Renormalization-theoretic analysis of non-equilibrium phase transitions: I. The Becker-Doring equations with power law rate coefficients

摘要

We study in detail the application of renormalization theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes, We investigate the Becker-Doring equations, originally formulated to describe and analyse non-equilibrium phase transitions, and more recently generalized to describe a wide range of physicochemical problems. In this paper we analyse how the systematic coarse-graining renormalization of the Becker-Doring system of equations affects the aggregation and fragmentation rate coefficients. We consider the case of power law size-dependent cluster rate coefficients which we show lead to only three classes of system that require analysis: coagulation-dominated systems, fragmentation-dominated systems and those where coagulation and fragmentation are exactly balanced. We analyse the late-time asymptotics associated with each class. [References: 44]