Eur. Phys. J. Plus (2017) 132: 382
https://doi.org/10.1140/epjp/i2017-11668-4

Regular Article

Relationship between flux and concentration gradient of diffusive particles with the usage of random walk model

Physics Department, Kazan Federal University, 4200008, Kazan, Russia

^* e-mail: marov514@gmail.com

Received: 9 June 2017
Accepted: 25 July 2017
Published online: 7 September 2017

Abstract

The fundamental solutions of the diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences between fundamental solutions, flows and concentration gradients were studied. The new modified non-local diffusion equation of the telegrapher type with correction function is suggested. It contains only microparameters of the random walk problem.