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We study in detail the application of renormalisation theory to models ofcluster aggregation and fragmentation of relevance to nucleation and growthprocesses. In particular, we investigate the Becker-Doring (BD) equations,originally formulated to describe and analyse non-equilibrium phasetransitions, but more recently generalised to describe a wide range ofphysicochemical problems. We consider here rate coefficients which depend onthe cluster size in a power-law fashion, but now perturbed by small amplituderandom noise. Power-law rate coefficients arise naturally in the theory ofsurface-controlled nucleation and growth processes. The noisy perturbations onthese rates reflect the effect of microscopic variations in such mean-fieldcoefficients, thermal fluctuations and/or experimental uncertainties. In thepresent paper we generalise our earlier work that identified the nine classesinto which all dynamical behaviour must fall by investigating how randomperturbations of the rate coefficients influence the steady-state and kineticbehaviour of the coarse-grained, renormalised system. We are hence able toconfirm the existence of a set of up to nine universality classes for such BDsystems.Comment: 30 pages, to appear in J Phys A Math Ge

journal of physics. a, mathematical and general/journal of physics. a, mathematical and general

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