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Active nematics are an important new paradigm in soft condensed mattersystems. They consist of rod-like components with an internal driving forcepushing them out of equilibrium. The resulting fluid motion exhibits chaoticadvection, in which a small patch of fluid is stretched exponentially inlength. Using simulation, this Letter shows that this system can exhibit stableperiodic motion when sufficiently confined to a square with periodic boundaryconditions. Moreover, employing tools from braid theory, we show that thismotion is maximally mixing, in that it optimizes the (dimensionless)``topological entropy'' -- the exponential stretching rate of a material lineadvected by the fluid. That is, this periodic motion of the defects,counterintuitively, produces more chaotic mixing than chaotic motion of thedefects. We also explore the stability of the periodic state. Importantly, weshow how to stabilize this orbit into a larger periodic tiling, a criticalnecessity for it to be seen in future experiments.

Maximally mixing active nematics