{"title":"Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations","authors":"Zhen Chao, Weihua Geng, Robert Krasny","doi":"10.1007/s10825-023-02092-y","DOIUrl":null,"url":null,"abstract":"<div><p>An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green’s 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by a combination of midpoint and trapezoid rules, and the resulting algebraic equations are solved by Gummel iteration. Numerical tests for electroneutral and non-electroneutral systems demonstrate the method’s 2nd order accuracy and ability to resolve sharp boundary layers. The method is applied to a 1D model of the K<span>\\(^+\\)</span> ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results.</p></div>","PeriodicalId":620,"journal":{"name":"Journal of Computational Electronics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10825-023-02092-y.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Electronics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10825-023-02092-y","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green’s 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by a combination of midpoint and trapezoid rules, and the resulting algebraic equations are solved by Gummel iteration. Numerical tests for electroneutral and non-electroneutral systems demonstrate the method’s 2nd order accuracy and ability to resolve sharp boundary layers. The method is applied to a 1D model of the K\(^+\) ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results.
期刊介绍：
he Journal of Computational Electronics brings together research on all aspects of modeling and simulation of modern electronics. This includes optical, electronic, mechanical, and quantum mechanical aspects, as well as research on the underlying mathematical algorithms and computational details. The related areas of energy conversion/storage and of molecular and biological systems, in which the thrust is on the charge transport, electronic, mechanical, and optical properties, are also covered.
In particular, we encourage manuscripts dealing with device simulation; with optical and optoelectronic systems and photonics; with energy storage (e.g. batteries, fuel cells) and harvesting (e.g. photovoltaic), with simulation of circuits, VLSI layout, logic and architecture (based on, for example, CMOS devices, quantum-cellular automata, QBITs, or single-electron transistors); with electromagnetic simulations (such as microwave electronics and components); or with molecular and biological systems. However, in all these cases, the submitted manuscripts should explicitly address the electronic properties of the relevant systems, materials, or devices and/or present novel contributions to the physical models, computational strategies, or numerical algorithms.
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