Periodic Defect Trajectories in Confined Active Nematic Flows

In active matter systems, energy consumed at the small scale by individual agents gives rise to emergent flows at large scales. For 2D active nematic microtubule systems these flows are largely characterized by the dynamics of mobile defects in the nematic director field. As these defects wind about each other, their trajectories trace out braids, and the topological properties of these braids encode the most important global features of the flow. In bulk flow, defect motion is chaotic, however recent work has shown that confining the active nematic systems - via boundary geometry or the surface topology - leads to periodic defect braiding. Furthermore, the braids that result from confinement are special and appear to maximize a measure of topological entropy. Using recent advances in braid theory, we compare newly discovered maximal mixing braids to the emergent trajectories of active nematic defects found in experiments and simulations.