Sum over Histories Representation for Kinetic Sensitivity Analysis: How Chemical Pathways Change When Reaction Rate Coefficients Are Varied

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 H₂ 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

Sum over Histories Representation for Chemical Kinetics

A new representation for chemical kinetics is introduced that is based on a sum over histories formulation that employs chemical pathways defined at a molecular level. The time evolution of a chemically reactive system is described by enumerating the most important pathways followed by a chemical moiety. An explicit formula for the pathway probabilities is derived and takes the form of an integral over a time-ordered product. When evaluating long pathways, the time-ordered product has a simple Monte Carlo representation that is computationally efficient. A small numerical stochastic simulation was used to identify the most important paths to include in the representation. The method was applied to a realistic H₂/O₂ combustion problem and is shown to yield accurate results