Spatiotemporal Optimal Control of an Extensile Active Nematic Suspension

Active nematic suspensions are self-driven fluids that exhibit rich spatiotemporal dynamics characterized by director field buckling, defect nucleation/annihilation and chaotic trajectories of those defects. Towards developing experimental methods for controlling these dynamics, we consider an optimal control problem which seeks to find the spatiotemporal pattern of active stress strength required to drive the system towards a desired director field configuration. As an exemplar, we consider an extensile active nematic fluid confined to a disk. In the absence of control, the system produces two topological defects that perpetually circulate. Optimal control identifies a time-varying active stress field that drives the defects to orbit in the opposite direction.