2020/09/21 by Hamid Mofidi, Mofidi, Hamid
Engineering · Physics and Astronomy · #34N05 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #NMR spectroscopy and applications #Phase Equilibria and Thermodynamics #Power Transformer Diagnostics and Insulation #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2009.09564
openalex publication_date 2020/09/21 · openalex created_date 2020/09/25 · openalex updated_date 2026/07/28
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.