Outflow probability for drift--diffusion dynamics

Details Outflow probability for drift--diffusion dynamics Outflow probability for drift--diffusion dynamics

2006-03-22

arxiv.org/abs/cond-mat/0603579v3

International Journal of Theoretical Physics 46 (2007) 1542-1561

Physics

Condensed Matter

Statistical Mechanics

18 pages, 17 figures

Scientific paper

10.1007/s10773-006-9291-0

The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time probability density distribution taking into account reflecting boundary on left hand side and absorbing border on right hand side. This quantity is calculated from balance equation which follows from conservation of probability. At first, the initial--boundary--value problem is solved analytically in terms of eigenfunction expansion which relates to Sturm--Liouville analysis. The results are obtained for all possible values of drift (positive, zero, negative). As application we get the cumulative breakdown probability which is used in theory of traffic flow.

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