Extended Fick-Jacobs equation: variational approach.
We derive an extended Fick-Jacobs equation for the diffusion of noninteracting particles in a two- and symmetric three-dimensional channels of varying cross section A(x), using a variational approach. The result is a diffusion differential equation of second order in only one space (longitudinal) coordinate. This equation is tested on the task of calculating the stationary flux through a hyperboloidal tube, and its solution is compared with that of other methods.
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
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Percus