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The structure of isolated disclinations and disclination dipoles in anisotropically elastic nematic liquid crystals is exploredviaa singular potential computational model. 

We study the dynamics of topological defects in active nematic films with spatially varying activity and consider two set-ups: (i) a constant activity gradient and (ii) a sharp jump in activity. A constant gradient of extensile (contractile) activity endows the comet-like +1/2 defect with a finite vorticity that drives the defect to align its nose in the direction of decreasing (increasing) gradient. A constant gradient does not, however, affect the known self-propulsion of the +1/2 defect and has no effect on the −1/2 that remains a non-motile particle. A sharp jump in activity acts like a wall that traps the defects, affecting the translational and rotational motion of both charges. The +1/2 defect slows down as it approaches the interface and the net vorticity tends to reorient the defect polarization so that it becomes perpendicular to the interface. The −1/2 defect acquires a self-propulsion towards the activity interface, while the vorticity-induced active torque tends to align the defect to a preferred orientation. This effective attraction of the negative defects to the wall is consistent with the observation of an accumulation of negative topological charge at both active/passive interfaces and physical boundaries. 

We study the active flow around isolated defects and the self-propulsion velocity of + 1 / 2 defects in an active nematic film with both viscous dissipation (with viscosity η ) and frictional damping Γ with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length ℓ d = η / Γ that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the shear vorticity around the defect is controlled by the system size R . In the presence of friction that leads to a finite value of ℓ d , the vorticity field decays to zero on the lengthscales larger than ℓ d . We show that the self-propulsion velocity of + 1 / 2 defects grows with R in small systems where R < ℓ d , while in the infinite system limit or when R ≫ ℓ d , it approaches a constant value determined by ℓ d .