Asymptotic Expansions of I-V Relations via a Poisson–Nernst–Planck System
From MaRDI portal
Publication:3624493
DOI10.1137/070691322zbMath1167.34361OpenAlexW2154030203MaRDI QIDQ3624493
Robert S. Eisenberg, Weishi Liu, Nicole Abaid
Publication date: 30 April 2009
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/070691322
Cell biology (92C37) Singular nonlinear boundary value problems for ordinary differential equations (34B16) Asymptotic expansions of solutions to ordinary differential equations (34E05) Physiological flow (92C35) Multiple scale methods for ordinary differential equations (34E13)
Related Items
A local approximation of fundamental measure theory incorporated into three dimensional Poisson-Nernst-Planck equations to account for hard sphere repulsion among ions ⋮ 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 ⋮ A new Poisson-Nernst-Planck model with ion-water interactions for charge transport in ion channels ⋮ 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 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 ⋮ Fractional Poisson-Nernst-Planck model for ion channels. I: Basic formulations and algorithms ⋮ Effects of ion sizes on Poisson–Nernst–Planck systems with multiple ions ⋮ 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 ⋮ Dynamics of classical Poisson-Nernst-Planck systems with multiple cations and boundary layers ⋮ Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson-Nernst-Planck Equations ⋮ Unconditional Positivity-Preserving and Energy StableSchemesforaReducedPoisson-Nernst-Planck System ⋮ A complete analysis of a classical Poisson-Nernst-Planck model for ionic flow ⋮ Second-order Poisson-Nernst-Planck solver for ion transport ⋮ Differential geometry based multiscale models ⋮ Small permanent charge effects on individual fluxes via Poisson-Nernst-Planck models with multiple cations ⋮ Finite Element Modeling of Biomolecular Systems in Ionic Solution ⋮ 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 ⋮ Dynamics of ionic flows via Poisson-Nernst-Planck systems with local hard-sphere potentials: competition between cations ⋮ 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