Volume 127, Number 2, July 2019
|Number of page(s)||6|
|Published online||02 September 2019|
Cauchy formulas for linear transport in random media
DEN-Service d'études des réacteurs et de mathématiques appliquées (SERMA), CEA, Université Paris-Saclay F-91191, Gif-sur-Yvette, France
Received: 13 May 2019
Accepted: 16 July 2019
In the context of linear transport in homogeneous non-stochastic media, the well-known Cauchy formulas express a remarkably elegant relation between the contributions to the angular flux within an arbitrary body due to particles starting from the body surface and those due to particles starting from the interior of the body. In this letter, we will extend these results to binary stochastic mixtures, a prototype class of random media that emerges in a broad spectrum of applications in physical and life sciences, ranging from hydrodynamical instabilities to tracer diffusion in biological tissues. In particular, for both quenched disorder and annealed disorder models we will establish generalized Cauchy-like formulas that appear to have a universal character and bear a close similarity to those previously derived for non-stochastic media.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.40.Fb – Random walks and Levy flights
© EPLA, 2019
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