@Article{CiCP-30-2,
author = {Weizhang, Huang and Weishi, Liu and Yufei, Yu},
title = {Permanent Charge Effects on Ionic Flow: A Numerical Study of Flux Ratios and Their Bifurcation},
journal = {Communications in Computational Physics},
year = {2021},
volume = {30},
number = {2},
pages = {486--514},
abstract = {<p style="text-align: justify;">Ionic flow carries electrical signals for cells to communicate with each other.
The permanent charge of an ion channel is a crucial protein structure for flow properties while boundary conditions play a role of the driving force. Their effects on flow
properties have been analyzed via a quasi-one-dimensional Poisson-Nernst-Planck
model for small and relatively large permanent charges. The analytical studies have
led to the introduction of flux ratios that reflect permanent charge effects and have a
universal property. The studies also show that the flux ratios have different behaviors
for small and large permanent charges. However, the existing analytical techniques
can reveal neither behaviors of flux ratios nor transitions between small and large permanent charges. In this work we present a numerical investigation on flux ratios to
bridge between small and large permanent charges. Numerical results verify the analytical predictions for the two extremal regions. More significantly, emergence of non-trivial behaviors is detected as the permanent charge varies from small to large. In
particular, saddle-node bifurcations of flux ratios are revealed, showing rich phenomena of permanent charge effects by the power of combining analytical and numerical
techniques. An adaptive moving mesh finite element method is used in the numerical
studies.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2020-0057},
url = {https://global-sci.com/article/79575/permanent-charge-effects-on-ionic-flow-a-numerical-study-of-flux-ratios-and-their-bifurcation}
}