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

TL;DR

This paper studies the survival probability of a diffusing prey in the presence of multiple diffusing predators in one dimension, revealing non-universal power-law decay and log-normal decay behaviors.

Contribution

It provides a detailed analysis of the survival probability dynamics of a prey among multiple predators, including crossover behaviors based on diffusivity ratios.

Findings

Survival probability decays as t^{-beta_N} with beta_N proportional to ln N.

For large N, survival probability exhibits a log-normal decay, exp(-ln^2 t).

Crossover behavior depends on the relative diffusivities of prey and predators.

Abstract

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).