## Abstract

We investigate the mean first passage time for the first out of N identical, independently diffusing particles on polymers which are embedded in a d-dimensional Euclidean space. The polymers are modelled by self avoiding walks. We obtain this arrival time in terms of a series in (lnN)^{-1}, independent of the dimension. We furthermore investigate the arrival time for particles which diffuse in free space, but under the additional constraint that they are not allowed to cross their own trails, i.e. the particles themselves perform self avoiding walks. In the latter case the N dependence of the mean first passage time is modified to (lnN)^{-(1-ν)/ν}, where the Flory exponent v describes how the mean end-to-end distance of a polymer increases with the number of monomers m, 〈r(m)〉 approximately m^{ν}. We verify our predictions by numerical simulations of self avoiding walks and of random walks on self avoiding walks in d = 2.

Original language | English |
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Pages (from-to) | 293-303 |

Number of pages | 11 |

Journal | Journal of Molecular Liquids |

Volume | 86 |

Issue number | 1 |

DOIs | |

State | Published - Jun 2000 |

Event | The Polish-Israeli-German Symposium 'Dynamical Processes in Condensed Molecular Systems' - Cracow, Pol Duration: 19 Jun 1999 → 23 Jun 1999 |