In this paper, a stationary one-dimensional Poisson-Nernst-Planck model with permanent charge is studied under the assumption that <em>n</em> - 1 positively charged ion species have the same valence and th...In this paper, a stationary one-dimensional Poisson-Nernst-Planck model with permanent charge is studied under the assumption that <em>n</em> - 1 positively charged ion species have the same valence and the permanent charge is small. By expanding the singular solutions of Poisson-Nernst-Planck model with respect to small permanent charge, the explicit formulae for the zeroth order approximation and the first order approximation of individual flux can be obtained. Based on these explicit formulae, the effects of small permanent charges on individual flux are investigated.展开更多
PNP models with an arbitrary number of positively charged ion species and one negatively charged ion species are studied in this paper under the assumption that positively charged ion species have the same valence and...PNP models with an arbitrary number of positively charged ion species and one negatively charged ion species are studied in this paper under the assumption that positively charged ion species have the same valence and the permanent charge is a piecewise constant function. The permanent charge plays the key role in many functions of an ion channel, such as selectivity and gating. In this paper, using the geometric singular perturbation theory, a flux ratio independent of the permanent charge is proved.展开更多
文摘In this paper, a stationary one-dimensional Poisson-Nernst-Planck model with permanent charge is studied under the assumption that <em>n</em> - 1 positively charged ion species have the same valence and the permanent charge is small. By expanding the singular solutions of Poisson-Nernst-Planck model with respect to small permanent charge, the explicit formulae for the zeroth order approximation and the first order approximation of individual flux can be obtained. Based on these explicit formulae, the effects of small permanent charges on individual flux are investigated.
文摘PNP models with an arbitrary number of positively charged ion species and one negatively charged ion species are studied in this paper under the assumption that positively charged ion species have the same valence and the permanent charge is a piecewise constant function. The permanent charge plays the key role in many functions of an ion channel, such as selectivity and gating. In this paper, using the geometric singular perturbation theory, a flux ratio independent of the permanent charge is proved.
