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We show that self-driven particles coupled to a periodic obstacle arrayexhibit novel active matter commensuration effects that are absent in theBrownian limit. As the obstacle size is varied for sufficiently large activity,a series of commensuration effects appear in which the motility induced phaseseparation produces commensurate crystalline states, while for other obstaclesizes we find frustrated or amorphous states. The commensuration effects areassociated with peaks in the amount of six-fold ordering and the maximumcluster size. When a drift force is added to the system, the mobility containspeaks and dips similar to those found in transport studies for commensurationeffects in superconducting vortices and colloidal particles.

Active Matter Commensuration and Frustration Effects on Periodic Substrates