Cluster renormalization in the Becker-Doring equations

Details Cluster renormalization in the Becker-Doring equations Cluster renormalization in the Becker-Doring equations

1999-08-27

arxiv.org/abs/cond-mat/9908402v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 1 figure, LaTeX2e, to appear in J. Phys. A, Math. Gen

Scientific paper

10.1088/0305-4470/32/41/308

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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