Speaker: Jean-Luc Thiffeault
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.