ON THE STOCHASTIC APPROACH TO CLUSTER-SIZE DISTRIBUTION DURING PARTICLE COAGULATION .1. ASYMPTOTIC-EXPANSION IN THE DETERMINISTIC LIMIT

Consideration is given to the stochastic problem of the coagulation of particles for the case of a size-independent coagulation kernel, and expressions are derived for the expectation value, variance and covariance of the cluster size distribution function, for both a discrete and a continuous spectrum of cluster sizes. The authors develop an asymptotic expansion in V-1 of these quantities (where V is the spatial volume), showing that as V to infinity the above expectation value tends to the deterministic result, and obtaining an explicit form for the first-order deviation from this expression for large (but finite) V. Analogous results are derived for the variance and covariance in the limit of large V. A discussion is given of the extent to which stochastic effects can produce significant changes to the deterministic results