Capture of particles undergoing discrete random walks
Disordered Systems and Neural Networks
2015-05-13 v2 Statistical Mechanics
Abstract
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.
Cite
@article{arxiv.0810.1565,
title = {Capture of particles undergoing discrete random walks},
author = {Robert M. Ziff and Satya N. Majumdar and Alain Comtet},
journal= {arXiv preprint arXiv:0810.1565},
year = {2015}
}
Comments
minor corrections and some elaboration. In press, Journal of Chemical Physics