### 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

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## Cite this

Carr, J., & Pego, R. L. (2000). Self-similarity in a cut-and-paste model of coarsening.

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,*456*(1997), 1281-1290.