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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.

Original publication

DOI

10.1088/0305-4470/26/12/016

Type

Journal article

Journal

Journal of Physics A: Mathematical and General

Publication Date

01/12/1993

Volume

26

Pages

2755 - 2767