Europhys. Lett., 61 (2) , pp. 168-173 (2003)
An invariance property of diffusive random walksS. Blanco and R. Fournier
Laboratoire d'Energétique, Université Paul Sabatier 118 route de Narbonne, 31062 Toulouse Cedex 4, France
(Received 28 June 2002; accepted in final form 21 October 2002)
Starting from a simple animal-biology example, a general, somewhat counter-intuitive property of diffusion random walks is presented. It is shown that for any (non-homogeneous) purely diffusing system, under any isotropic uniform incidence, the average length of trajectories through the system (the average length of the random walk trajectories from entry point to first exit point) is independent of the characteristics of the diffusion process and therefore depends only on the geometry of the system. This exact invariance property may be seen as a generalization to diffusion of the well-known mean-chord-length property (CASE K. M. and ZWEIFEL P. F., Linear Transport Theory (Addison-Wesley) 1967), leading to broad physics and biology applications.
05.60.Cd - Classical transport.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
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