Shape matters: a Brownian microswimmer in a channel

We consider the active Brownian particle (ABP) model for a two-dimensional microswimmer with fixed speed, whose direction of swimming changes according to process. The probability density swimmer evolves Fokker-Planck equation defined on configuration space, structure depends swimmer's shape, center rotation and domain swimming. enforce zero flux at boundaries space. derive reduced in an infinite channel, limit small rotational diffusivity, find that invariant strongly precise shape rotation. also give formula mean reversal time: expected time taken completely reverse channel. Using homogenization theory, we expression effective longitudinal diffusivity show it is bounded by time.