## Abstract

We consider a system consisting of an infinite number of identical particles on a lattice initially uniformly distributed, which diffuese in the presence of a singke mobile trap and ask for the time-dependent behavior of the distance of the trap from the nearest particle. This quantity is a measure of the tendency of the system to self-segregate. We show, by a simulation incorporating the exact enumeration method, that in one dimension the expected distance 〈L(t)〉 scales as 〈L(t)〉≈t^{α} as t→∞, where the exponent α depends only on the ratio of the diffusion constant. A heuristic expression for α is suggested, analogous to a rigorous exponent found by ben-Avraham for a similar but not identical problem. The flux into the trap is found to vary as t^{- 1 2} independent of the diffusion constants.

Original language | English |
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Pages (from-to) | 232-238 |

Number of pages | 7 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 171 |

Issue number | 2 |

DOIs | |

State | Published - 15 Feb 1991 |

Externally published | Yes |

### Bibliographical note

Funding Information:The work of R.S. and R.K. was supported by NSF Grant No. DMR 8801120. D. b-A is grateful for the support of a grant from the Petroleum Research Foundation. The work of S.H. was partially supported by the U.S.-Israel Bi-National Science Foundation.