  Vortices confined to superconducting easy flow channels with periodic
constrictions exhibit reversible oscillations in the critical current at which
vortices begin moving as the external magnetic field is varied. This
commensurability scales with the channel shape and arrangement, although
screening effects play an important role. For large magnetic fields, some of
the vortices become pinned outside of the channels, leading to magnetic
hysteresis in the critical current. Some channel configurations also exhibit a
dynamical hysteresis in the flux-flow regime near the matching fields.
