Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-09-06
Physics
Condensed Matter
Statistical Mechanics
18 pages, to appear in J Phys A Math Gen
Scientific paper
10.1088/0305-4470/34/41/320
We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. We investigate the Becker-Dorging equations, originally formulated to describe and analyse non-equilibrium phase transitions, and more recently generalised to describe a wide range of physicochemical problems. In the present paper we analyse how the systematic coarse-graining renormalisation of the \BD system of equations affects the aggregation and fragmentation rate coefficients. We consider the case of power-law size-dependent cluster rate coefficients which we show lead to only three classes of system that require analysis: coagulation-dominated systems, fragmentation-dominated systems and those where coagulation and fragmentation are exactly balanced. We analyse the late-time asymptotics associated with each class.
Coveney Peter V.
Wattis Jonathan AD
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