Center for Nonlinear Phenomena and Complex
Systems, Université Libre de Bruxelles 1050 Bruxelles, Belgium
Corresponding author: email@example.com
Accepted: 19 May 2003
We consider the general problem of the first-passage distribution of particles whose displacements are subject to time delays. We show that this problem gives rise to a propagation-dispersion equation which is obtained as the large-distance (hydrodynamic) limit of the exact microscopic first-visit equation. The propagation-dispersion equation should be contrasted with the advection-diffusion equation as the roles of space and time are reversed, hence the name temporal diffusion, which is a generic behavior encountered in an important class of systems.
PACS: 05.60.-k – Transport processes / 02.50.Ey – Stochastic processes / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
© EDP Sciences, 2003