By application of matched asymptotic expansions, a simplified partial differential equation (PDE) model for the dynamic electrochemical processes occurring in the vicinity of a membrane, as ions selectively permeate across it, is formally derived from the Poisson-Nernst-Planck equations of electrochemistry. It is demonstrated that this simplified model reduces itself, in the limit of a long thi...

In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin (DG) schemes for solving the time-dependent system of Poisson--Nernst--Planck (PNP) equations, which has found much use in diverse applications. Our DG method with Euler forward time discretization is shown to preserve positivity cell averages at all steps. The numerical solutions then restored by a sc...

We demonstrated previously that the two continuum theories widely used in modeling biological ion channels give unreliable results when the radius of the conduit is less than two Debye lengths. The reason for this failure is the neglect of surface charges on the protein wall induced by permeating ions. Here we attempt to improve the accuracy of the Poisson-Boltzmann and Poisson-Nernst-Planck th...

In this paper we developed a Poisson–Nernst– Planck model of an ionic current flowing through a nanopore in a layered solid-state membrane made of a single highlydoped n-Si layer sandwiched between two thick oxide layers which we call the ionic transistor. We studied this layered membrane for a range of source-drain voltages while keeping the gate (the semiconductor membrane) voltage fixed at a...

Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with dif...

A computational model is presented for the simulation of three-dimensional electrodiffusion of ions. Finite volume techniques were used to solve the Poisson-Nernst-Planck equation, and a dual Delaunay-Voronoi mesh was constructed to evaluate fluxes of ions, as well as resulting electric potentials. The algorithm has been validated and applied to a generalized node of Ranvier, where numerical re...

We deal with the transmembrane sodium diffusion in a nerve. We study amathematical model of a nerve fibre in response to an imposed extracellular stimulus. The presentedmodel is constituted by a diffusion-drift vectorial equation in a bidomain, that is, two parabolic equations defined in each of the intraand extra-regions. This system of partial differential equations can be understood as a red...