Kalinay and Percus Projection Method

In this chapter, we introduce the projection method, first presented by P. Kalinay and J. K. Percus. We found the enhanced Fick-Jacobs operator in differential form for a quasi-one-dimensional asymmetric two-dimensional channel with a curved midline and varying width along the longitudinal coordinate, as well as for a three-dimensional symmetric tube. The reduction of axial diffusion in two-dimensional channels and three-dimensional tubes to the effective one-dimensional description in terms of the modified Fick-Jacobs equation is applicable when the channel width variation rate, or radius variation rate, does not exceed unity.