DIFFUSION APPROACH TO THE LINEAR POISSON-BOLTZMANN EQUATION

The linear Poisson-Boltzmann equation (LPBE) is mapped onto a transien t diffusion problem in which the charge density becomes an initial dis tribution, the dielectric permittivity plays the role of either a diff usion coefficient or a potential of interaction and screening becomes a sink term. This analogy can be useful in two ways. From the analytic al point of view, solutions of the LPBE with seemingly different funct ional forms are unified as Laplace transforms of the fundamental Gauss ian solution for diffusion. From the numerical point of view, a first off-grid algorithm for solving the LPBE is constructed by running Brow nian trajectories in the presence of scavenging. (C) 1998 Elsevier Sci ence B.V.