时间：2018年6月29日(星期五) 16:00
地点：旗山校区理工楼北楼601报告厅
主办：数学与信息学院、福建省分析数学及应用重点实验室
主讲：美国新墨西哥矿业理工学院 张明吉博士
专家简介：张明吉，博士，目前就职于美国新墨西哥矿业理工学院（New Mexico Institute of Mining and Technology）。2013年毕业于美国堪萨斯大学，获博士学位；2013-2015年跟随著名数学家Peter W. Bates做博士后研究。研究方向为非线性动力系统、微分方程及其应用，特别是在Poisson-Nernst-Planck（PNP）和发展生物学（developing biology）中的应用。研究主要工具是非线性动力系统不变流形理论发展起来的几何奇异摄动理论。在研究PNP理论中，特别是对离子流的动力学行为的研究，做出了突出贡献，得到了医学界的高度认可和评价。已在《J. Differential Equations》、《SIAM J. Appl. Math.》、《SIAM J. Appl. Dyn. Syst.》等发表论文20余篇。所发表论文2013年至今已被引用110次，其中他引90次。
报告摘要：We analyze a one-dimensional Poisson-Nernst-Planck type model for ionic flow through a membrane channel with oppositely charged ion species. A local hard-sphere potential is included in the model to account for ion size effects on ionic flows. The model problem is treated as a boundary value problem of a singularly perturbed differential system. Our analysis is based on the geometric singular perturbation theory but, most importantly, on specific structures of this concrete model. The existence of solutions to the boundary value problem for small ion sizes is established and, treating the ion sizes as small parameters, we also derive approximations of the individual fluxes, the I-V (current-voltage) relation and identify eight critical potentials or voltages for ion size effects. Important scaling laws of I-V relations and critical potentials in boundary concentrations are obtained. The flow properties of interest depend on multiple physical parameters such as boundary conditions (boundary concentrations and boundary potentials) and diffusion coefficients, in addition to ion sizes and ion valences. For the relatively simple setting and assumptions of the model in this paper, we are able to characterize, almost completely, the distinct effects of the nonlinear interplay between these physical parameters.