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.


src, ps, pdf