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NCTS Interdisciplinary Research Seminar
15:30 - 16:30, July 3, 2018 (Tuesday)
Room 201, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 201室)
Geometric Singular Perturbation Theory for Poisson-Nernst-Planck Models
Weishi Liu (University of Kansas)


In this talk, I will briefly review some basic theories (Gouy-Chapman theory and Debye-H\"{u}ckel theory) from the Poisson-Boltzmann theory for electrolyte mixtures and indicate why new mathematical methods are needed to handle Poisson-Nernst-Planck (PNP) models for ionic flow through membrane channels – a nonlinear problem with multi-scales and multiple physical parameters.
I will then discuss a dynamical system approach, or more precisely, a geometric singular perturbation framework for an analysis of PNP models. The
framework relies heavily on the general theory of geometric singular perturbation and, most importantly, on two special structures of PNP systems–
one for each limiting behavior from the multi-scale structure. As a result, the analysis within this framework results in a governing (algebraic) system for the boundary value problem of PNP model. A promising aspect of the governing system is that it involves “all” relevant physical parameters of PNP model, which is crucial for the present problem since “everything interacts with everything else”.


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 (C) 2018 National Center for Theoretical Sciences