(195p) Optimal Control of Active Liquid Crystals

Soft, active matter represents a broad class of materials comprising interacting and energy-consuming constituents such as cytoskeletal proteins, bacterial colonies, and tissues capable of organizing into large-scale spatiotemporal structures. An active liquid crystal composed of microtubules and kinesin motor proteins has emerged as a model experimental system for studying how patterns form in materials built from active constituents. Extensile stresses created by the motors render this material unstable to bend fluctuations. Such distortions, therefore, tend to grow and saturate into motile, topological defects that drive large-scale chaotic material flows. Understanding how to shape these flows, and those of other active materials, in productive ways is a grand challenge in active matter. Towards furnishing experimentalists with a principled method for calculating control inputs, we computationally demonstrate the use of two different spatiotemporal control fields: applied vorticity and activity strength (considered separately), to shape the dynamics of an extensile active nematic that is confined to a disk. In the absence of control inputs, the system exhibits two attractors, clockwise and counterclockwise circulating states characterized by two co-rotating topological +1/2 defects. We identify spatiotemporal inputs that switch the system from one attractor to the other; we also examine phase-shifting perturbations. Control inputs are identified by optimizing a penalty functional with three contributions: total control effort, spatial gradients in the control field, and deviations from the desired trajectory. We hope that understanding control in the context of this model system will enable the development of devices that steer the flows of living systems and ultimately move us towards developing self-regulating, programmable active materials.