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

Abstract

© 2017, Società Italiana di Fisica and Springer-Verlag GmbH Germany. 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.