Sum over Histories Representation for Kinetic Sensitivity
Analysis: How Chemical Pathways Change When Reaction Rate Coefficients
Are Varied
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Abstract
The
sensitivity of kinetic observables is analyzed using a newly
developed sum over histories representation of chemical kinetics.
In the sum over histories representation, the concentrations of the
chemical species are decomposed into the sum of probabilities for
chemical pathways that follow molecules from reactants to products
or intermediates. Unlike static flux methods for reaction path analysis,
the sum over histories approach includes the explicit time dependence
of the pathway probabilities. Using the sum over histories representation,
the sensitivity of an observable with respect to a kinetic parameter
such as a rate coefficient is then analyzed in terms of how that parameter
affects the chemical pathway probabilities. The method is illustrated
for species concentration target functions in H<sub>2</sub> combustion
where the rate coefficients are allowed to vary over their associated
uncertainty ranges. It is found that large sensitivities are often
associated with rate limiting steps along important chemical pathways
or by reactions that control the branching of reactive flux