Poisson-Nernst-Planck模型下零电流离子流中浓度几何平均值和剩余永久电荷
Geometric Mean of Concentrations and Reversal Permanent Charge in Zero-Current Ionic Flows via Poisson-Nernst-Planck Models
摘要：
这项工作检查的几何平均浓度和它的行为在各种情况下，以及反转永久电荷的问题，在X射线衍射中看到的电荷共享。观测结果是从使用经典Poisson-Nernst-Planck模型的几何奇异扰动分析建立的分析结果中获得的。对于多个离子种类的离子混合物，Mofidi和Liu [{ \em SIAM J. Appl. Math. { \bf 80}（2020），1908-1935}]以具有不等扩散常数的两个离子种类为中心，以获得用于确定反转电势和反转永久电荷的系统。他们研究了反转电位问题及其对扩散系数、膜电位、膜浓度等的依赖性。在这里，我们使用相同的方法来研究反转永久电荷的对偶问题及其对其他条件的依赖性。我们考虑两个离子物种的正电荷和负电荷，即Ca $^+$和Cl $^-$，以确定特定的条件下，永久电荷是唯一的。此外，我们调查的行为的几何平均浓度的不同值的跨膜电位和永久电荷。
英文摘要：
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.
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