# *CANCELLED* Shape matters: Homogenization for a confined Brownian microswimmer

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*CANCELLED* Jean-Luc Thiffeault, University of Wisconsin-Madison
Fine Hall 322

*CANCELLED*

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.