Capture of particles undergoing discrete random walks

Details Capture of particles undergoing discrete random walks Capture of particles undergoing discrete random walks

2008-10-09

arxiv.org/abs/0810.1565v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

minor corrections and some elaboration. In press, Journal of Chemical Physics

Scientific paper

It is shown that particles undergoing discrete-time jumps in 3D, starting at a distance r0 from the center of an adsorbing sphere of radius R, are captured with probability (R - c sigma)/r0 for r0 much greater than R, where c is related to the Fourier transform of the scaled jump distribution and sigma is the distribution's root-mean square jump length. For particles starting on the surface of the sphere, the asymptotic survival probability is non-zero (in contrast to the case of Brownian diffusion) and has a universal behavior sigma/(R sqrt(6)) depending only upon sigma/R. These results have applications to computer simulations of reaction and aggregation.

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