Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions
Abstract
The survival probability, SN(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, SN(t) is proportional to t-betaN, with the decay exponent betaN 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(-ln2 t).
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.