论文标题
浓度和逆转永久性电荷的几何平均值通过Poisson-Nernst-Planck模型
Geometric Mean of Concentrations and Reversal Permanent Charge in Zero-Current Ionic Flows via Poisson-Nernst-Planck Models
论文作者
论文摘要
这项工作研究了在各种情况下浓度及其行为的几何平均值，以及逆向永久性电荷问题，即X射线衍射中看到的电荷共享。观察结果是从使用经典泊松 - 尼尔斯特 - 宾夕法尼亚州模型的几何奇异扰动分析建立的分析结果获得的。 对于多种离子物种Mofidi和Liu的离子混合物[{\ Em Siam J. Appl。数学。 {\ bf 80}（2020），1908-1935}]以不等扩散常数为中心，以获取一个系统来确定逆转电势和逆转永久电荷的系统。他们研究了逆转潜在问题及其对扩散系数，膜电位，膜浓度等的依赖。在这里，我们使用相同的方法来研究逆转永久性电荷的双重问题及其对其他条件的依赖。我们考虑两种具有正电荷和负电荷的离子物种，例如ca $^+$和cl $^ - $，以确定永久性电荷独特的特定条件。此外，我们研究了跨膜电位和永久电荷的各种值的浓度的几何平均值的行为。
This work examines the geometric mean of concentrations and its behavior in various situations, as well as the reversal permanent charge problem, the charge sharing seen in x-ray diffraction. Observations are obtained from analytical results established using geometric singular perturbation analysis of classical Poisson-Nernst-Planck models. For ionic mixtures of multiple ion species Mofidi and Liu [{\em SIAM J. Appl. Math. {\bf 80} (2020), 1908-1935}] centered two ion species with unequal diffusion constants to acquire a system for determining the reversal potential and reversal permanent charge. They studied the reversal potential problem and its dependence on diffusion coefficients, membrane potential, membrane concentrations, etc. Here we use the same approach to study the dual problem of reversal permanent charges and its dependence on other conditions. We consider two ion species with positive and negative charges, say Ca$^+$ and Cl$^-$, to determine the specific conditions under which the permanent charge is unique. Furthermore, we investigate the behavior of geometric mean of concentrations for various values of transmembrane potential and permanent charge.
