Poisson-Nernst-Planck (PNP) systems are considered in the case of vanishing permanent charge. A detailed case study, based on natural categories described by system boundary conditions and flux, is carried out via simulation and singular perturbation analysis. Our results confirm the rich structure inherent in these systems. A natural quantity, the quotient of the Debye and characteristic lengt...

In this paper we study the a priori error estimates of finite element method for the system of time-dependent Poisson–Nernst–Planck equations, and for the first time, we obtain its optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm,with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semia...

scott and szewczyk in technometrics, 2001, have introduced a similarity measure for twodensities f1 and f2 , by1, 21 21 1 2 2( , ), ,f fsim f ff f f f< >=< >< >wheref1, f2 f1(x, θ1)f2(x, θ2)dx.+∞−∞< >=∫sim(f1, f2) has some appropriate properties that can be suitable measures for the similarity of f1 and f2 .however, due to some restrictions on the value of parameters and the kind of densities, ...

We derive a one-dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of a symmetric binary electrolyte in channels whose section is nanometric and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs diffusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the wa...

The reduced 1D Poisson-Nernst-Planck (PNP) model of artificial nanopores in the presence of a permanent charge on the channel wall is studied. More specifically, we consider the limit where the channel length exceed much the Debye screening length and channel’s charge is sufficiently small. Ion transport is described by the nonequillibrium steady-state solution of the PNP system within a singul...

We have studied single-stranded DNA translocation through a semiconductor membrane consisting of doped p and n layers of Si forming a p-n-junction. Using Brownian dynamics simulations of the biomolecule in the self-consistent membrane-electrolyte potential obtained from the Poisson-Nernst-Planck model, we show that while polymer length is extended more than when its motion is constricted only b...

The Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions (PNP-FBV) describe ion transport Faradaic reactions, and have applications in a number of fields. In this article, we develop an adaptive time-stepping scheme for the solution PNP-FBV system based on two methods: fully-implicit (VSBDF2) method, semi-implicit (VSSBDF2) method. We present simulations un...

Recent results of X-Ray crystallography have provided important information for functional studies of membrane ion channels based on computer simulations. Because of the large number of atoms that constitute the channel proteins, it is prohibitive to approach functional studies using molecular dynamic methods. To overcome the current computational limit we propose a novel approach based on the ...