title: Mapping of diffusion in a channel with abrupt change of diameter.
abstract: Mapping of the diffusion equation in a channel of varying cross section onto the longitudinal coordinate is already a well studied procedure for a slowly changing radius. We examine here the mapping of diffusion in a channel with abrupt change of diameter. In two dimensions, our considerations are based on solution of the exactly solvable geometry with abruptly doubled width at x=0. We verify the surmise of Berezhkovskii [J. Chem. Phys. 131, 224110 (2009)] that one-dimensional diffusion behaves as free in such channels everywhere except at the point of change, which looks like a local trap for the particles. Applying the method of "sewing" of solutions, we show that this picture is valid also for three-dimensional symmetric channels.
authors.affiliation: Institute of Physics, Slovak Academy of Sciences, Dúbravska cesta 9, 84511 Bratislava, Slovakia.
authors.forename: Pavol
authors.initials: P
authors.lastname: Kalinay
authors.forename: Jerome K
authors.initials: JK
authors.lastname: Percus