The Becker-Döring equations with exponentially size-dependent rate coefficients

This paper is concerned with an analysis of the Becker-Döring equations which lie at the heart of a number of descriptions of non-equilibrium phase transitions and related complex dynamical processes. The Becker-Döring theory describes growth and fragmentation in terms of stepwise addition or removal of single particles to or from clusters of similar particles and has been applied to a wide range of problems of physicochemical and biological interest within recent years. Here we consider the case where the aggregation and fragmentation rates depend exponentially on cluster size. These choices of rate coefficients at least qualitatively correspond to physically realistic molecular clustering scenarios such as occur in, for example, simulations of simple fluids. New similarity solutions for the constant monomer Becker-Döring system are identified, and shown to be generic in the case of aggregation and fragmentation rates that depend exponentially on cluster size.

Similarity solutions of a Becker-Döring system with time-dependent monomer input

We formulate the Becker-Döring equations for cluster growth in the presence of a time-dependent source of monomer input. In the case of size-independent aggregation and ragmentation rate coefficients we find similarity solutions which are approached in the large time limit. The form of the solutions depends on the rate of monomer input and whether fragmentation is present in the model; four distinct types of solution are found.