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Mathematical Biology Colloquium Title: Nonlinear Poisson-Nernst- Planck Equations for Ion Flux Through Con ned Geometries Time: 3:00 PM - 4:00 PM Place: C304 WH Speaker: Marie-Therese Wolfram Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences Abstract: The mathematical modeling and simulation of ion transport trough biological and synthetic channels is a challenging problem, with direct application in biophysics, physiology and chemistry. At least two major effects should be taken into account in mathematical models: the electrostatic interaction of ions and the effects due to size exclusion in narrow regions. While mathematical models and methods for electrostatic interactions are well-developed, less is known about the appropriate macroscopic modeling of size exclusion effects. Recently several papers proposed various approaches for including size exclusion effects into entropies, in equilibrium as well as off equilibrium. In this talk we present a generalization of the entropy due to size exclusion, which is based on the modi cation of the mobilities. We discuss a simple model derived from a self-consisted random walk and investigate its stationary solutions as well as the computation of conductance. Numerical simulations illustrate the behavior of this nonlinear Poisson-Nernst-Planck (PNP) model in high density situations, in which we observe saturation effects not covered by the classical PNP equations.