Statistical properties of the distance between a trapping center and a uniform density of diffusing particles in two dimensions

S. Havlin; H. Larralde; R. Kopelman; G. H. Weiss

doi:10.1016/0378-4371(90)90105-2

Statistical properties of the distance between a trapping center and a uniform density of diffusing particles in two dimensions

S. Havlin
, H. Larralde
, R. Kopelman
, G. H. Weiss

National Institutes of Health
Boston University
University of Michigan, Ann Arbor

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

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
Pages (from-to)	337-341
Number of pages	5
Journal	Physica A: Statistical Mechanics and its Applications
Volume	169
Issue number	3
DOIs	https://doi.org/10.1016/0378-4371(90)90105-2
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.

Funding

H. Larralde acknowledges support by CONACYT (Mexico) by Grant 57312. The work of S. Havlin and G.H. Weiss was supported in part by the US-Israel Binational Science Foundation.

Funders	Funder number
US-Israel Binational Science Foundation
Consejo Nacional de Ciencia y Tecnología	57312

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10.1016/0378-4371(90)90105-2

Cite this

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title = "Statistical properties of the distance between a trapping center and a uniform density of diffusing particles in two dimensions",

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).",

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AU - Weiss, G. H.

N1 - 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.

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N2 - 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).

AB - 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).

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Statistical properties of the distance between a trapping center and a uniform density of diffusing particles in two dimensions

Abstract

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