Shape matters: Homogenization for a confined Brownian microswimmer

Shape matters: Homogenization for a confined Brownian microswimmer

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Jean-Luc Thiffeault, University of Wisconsin-Madison

Please note that this seminar will take place online via Zoom. You can connect to this seminar via the following link:

https://princeton.zoom.us/j/9148065146

https://www.youtube.com/watch?v=B0GNtFApUQ8&feature=youtu.be


We consider a simple model of a two-dimensional microswimmer with fixed swimming speed. The direction of swimming changes according to a Brownian process, and the swimmer interacts with solid boundaries.The shape of the swimmer determines the range of allowable values that its degrees of freedom can assume --- its configuration space. Using natural assumptions about reflection of the swimmer at boundaries, we compute the swimmer's invariant distribution across a channel consisting of two parallel walls. We then solve the mean reversal time problem, which is the expected time taken for the swimmer to completely reverse direction in the channel. A homogenization theory approach then connects the mean reversal time to the effective diffusion constant of the swimmer's large scale motion.

This is joint work with Hongfei Chen.