Finite-dimensional coagulation-fragmentation dynamics

Abstract

We examine a finite-dimensional truncation of the discrete coagulation-fragmentation equations that is designed to allow mass to escape from the system into clusters larger than those in the truncated problem. The aim is to model within a finite system the process of gelation, which is a type of phase transition observed in aerosols, colloids, etc. The main result is a centre manifold calculation that gives the asymptotic behaviour of the truncated model as time [Formula: see text]. Detailed numerical results show that truncated system solutions are often very close to this centre manifold, and the range of validity of the truncated system as a model of the full infinite problem is explored for systems with and without gelation. The latter cases are mass conserving, and we provide an estimate using quantities from the centre manifold calculations of the time period and the truncated system can be used for before loss of mass which is apparent. We also include some observations on how numerical approximation can be made more reliable and efficient.