Applied Mathematics Colloquium
Dr. Joseph Jerome, Northwestern and GW Universities
Friday, October 10, 2014 · 12 - 1 PM
Title: Classical Ion Transport Models Beyond PNP for Biological Applications
Abstract: The talk will survey models, results, and questions related
to generalizations of PNP (Poisson-Nernst-Planck) theory. Original PNP
theory modeled the flow of anions and cations within so-called ion
channels in cell membranes. The mathematical PNP system, in analogy
with the transport of electrons and holes in semiconductors, consists
of an electric potential equation, and drift-diffusion equations for
the carriers. Both the steady and unsteady models are of interest.
This talk will discuss extensions beyond PNP modeling, and will survey
several such extended models: (1) the Rubinstein model (PNP, coupled
to Navier-Stokes); (2) the hydrodynamic model (a three moment model);
(3) a gating model; (4) a recent `crowded ions' model developed by
Chun Lui at Penn State. Some of the fundamental analytical work on the
original drift-diffusion model was carried out by Tom Seidman in the
1980s. The present talk focuses on the last two decades, and
emphasizes work with which the speaker is most familiar. A version of
the talk was presented at the Fields Institute in July.