Related Experiment Video
Updated: Aug 8, 2025

Finite Element Modelling of a Cellular Electric Microenvironment
Published on: May 18, 2021
Mathematical Analysis on Current-Voltage Relations via Classical Poisson-Nernst-Planck Systems with Nonzero Permanent
Yiwei Wang1, Lijun Zhang1, Mingji Zhang1,2
1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
Abstract:
We focus on a quasi-one-dimensional Poisson-Nernst-Planck model with small permanent charges for ionic flows of two oppositely charged ion species through an ion channel. Of particular interest is to examine the dynamics of ionic flows in terms of I-V (current-voltage) relations with boundary layers due to the relaxation of neutral conditions on boundary concentrations. This is achieved by employing the regular perturbation analysis on the solutions established through geometric singular perturbation analysis. Rich dynamics are observed, particularly, the nonlinear interplays among different physical parameters are characterized. Critical potentials are identified, which play critical roles in the study of ionic flows and can be estimated experimentally. Numerical simulations are performed to further illustrate and provide more intuitive understandings of our analytical results.
Related Concept Videos
Poisson's And Laplace's Equation
Electrostatic Boundary Conditions
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
P-N junction
Calculations of Electric Potential II
Consider a...
Kirchhoff's Current Law
Kirchhoff's Current Law is based on the principle of charge conservation. It states that at any node (a point where two or more circuit elements meet) in an...
Boundary Conditions for Current Density

