Long-time crossover phenomena in coagulation kinetics

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Abstract
We employ scaling arguments and numerical simulations to investigate the kinetics of general classes of coagulation processes. Within the rate-equation, or mean-field, approximation, a scaling form for the cluster density is used to predict the asymptotic kinetic behavior for the ‘‘product,’’ ‘‘sum,’’ and ‘‘Brownian’’ kernels. These predictions are tested by simulations of the particle coalescence model, a model which corresponds exactly to the rate-equation description of coagulation. Our numerical results indicate the presence of an intermediate-time regime of behavior in coagulation kinetics, which is characterized by effective exponents whose values are consistent with scaling. This new and unexpected regime persists for an extraordinarily long time before a crossover to asymptotic behavior sets in. Furthermore, for the sum kernel, our numerical estimates for the exponents which describe the asymptotic kinetic behavior are in disagreement with current theoretical predictions. Finally, new fluctuation-controlled kinetic behavior below an upper critical dimension equal to 2 is also reported.