Nearest-neighbor distances in diffusion-controlled reactions modelled by a single mobile trap

Rodney Schoonover, Daniel Ben-Avraham, Shlomo Havlin, Raoul Kopelman, George H. Weiss

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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)〉≈tα 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 languageEnglish
Pages (from-to)232-238
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume171
Issue number2
DOIs
StatePublished - 15 Feb 1991
Externally publishedYes

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.

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