Investigating the effect of hydrodynamic and topological constraints on a confined active nematic material

Understanding the role of boundary conditions on non-equilibrium materials is key to creating systems with designed behaviors. In this work we numerically investigate the behavior of a 2D active nematic confined to a circular container. The evolution of the nematic order tensor is governed by Landau-deGennes free energy descent with convection and flow-alignment; hydrodynamics are driven by the active, extensile stress and balanced by viscous dissipation. Boundaries plays a dual role, enforcing both no-slip {\&} impermeable conditions, and setting the total topological charge of the system (for parallel anchoring the net charge is $+$1). We examine the dynamics of $+$/- 1/2 defects, which spontaneously form, as a function of nematogen density and activity. We identify an activity/density threshold below which the system coarsens into two co-rotating $+$1/2 defects; above this threshold, defects proliferate similar to a bulk nematic. We observe interplay between hydrodynamics and topology by introducing patches of perpendicular (rather than parallel) anchoring. While a net charge of $+$1 is maintained under strong activity, below a threshold activity the system transitions to a charge of $+$3/2.