Analysis, Dynamics, and Applications Seminar

Analytic solution of the Poisson-Boltzmann distribution of ions in a solution for a 1d model: the Gouy-Chapman-Stern layer revisited for a biological cell

When

12:30 p.m., April 4, 2023

Where

A traditional model (1910) is the Gouy-Chapman model, which predicts the distribution of ions and the shape of a poential in a solution, assumed to be semi-infinite. This model, refined by Stern in 1924, takes into account the Debye length. We propose a variational formulation of the Poisson-Boltzmann system, both for electroneutral and non electroneutral cells. We prove the existence and uniqueness of a solution in the 1d setup (radial solutions in 2d and 3d are included), give ideas for the existence and uniqueness of a solution in higher dimension, and obtain an analytic solution in the 1d set-up for non electroneutral cells. This analytic solution relies on incomplete Jacobi elliptic functions, and the unique solution is obtained by solving a system of equations in $\R_+^2$ (two equations with two unknowns)

Joint work with Clair Poignar (Inria Bordeaux Sud Ouest)

Math, 402 and Zoom:  https://arizona.zoom.us/j/89568982253     Password:    applied