Jean-Luc Thiffeault : A Brownian rod in a lattice of obstacles

Posted by Ian Tobasco , part of the Analysis and Applied Mathematics Seminar.

At

Sept. 20, 2021, 4 p.m.

In

636 SEO

Abstract

A Brownian rod is a long, thin particle undergoing translational and rotational diffusion, due for instance to thermal fluctuations in an ambient fluid.  We consider such a rod in a regular lattice of point obstacles.  The rod interacts with the obstacles, in the sense that it reflects off of them.  An interesting question is then to compute the effective diffusion constant for the rod.  I will show how this problem can be partially mapped to a heat conduction problem in a porous medium solved by Rayleigh, and discuss other limits of interest, such as that of anisotropic diffusivities.  I will also briefly discuss ongoing work for a swimming organism.  This is joint work with Hongfei Chen and Ziheng Zhang.