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Applied Mathematics Colloquium

Joseph Jerome, Northwestern & George Washington Universities


Mathematics/Psychology : TBD

Date & Time

September 8, 2014, 12:00 am1:00 am


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.