Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes

Details Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes

2005-08-02

arxiv.org/abs/cond-mat/0508067v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

10.1209/epl/i2005-10403-9

We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates proportional to their sizes, conserving the total mass. The total number of clusters grows continuously but the full time-dependent distribution can be rescaled over at least 15 decades onto a universal curve which we derive analytically. This curve includes a scale free solution with a scaling exponent of -3/2 for the cluster sizes.

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