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).
|Number of pages||5|
|Journal||Physica A: Statistical Mechanics and its Applications|
|State||Published - 1 Dec 1990|
Bibliographical noteFunding Information:
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.