Ordering kinetics and steady state in Active Nematic with quenched disorder*

A finite disorder in an active liquid crystal has a significant effect on the ordering dynamics and the steady-state. System of self-propelled apolar particles with nematic interaction is one of the way to understand the defect topology and their dynamics in an active liquid crystal and hence, the ordering kinetics in the system. We construct a two-dimensional monolayer of self-propelled apolar particles with the quenched inhomogeneous field. We write hydrodynamic equations of motion for the hydrodynamics fields, viz. density ρ and orientation Q in a coarse-grained description with the addition of finite quenched disorder. We found that, although the presence of disorder in the system slows down the ordering dynamics, static and dynamic scaling properties remains the same. Our study will motivate experimentalists to verify results and may find applications in living and artificial systems in the presence of inhomogeneous quenched disorder.