dimensional 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 one-dimensional
systems, while predicting similar system dynamics and steady states as KMC methods.
We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110),
showing that low-order 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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https://hdl.handle.net/10161/12397Published Version (Please cite this version)
10.1063/1.4922515Publication Info
Herschlag, Gregory J; Mitran, Sorin; & Lin, Guang (2015). A consistent hierarchy of generalized kinetic equation approximations to the master
equation applied to surface catalysis. J Chem Phys, 142(23). pp. 234703. 10.1063/1.4922515. Retrieved from https://hdl.handle.net/10161/12397.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Gregory Joseph Herschlag
Phillip Griffiths Assistant Research Professor
I am interested in studying techniques to understand fairness in redistricting. I
am also interested in computational fluid dynamics and high-performance computing.

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