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Cluster renormalization in the Becker-Doring equations

Peter V. Coveney·Jonathan A. D. Wattis
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Abstract

We apply ideas from renormalization theory to models of cluster formation in nucleation and growth processes. We study a simple case of the Becker-Doring system of equations and show how a novel coarse-graining procedure applied to the cluster aggregation space affects the coagulation and fragmentation rate coefficients. A dynamical renormalization structure is found to underlie the Becker-Doring equations, nine archetypal systems are identified, and their behaviour is analysed in detail. These architypal systems divide into three distinct groups: coagulation-dominated systems, fragmentation-dominated systems and those systems where the two processes are balanced. The dynamical behaviour obtained for these is found to be in agreement with certain fine-grained solutions previously obtained by asymptotic methods. This work opens the way for the application of renormalization ideas to a wide range of non-equilibrium physicochemical processes, some of which we have previously modelled on the basis of the Becker-Doring equations.

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Peter V. Coveney, Jonathan A. D. Wattis. 1999-08-27. Cluster renormalization in the Becker-Doring equations. https://doi.org/10.1088/0305-4470%2F32%2F41%2F308

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