Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions

Details Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions

1996-03-28

arxiv.org/abs/cond-mat/9603176v1

J. Phys. A 29, 5347 (1996).

Physics

Condensed Matter

12 pages, no figures, macro files prepended, to be submitted to J. Phys. A

Scientific paper

10.1088/0305-4470/29/17/011

The survival probability, S_N(t), of a diffusing prey (``lamb'') in the proximity of N diffusing predators (a ``pride of lions'') in one dimension is investigated. When the lions are all to one side of the lamb, the survival probability decays as a non-universal power law, S_N(t) is proportional to t^{-beta_N}, with the decay exponent beta_N proportional to ln N. The crossover behavior as a function of the relative diffusivities of the lions and the lamb is also discussed. When N--->oo, the lamb survival probability exhibits a log-normal decay, exp(-ln^2 t).

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