Time-Series Expansion for Reaction Processes,
E. Ben-Naim and J. Zhuo
The temporal evolution of reactive systems is studied by means of
exact enumeration of all states of the system for short times. An
algorithm for the evaluation of the power series for basic quantities
of interest is presented. In addition, a consistent methd of
estimating the asymptotic behavior of the series is suggested. This
approach is applied to two reaction schemes, ballistic annihilation
and diffusive-driven three species annihilation, where previous Monte
Carlo simulations suggest power-law decays for the concentration. In
both cases, reasonable estimates for the decay exponents are obtained.
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