Scale-free cluster distributions from conserving merging-fragmentation processesJ. Ferkinghoff-Borg1, 2, M. H. Jensen2, J. Mathiesen2, 3 and P. Olesen2
1 NORDITA - Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
2 Niels Bohr Institute - Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
3 NTNU, Institutt for fysikk - N-7491 Trondheim, Norway
received 15 September 2005; accepted in final form 2 December 2005
published online 23 December 2005
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.
82.30.Lp - Decomposition reactions (pyrolysis, dissociation, and fragmentation).
05.70.Jk - Critical point phenomena.
68.35.Fx - Diffusion; interface formation.
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