Pgj. Vandongen, AGGREGATION BEYOND THE GEL POINT - A NEW CLASS OF EXACTLY SOLVABLE MODELS, Journal of statistical physics, 87(5-6), 1997, pp. 1273-1286
The existing models describing the kinetics of aggregation in the pres
ence of an infinite cluster, or gel, are reviewed, and a new class of
post-gel models is proposed. In this new class of models, clusters are
assumed to be acyclic and the rate constant for reactions involving t
he gel call be varied. The model is called the generalized acyclic mod
el (GAM) since it generalizes Stockmayer's model and Ziff's third mode
l. It is shown that the GAM can be solved exactly in terms of standard
(hypergeometric) functions. The solutions are analyzed in detail, bot
h asymptotically in various limits and numerically.