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

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

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 t14. We show that this rate in a two-dimensional system is asymptotically proportional to (In t)12, and that the concentration profile in the neighborhood of the trap is proportional to (ln rlnt).

Suggested Citation

  • Havlin, S. & Larralde, H. & Kopelman, R. & Weiss, G.H., 1990. "Statistical properties of the distance between a trapping center and a uniform density of diffusing particles in two dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 169(3), pages 337-341.
    • Handle: RePEc:eee:phsmap:v:169:y:1990:i:3:p:337-341
    DOI: 10.1016/0378-4371(90)90105-2
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    Cited by:

    1. Havlin, S. & Araujo, M. & Larralde, H. & Stanley, H.E. & Trunfio, P., 1992. "Diffusion-controlled reaction, A+B→C, with initially separated reactants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 143-152.
    2. Taitelbaum, Haim, 1993. "Segregation in reaction-diffusion systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 155-164.

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