### 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 |

### Fingerprint

### Keywords

- Coagulation
- Coarsening
- Scaling relation
- Self-similar form

### Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*456*(1997), 1281-1290.

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*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 456, no. 1997, pp. 1281-1290.

**Self-similarity in a cut-and-paste model of coarsening.** / Carr, Jack; Pego, Robert L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Self-similarity in a cut-and-paste model of coarsening

AU - Carr, Jack

AU - Pego, Robert L.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

KW - Coagulation

KW - Coarsening

KW - Scaling relation

KW - Self-similar form

UR - http://www.scopus.com/inward/record.url?scp=4944223273&partnerID=8YFLogxK

M3 - Article

VL - 456

SP - 1281

EP - 1290

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 1997

ER -