Abstract
We study certain redistribution processes for a resource distributed among a large number of resource holders (clusters). In the processes we consider, the smallest clusters are cut up into pieces according to a given statistical law, and the pieces are randomly redistributed among the remaining clusters. We derive an evolution equation for the cluster size distribution, show that self-similar solutions exist and characterize their structure. In a limiting case when the pieces are small, we show that in general solutions approach a singular self-similar form. © 2000 The Royal Society.
Original language | English |
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Pages (from-to) | 1281-1290 |
Number of pages | 10 |
Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume | 456 |
Issue number | 1997 |
Publication status | Published - 2000 |
Keywords
- Coagulation
- Coarsening
- Scaling relation
- Self-similar form