Orientational Order of Active Nematic Defects: From Flat Space to Curved Geometries

Topological defects are signatures of active nematics, that are systems intrinsically out of equilibrium. We study defects in flat and curved space, and how their dynamics is influenced by other defects and the underlying director field. In our experiments, we look at turbulent motion of +1/2 and -1/2 defects in a microtubule-kinesin active nematic. In this talk, we explain how we confine this system to flat 2D cells and shapes of varying Gaussian curvature, K, like ellipsoids and tori. We identify the defects using image analysis, and calculate the defect orientations from the divergence of the nematic tensor order parameter. Using defect positions and orientations, we compute spatial and orientational correlations to investigate defect-ordering. In flat space, we observe short-range ordering of defects, and absence of any global orientational order. The qualitative features of the correlations persist independent of the defect density. We confirm these observations with simulation results. In curved geometries, we study the evolution of defect distributions and how the dynamics couple to the underlying K. We analyze the fluctuations about the steady state of the nematic to extract sound modes, in an attempt to test recent theoretical predictions.