Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. II: Numerics
type: Item
instance of: scholarly article
title: Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. II: Numerics
zbMATH Open document ID: 1329.34104
author: Weishi Liu
author: Xuemin Tu
author: Mingji Zhang
published in: Journal of Dynamics and Differential Equations
publication date: 2013-01-30T00:00:00Z
review text: In this paper, the one dimensional steady-state Poisson-Nernst-Planck (PNP) type model for ionic flow through membrane channels is considered. Improving the classical PNP models where ion species are treated as point charges, this model includes ionic interaction due to finite sizes of ion species modeled by hard sphere potential from the Density Functional Theory (DFT). The resulting problem is a singularly perturbed boundary value problem of an integro-differential system. It is investigated the ion size effect on the current-voltage (I-V) relations numerically, focusing on the case where two oppositely charged ion species are involved and only the hard sphere components of the excess chemical potentials are included. Two numerical tasks are considered. The first one is a numerical approach of solving the boundary value problem and obtaining I-V curves. The second task is to numerically detect two critical potential values \(V_c\) and \(V^c\) which existence was theoretically proved early. It is proposed an algorithm of numerical detection of \(V_c\) and \(V^c\) without using any analytical formulas but based on the defining properties and numerical I-V curves directly. Numerical values for \(V_c\) and \(V^c\) agree well with the analytical predictions. For a setting including a nonzero permanent charge in which case no analytic formula for the I-V relation is available, the proposed algorithm can still be applied to find \(V_c\) and \(V^c\) numerically. Part I, see J. Dyn. Differ. Equations 24, No. 4, 955--983 (2012; Zbl 1270.93011).
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 35J57
Mathematics Subject Classification ID: 35R09
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L11
Mathematics Subject Classification ID: 78A37
Mathematics Subject Classification ID: 82B31
Mathematics Subject Classification ID: 92C35
zbMATH DE Number: 6132840
zbMATH Keywords: ion flow
zbMATH Keywords: PNP-DFT
zbMATH Keywords: hard-sphere
zbMATH Keywords: I-V relation
zbMATH Keywords: critical potential
reviewed by: Vasile Dragan
MaRDI profile type: Publication
full work available at URL: s10884-012-9278-x
OpenAlex ID: W4246164144
cites work: Asymptotic Expansions of I-V Relations via a Poisson–Nernst–Planck System
cites work: Ion Flow through Narrow Membrane Channels: Part I
cites work: Ion Flow through Narrow Membrane Channels: Part II
cites work: Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Perturbation and Simulation Study
cites work: Inverse Problems Related to Ion Channel Selectivity
cites work: Discrete-state model of coupled ion permeation and fast gating in ClC chloride channels
cites work: Poisson–Nernst–Planck Systems for Ion Channels with Permanent Charges
cites work: Two- and three-dimensional Poisson--Nernst--Planck simulations of current flow through gramicidin A
cites work: A mathematical model for the hard sphere repulsion in ionic solutions
cites work: Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation
cites work: Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. I: Analysis
cites work: A BVP solver based on residual control and the Maltab PSE
cites work: Geometric Singular Perturbation Approach to Steady-State Poisson--Nernst--Planck Systems
cites work: One-dimensional steady-state Poisson-Nernst-Planck systems for ion channels with multiple ion species
cites work: Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Mathematical Study
cites work: On the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids
cites work: A Poisson–Nernst–Planck Model for Biological Ion Channels—An Asymptotic Analysis in a Three-Dimensional Narrow Funnel
cites work: Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels
cites work: Asymptotic Analysis of the Current-Voltage Curve of a pnpn Semiconductor Device
cites work: A Bifurcation Analysis of the One-Dimensional Steady-State Semiconductor Device Equations
DOI: 10.1007/S10884-012-9278-X
description: scientific article; zbMATH DE number 6132840