Propagation-Dispersion Equation

摘要

A {\em propagation-dispersion equation} is derived for the first passagedistribution function of a particle moving on a substrate with time delays. Theequation is obtained as the continuous limit of the {\em first visit equation},an exact microscopic finite difference equation describing the motion of aparticle on a lattice whose sites operate as {\em time-delayers}. Thepropagation-dispersion equation should be contrasted with theadvection-diffusion equation (or the classical Fokker-Planck equation) as itdescribes a dispersion process in {\em time} (instead of diffusion in space)with a drift expressed by a propagation speed with non-zero bounded values. The{\em temporal dispersion} coefficient is shown to exhibit a form analogous toTaylor's dispersivity. Physical systems where the propagation-dispersionequation applies are discussed.