## Abstract

Several analyses of self-segregation properties of reaction-diffusion systems in low dimensions have been based on a simplified model in which an initially uniform concentration of point particles is depleted by reaction with an immobilized trap. A measure of self-segregation in this system is the distance of the trap from the nearest untrapped particle. In one dimension the average of this distance has been shown to increase at a rate proportional to t^{ 1 4}. We show that this rate in a two-dimensional system is asymptotically proportional to (In t)^{ 1 2}, and that the concentration profile in the neighborhood of the trap is proportional to (ln r ln t).

Original language | English |
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Pages (from-to) | 337-341 |

Number of pages | 5 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 169 |

Issue number | 3 |

DOIs | |

State | Published - 1 Dec 1990 |

Externally published | Yes |

### Bibliographical note

Funding Information:H. Larralde acknowledges support by CONACYT (Mexico) by Grant 57312.

Funding Information:

The work of S. Havlin and G.H. Weiss was supported in part by the US-Israel Binational Science Foundation.