  Using numerical simulations, we demonstrate that superconductors containing
periodic pinning arrays which have been diluted through random removal of a
fraction of the pins have pronounced commensurability effects at the same
magnetic field strength as undiluted pinning arrays. The commensuration can
occur at fields significantly higher than the matching field, produces much
greater critical current enhancement than a random pinning arrangement due to
suppresion of vortex channeling, and persists for arrays with up to 90%
dilution. These results suggest that diluted periodic pinning arrays may be a
promising geometry to increase the critical current in superconductors over a
wide magnetic field range.
