  Transport and diffusion of paramagnetic ellipsoidal particles under the
action of a rotating magnetic field are numerically investigated in a
two-dimensional channel. It is found that paramagnetic ellipsoidal particles in
a rotating magnetic field can be rectified in the upper-lower asymmetric
channel. The transport and the effective diffusion coefficient are much more
different and complicated for active particles, while they have similar
behaviors and change a little when applying rotating magnetic fields of
different frequencies for passive particles. For active particles, the
back-and-forth rotational motion facilitates the effective diffusion
coefficient and reduces the rectification, whereas the rotational motion
synchronous with the magnetic field suppresses the effective diffusion
coefficient and enhances the rectification. There exist optimized values of the
parameters (the anisotropic degree, the amplitude and frequency of magnetic
field, the self-propelled velocity, and the rotational diffusion rate) at which
the average velocity and diffusion take their maximal values. Particles with
different shapes, self-propelled speeds, or rotational diffusion rates will
move to the opposite directions and can be separated by applying rotating
magnetic fields of suitable strength and frequency. Our results can be used to
separate particles, orient the particles along any direction at will during
motion, and control the particle diffusion.
