Scale free cluster distributions from conserving merging-fragmentation processes

Jesper Ferkinghoff-Borg, Mogens Høgh Jensen, Joachim Mathiesen, Poul Olesen

Research output: Contribution to journalJournal articleResearchpeer-review


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.
Original languageEnglish
Pages (from-to)422
Publication statusPublished - 2006
Externally publishedYes


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