Diffusion in Narrow Channels Embedded on Curved Manifolds

In this chapter we extend the generalization of the Kalinay-Percus projection method for asymmetric channels. We project the anisotropic two-dimensional diffusion equation on a curved manifold into an effective one-dimensional generalized Fick-Jacobs equation that is modified according to the curvature of the surface. To have a complete description of this reduction, we also derive a general position-dependent effective diffusion coefficient and analyze a collection of systems having major symmetries.