Dynamics of Active Nematics on a Toroidal Surface

Two dimensional nematic textures can contain topological defects, singular regions where the orientational order is not defined. On a curved manifold, these defects interact energetically with the underlying local Gaussian curvature. Active nematics contain additional force generating components that generate an active stress; this stress generates a flow that causes +1/2 defects to self propel due to a lack of orientational symmetry. When the active stress is sufficiently large this leads to a turbulent regime, in which there are many defects moving chaotically. The local topological charge density of the defects is shown to be linear in the local Gaussian curvature of the underlying manifold. This can be observed experimentally using dense microtubule, kinesin suspensions on the surface of a toroidal water droplet. I will present here a theory describing the motion of the topological defects, and the hydrodynamics of the solvent and compare it directly with experimental observations.