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

We study in detail the application of renormalization theory to models of c luster aggregation and fragmentation of relevance to nucleation and growth processes, We investigate the Becker-Doring equations, originally formulate d to describe and analyse non-equilibrium phase transitions, and more recen tly generalized to describe a wide range of physicochemical problems. In th is paper we analyse how the systematic coarse-graining renormalization of t he Becker-Doring system of equations affects the aggregation and fragmentat ion rate coefficients. We consider the case of power law size-dependent clu ster rate coefficients which we show lead to only three classes of system t hat require analysis: coagulation-dominated systems, fragmentation-dominate d systems and those where coagulation and fragmentation are exactly balance d. We analyse the late-time asymptotics associated with each class.