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

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

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−12 independent of the diffusion constants.

Suggested Citation

  • Schoonover, Rodney & Ben-Avraham, Daniel & Havlin, Shlomo & Kopelman, Raoul & Weiss, George H., 1991. "Nearest-neighbor distances in diffusion-controlled reactions modelled by a single mobile trap," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 171(2), pages 232-238.
    • Handle: RePEc:eee:phsmap:v:171:y:1991:i:2:p:232-238
    DOI: 10.1016/0378-4371(91)90275-H
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    References listed on IDEAS

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    1. Carrington, Peter J. & Moyer, Sharon & Kopelman, Faigie, 1988. "Factors affecting pre-dispositional detention and release in Canadian juvenile courts," Journal of Criminal Justice, Elsevier, vol. 16(6), pages 463-476.
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    Cited by:

    1. Taitelbaum, Haim, 1993. "Segregation in reaction-diffusion systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 155-164.
    2. Koza, Zbigniew, 1997. "Asymptotic behaviour of initially separated A + B(static) → 0 reaction-diffusion systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(3), pages 622-634.

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