Mean arrival times of N regular and self avoiding random walkers

Julia Dräger, Joseph Klafter

Research output: Contribution to journalConference articlepeer-review

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 mν. We verify our predictions by numerical simulations of self avoiding walks and of random walks on self avoiding walks in d = 2.

Original languageEnglish
Pages (from-to)293-303
Number of pages11
JournalJournal of Molecular Liquids
Volume86
Issue number1
DOIs
StatePublished - Jun 2000
EventThe Polish-Israeli-German Symposium 'Dynamical Processes in Condensed Molecular Systems' - Cracow, Pol
Duration: 19 Jun 199923 Jun 1999

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