Selection of the Scaling Solution in a Cluster Coalescence Model

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Abstract
The scaling properties of the cluster size distribution of a system of diffusing clusters is studied in terms of a simple kinetic mean field model. It is shown that a one parameter family of mathematically valid scaling solutions exists. Despite this, the kinetics reaches a unique scaling solution independent of initial conditions. This selected scaling solution is marginally physical, i.e., it is the borderline solution between the unphysical and physical branches of the family of solutions.
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