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The motion of topological defects is an important feature of the dynamics ofall liquid crystals, and is especially conspicuous in active liquid crystals.Understanding defect motion is a challenging theoretical problem, because thedynamics of orientational order is coupled with backflow of the fluid, andbecause a liquid crystal has several distinct viscosity coefficients. Here, wesuggest a coarse-grained, variational approach, which describes the motion ofdefects as effective `particles.' For passive liquid crystals, the theory showshow the drag depends on defect orientation, and shows the coupling betweentranslational and rotational motion. For active liquid crystals, the theoryprovides an alternative way to describe motion induced by the activitycoefficient.

Theory of defect motion in 2D passive and active nematic liquid crystals