# Applied Mathematics Colloquium

### Joseph Jerome, Northwestern & George Washington Universities

Location

Mathematics/Psychology : TBD

Date & Time

September 8, 2014, 12:00 am – 1:00 am

Description

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.

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