Asymptotic Analysis of Steric Poisson-Nernst-Planck Model for Multi-Species Ions
Date Issued
2014
Date
2014
Author(s)
Chang, Wei-Chan
Abstract
Poisson-Nernst-Planck system models ionic flow in ion channels. Differ from basic Poisson-Nernst-Planck, steric Poisson-Nernst-Planck accurately describes the behaviour of ions for size effect terms are added into steric Poisson-Nernst-Planck in order to make a description of the fact that ions complete to each other to hold exact spaces in ion channel. The goal in this paper is to analyse the asymptotic behaviour we may say asymptotic stability of steric Poisson-Nernst-Planck. In the text, We make use of the skill for eigenvalues including positive semi-definite pencil in linear algebra to simplify the difficulties in the analysis. More important thing is that the way in this paper is easier and extends more cases than one which is changing variable in former literature. On the other hand, we also write some programs to simulate various situations we encounter. Though we get lots of numerical results; however, all of them support the conclusions in the analysis. Furthermore, in the future, the further goal is to take advantage of steric Poisson-Nernst-Planck systems to modify Hodgkin-Huxley equations which describe the behaviour of neuron.
Subjects
具位阻效應之普瓦松-能斯特-普朗克模型
漸近穩定
特徵值
半正定理論
電導
霍奇金 - 赫胥黎模型
Type
thesis
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