Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Perturbation and Simulation Study

DOI10.1137/S0036139995312149zbMath0874.34018OpenAlexW2047841961MaRDI QIDQ4337686

Joseph W. Jerome, Robert S. Eisenberg, Victor Barcilon, Duan-Pin Chen

Publication date: 26 May 1997

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036139995312149

zbMATH Keywords

simulationsingular perturbation solutionboundary layer solutioninterior solutionPoisson-Nernst-Planck systemscategories of boundary conditions

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Nonlinear ordinary differential equations and systems (34A34) Biophysics (92C05) Singular perturbations of ordinary differential equations (34D15) Motion of charged particles (78A35) Physiological flow (92C35) Numerical analysis in abstract spaces (65J99)

Related Items (54)

Modeling the response of polymer-ionic liquid electromechanical actuators ⋮ One-dimensional steady-state Poisson-Nernst-Planck systems for ion channels with multiple ion species ⋮ Qualitative properties of ionic flows via Poisson-Nernst-Planck systems with Bikerman's local hard-sphere potential: ion size effects ⋮ Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes. I: Finite element solutions ⋮ The time decay rates of the classical solution to the Poisson-Nernst-Planck-Fourier equations in \(\mathbb{R}^3\) ⋮ Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations ⋮ Non-localness of excess potentials and boundary value problems of Poisson-Nernst-Planck systems for ionic flow: a case study ⋮ Boundary layer effects on ionic flows via Poisson-Nernst-Planck systems with nonuniform ion sizes ⋮ Geometric singular approach to Poisson-Nernst-Planck models with excess chemical potentials: ion size effects on individual fluxes ⋮ Ion size effects on individual fluxes via Poisson-Nernst-Planck systems with Bikerman's local hard-sphere potential: analysis without electroneutrality boundary conditions ⋮ Asymptotic Analysis on Dielectric Boundary Effects of Modified Poisson--Nernst--Planck Equations ⋮ Poisson-Nernst-Planck systems for narrow tubular-like membrane channels ⋮ Nanoscale Poiseuille flow of charged particles ⋮ Exponential Decay Estimates for the Stability of Boundary Layer Solutions to Poisson--Nernst--Planck Systems: One Spatial Dimension Case ⋮ Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. I: Analysis ⋮ Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. II: Numerics ⋮ Existence and local uniqueness of classical Poisson-Nernst-Planck systems with multi-component permanent charges and multiple cations ⋮ Dynamics of Poisson-Nernst-Planck Systems and Ionic Flows Through Ion Channels: A Review ⋮ Finite ion size effects on ionic flows via Poisson-Nernst-Planck systems: higher order contributions ⋮ Flux ratios for effects of permanent charges on ionic flows with three ion species: new phenomena from a case study ⋮ Individual Flux Study via Steady-State Poisson--Nernst--Planck Systems: Effects from Boundary Conditions ⋮ Asymptotic expansions and numerical simulations of I-V relations via a steady state Poisson-Nernst-Planck system ⋮ Reversal Potential and Reversal Permanent Charge With Unequal Diffusion Coefficients via Classical Poisson--Nernst--Planck Models ⋮ Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels ⋮ Dynamics of classical Poisson-Nernst-Planck systems with multiple cations and boundary layers ⋮ An energy preserving finite difference scheme for the Poisson-Nernst-Planck system ⋮ Optimal decay rates of the solution for generalized Poisson-Nernst-Planck-Navier-Stokes equations in \(\mathbb{R}^3\) ⋮ Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson-Nernst-Planck Equations ⋮ A complete analysis of a classical Poisson-Nernst-Planck model for ionic flow ⋮ The charge conserving Poisson-Boltzmann equations: Existence, uniqueness, and maximum principle ⋮ Electro-osmotic transport in charged cylindrical micro- and nano-channels ⋮ Electrodiffusion near an ion channel and the effect of mobile buffer ⋮ Small permanent charge effects on individual fluxes via Poisson-Nernst-Planck models with multiple cations ⋮ Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients ⋮ Multi-physics models for bio-hybrid device simulation ⋮ Finite Element Modeling of Biomolecular Systems in Ionic Solution ⋮ Three-dimensional simulation of biological ion channels under mechanical, thermal and fluid forces ⋮ Parabolic-elliptic system modeling biological ion channels ⋮ Boundary layer effects on ionic flows via classical Poisson-Nernst-Planck systems ⋮ A flux ratio and a universal property of permanent charges effects on fluxes ⋮ Debye layer in Poisson-Boltzmann model with isolated singularities ⋮ A Generalized Poisson--Nernst--Planck--Navier--Stokes Model on the Fluid with the Crowded Charged Particles: Derivation and Its Well-Posedness ⋮ Finite Domain Effects in Steady State Solutions of Poisson--Nernst--Planck Equations ⋮ Mathematical studies of Poisson-Nernst-Planck model for membrane channels: finite ion size effects without electroneutrality boundary conditions ⋮ Flux ratios and channel structures ⋮ Geometric singular perturbation approach to Poisson-Nernst-Planck systems with local hard-sphere potential: studies on zero-current ionic flows with boundary layers ⋮ Mathematical analysis of Poisson–Nernst–Planck models with permanent charges and boundary layers: studies on individual fluxes ⋮ Effects on I–V relations from small permanent charge and channel geometry via classical Poisson–Nernst–Planck equations with multiple cations ⋮ Studies on reversal permanent charges and reversal potentials via classical Poisson-Nernst-Planck systems with boundary layers ⋮ Qualitative properties of zero-current ionic flows via Poisson-Nernst-Planck systems with nonuniform ion sizes ⋮ A positivity preserving and free energy dissipative difference scheme for the Poisson-Nernst-Planck system ⋮ Modified Poisson--Nernst--Planck Model with Coulomb and Hard-sphere Correlations ⋮ Homogenization of the Poisson--Nernst--Planck equations for Ion Transport in Charged Porous Media ⋮ Asymptotic analysis of charge conserving Poisson-Boltzmann equations with variable dielectric coefficients

This page was built for publication: Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Perturbation and Simulation Study