Cluster renormalization in the Becker-Doring equations

We apply ideas from renormalization theory to models of cluster formation i n nucleation and growth processes. We study a simple case of the Becker-Dor ing system of equations and show how a novel coarse-graining procedure appl ied to the cluster aggregation space affects the coagulation and fragmentat ion rate coefficients. A dynamical renormalization structure is found to un derlie the Becker-Doring equations, nine archetypal systems are identified, and their behaviour is analysed in detail. These archetypal systems divide into three distinct groups: coagulation-dominated systems, fragmentation-d ominated systems and those systems where the two processes are balanced. Th e dynamical behaviour obtained for these is found to be in agreement with c ertain fine-grained solutions previously obtained by asymptotic methods. Th is work opens the way for the application of renormalization ideas to a wid e range of non-equilibrium physicochemical processes, some of which we have previously modelled on the basis of the Becker-Doring equations.