Defect Ordering and Patterning in Active Nematics*

Active nematics combine liquid crystalline orientational order with internal active driving to generate novel dynamical states involving complex spatio-temporal flows along with spontaneous defect pair creation and proliferation. Topological defects acquire self-propulsion due to activity and play a prominent role in driving large scale flows in two-dimensional active nematics. By focusing on defects as the relevant excitations, we develop a hydrodynamic theory of active defects incorporating both defect motility and active torques that align defect orientations. Our model predicts a defect ordered polar flock at high activity and uncovers the underlying physical mechanism for defect ordering. Extending our framework to include spatially inhomogeneous activity, we show how activity gradients act as ''electric fields'' that can sort defects based on their topological charge. Our continuum model hence offers a useful and versatile approach to quantify the patterning of defects and flow in active nematics by the spatial control of activity.