Kinetics of 'cluster eating'

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Abstract
The authors introduce and study the kinetics of 'cluster eating', in which a cluster of mass i and a cluster of mass j react to form a lighter cluster of mass mod i-j mod . They write the rate equations for this process, which describe the kinetics in the mean-field limit, where spatial fluctuations in cluster density and in cluster shape are neglected. An asymptotic solution to these equations is derived for the particular case in which the reaction rate is independent of the masses of the reacting clusters. At long times, they find that the density of clusters of mass k, ck(t) decays as Ak/( tau logk-1 tau ), where tau is proportional to the time, Ak=(N-1)!/(N-k)! and N is the largest cluster mass in the initial state. This very unusual behaviour is checked by numerical simulations. A more general situation where the reaction matrix depends on the parities of the masses of the two incident clusters is also discussed briefly and a wide variety of possible kinetic behaviours is delineated. Finally, the authors study cluster eating below the upper critical dimension, where fluctuations in cluster density give rise to a non-classical kinetic behaviour.

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