Spontaneous flows and dynamics of full-integer topological defects in polar active matter

Polar active matter of self-propelled particles sustain spontaneous flows through the full-integer topological defects. We study theoretically the effect of both polar and dipolar active forces on the flow profile around $\pm 1$ defects and their interaction in the presence of both viscosity and frictional dissipation. The vorticity induced by the active stress is non-zero at the $+1$ defect contributing to the active torque acting on the defect. A near-core flow reversal is predicted in absence of hydrodynamic screening (zero friction) as observed in numerical simulations. While $\pm 1$ defects are sources of spontaneous flows due to active stresses, they become sinks of flows induced by the polar active forces. We show analytically that the flow velocity induced by polar active forces increases away from a $\pm 1$ defect towards the uniform far-field, while its associated vorticity field decays as $1/r$ in the far-field. In the friction-dominated regime, we demonstrate that the flow induced by polar active forces enhances defect pair annihilation, and depends only on the orientation between a pair of oppositely charged defects relative to the orientation of the background polarization field. Interestingly, we find that this annihilation dynamics through mutual defect-defect interactions is distance independent, in contradiction with the effect of dipolar active forces which decay inversely proportional to the defect separation distance. As such, our analyses reveals a new, truly long-ranged mechanism for the pairwise interaction of oppositely-charged topological defects in polar active matter.