Collision statistics for random flights with anisotropic scattering and absorption

Details Collision statistics for random flights with anisotropic scattering and absorption Collision statistics for random flights with anisotropic scattering and absorption

2011-10-04

arxiv.org/abs/1110.0789v1

Phys. Rev. E 84, 061130 (2011)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 5 figures

Scientific paper

10.1103/PhysRevE.84.061130

For a broad class of random walks with anisotropic scattering kernel and absorption, we derive explicit formulas that allow expressing the moments of the collision number $n_V$ performed in a volume $V$ as a function of the particle equilibrium distribution. Our results apply to arbitrary domains $V$ and boundary conditions, and allow assessing the hitting statistics for systems where the typical displacements are comparable to the domain size, so that the diffusion limit is possibly not attained. An example is discussed for one-dimensional (1d) random flights with exponential displacements, where analytical calculations can be carried out.

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