  Topological defects are at the root of the large-scale organization of liquid
crystals. In two-dimensional active nematics, two classes of topological
defects of charges $\pm 1/2$ are known to play a major role due to active
stresses. Despite this importance, few analytical results have been obtained on
the flow-field and active-stress patterns around active topological defects.
Using the generic hydrodynamic theory of active systems, we investigate the
flow and stress patterns around these topological defects in unbounded,
two-dimensional active nematics. Under generic assumptions, we derive
analytically the spontaneous velocity and stall force of self-advected defects
in the presence of both shear and rotational viscosities. Applying our
formalism to the dynamics of monolayers of elongated cells at confluence, we
show that the non-conservation of cell number generically increases the
self-advection velocity and could provide an explanation for their observed
role in cellular extrusion and multilayering. We finally investigate
numerically the influence of the Ericksen stress. Our work paves the way to a
generic study of the role of topological defects in active nematics, and in
particular in monolayers of elongated cells.
