学术报告

报告题目：Competition between cations via Poisson-Nernst-Planck systems with local excess chemical potentials: Effects from finite ion sizes

报告人：张明吉 博士（美国新墨西哥矿业理工学院）

报告时间：2018年6月9日上午11:20-12:00

报告地点：25教14楼报告厅

报告摘要：We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flows through a membrane channel. We consider {\em three} ion species, two positively charged with the same valence and one negatively charged, and assume zero permanent charge. Bikerman's local hard-sphere potential is included in the model to account for finite ion size effects. The problem is treated as a boundary value problem of a singularly perturbed differential system. Under the framework of a geometric singular perturbation theory, together with specific structures of this concrete model, the existence and (local) uniqueness of solutions to the boundary value problem for small ion sizes is established. Furthermore, treating the ion sizes as small parameters, we derive an approximation of individual fluxes, from which one can further study the qualitative properties of ionic flows and extract concrete information directly related to biological measurements. Of particular interest is the competition between two cations (positively charged ion species) due to finite ion sizes, which is closely related to selectivity phenomena of open ion channels with given protein structures. Furthermore, we are able to characterize the distinct effects of the nonlinear interplays between physical parameters, such as ion sizes, diffusion coefficients, boundary concentrations and boundary potentials. This is the novelty of our work. We believe this work will be useful for future numerical studies and stimulate further analytical studies of ionic flows concerning the selectivity of cations.

报告人简介：张明吉博士2013年获得美国堪萨斯大学数学系博士学位，随后在美国密歇根州立大学做博士后。2015在美国新墨西哥矿业理工学院任副教授。其主要研究领域包括几何奇异摄动理论及其在Poisson-Nernst-Planck模型上的应用、生物学上的多尺度分析及非线性偏微分方程的动力行为。在《SIAM J. on Applied Dynamical Systems》、《SIAM J. on Applied Mathematics》、《Rocky Mountain J. Mathematics》、《J. Dynamics and Differential Equations》、《J. Differential Equations》、《Advances in Computational Mathematics》、《Communications in Mathematical Sciences》及《Discrete and Continue Dynamical Systems》等国际数学杂志发表论文二十余篇。