Selection of the scaling solution in a cluster coalescence model

TL;DR

This paper investigates the scaling behavior of cluster size distributions in a diffusing system, revealing a unique, marginally physical scaling solution selected by the system's kinetics.

Contribution

It demonstrates the existence of a family of scaling solutions and identifies the kinetic selection of a unique, marginally physical solution in a cluster coalescence model.

Findings

A one-parameter family of scaling solutions exists.

Kinetics select a unique, marginally physical scaling solution.

The selected solution is at the boundary between physical and unphysical solutions.

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.