Renormalisation-theoretic analysis of non-equilibrium phase transitions: II. The effect of perturbations on rate coefficients in the Becker-Doring equations

We study in detail the application of renormalization theory to models of c luster aggregation and fragmentation of relevance to nucleation and growth processes, In particular, we investigate the Becker-Doring equations, origi nally formulated to describe and analyse non-equilibrium phase transitions, but more recently generalized to describe a wide range of physicochemical problems. We consider here rate coefficients which depend on the cluster si ze in a power law fashion, but now perturbed by small-amplitude random nois e. Power law rate coefficients arise naturally in the theory of surface-con trolled nucleation and growth processes. The noisy perturbations on these r ates reflect the effect of microscopic variations in such mean-field coeffi cients, thermal fluctuations and/or experimental uncertainties. In this pap er we generalize our earlier work that identified the nine classes into whi ch all dynamical behaviour must fall (Wattis J A D and Coveney P V 2001 J. Phys. A: Math. Gen. 34 8679-95) by investigating how random perturbations o f the rate coefficients influence the steady-state and kinetic behaviour of the coarse-grained, renormalized system. We are hence able to confirm the existence of a set of up to nine universality classes for such Becker-Dorin g systems.