  There are many examples of driven and active matter systems containing
particles that exhibit circular motion with different chiralities, such as
swimming bacteria near surfaces or certain types of self-driven colloidal
particles. Circular motion of passive particles can also be induced with an
external rotating drive. Here we examine particles that move in circles and
interact with a periodic array of asymmetric L-shaped obstacles. We find a
series of dynamical phases as a function of swimming radius, including regimes
where the particle motion is rectified, producing a net dc motion. The
direction of the rectification varies with the swimming radius, permitting the
separation of particles with different swimming radii. Particles with the same
swimming radius but different chirality can also move in different directions
over the substrate and be separated. The rectification occurs for specific
windows of swimming radii corresponding to periodic orbits in which the
particles interact one or more times with the barriers per rotation cycle. The
rectification effects are robust against the addition of thermal or diffusive
effects, and are in some cases even enhanced by these effects.
