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arXiv · 0810.1565

Capture of particles undergoing discrete random walks

Robert M. Ziff·Satya N. Majumdar·Alain Comtet
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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.

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Robert M. Ziff, Satya N. Majumdar, Alain Comtet. 2009-04-28. Capture of particles undergoing discrete random walks. https://doi.org/10.1063/1.3137062

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