1 research outputs found
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
a Brownian process. The probability density for the swimmer evolves according
to a Fokker-Planck equation defined on the configuration space, whose structure
depends on the swimmer's shape, center of rotation and domain of swimming. We
enforce zero probability flux at the boundaries of configuration space. We
derive a reduced equation for a swimmer in an infinite channel, in the limit of
small rotational diffusivity, and find that the invariant density depends
strongly on the swimmer's precise shape and center of rotation. We also give a
formula for the mean reversal time: the expected time taken for a swimmer to
completely reverse direction in the channel. Using homogenization theory, we
find an expression for the effective longitudinal diffusivity of a swimmer in
the channel, and show that it is bounded by the mean reversal time.Comment: 46 pages, 24 figures. AMSart styl