Title: Ordering dynamics of self-propelled particles in an inhomogeneous medium,
Abstract: Ordering dynamics of self-propelled particles in an inhomogeneous medium in
two-dimensions is studied. We write coarse-grained hydrodynamic equations of
motion for coarse-grained density and velocity fields in the presence of an
external random disorder field, which is quenched in time. The strength of
inhomogeneity is tuned from zero disorder (clean system) to large disorder. In
the clean system, the velocity field grows algebraically as $L_{\rm V} \sim
t^{0.5}$. The density field does not show clean power-law growth; however, it
follows $L_{\rm \rho} \sim t^{0.8}$ approximately. In the inhomogeneous system,
we find a disorder dependent growth. For both the density and the velocity,
growth slow down with increasing strength of disorder. The velocity shows a
disorder dependent power-law growth $L_{\rm V}(t,\Delta) \sim t^{1/\bar z_{\rm
V}(\Delta)}$ for intermediate times. At late times, there is a crossover to
logarithmic growth $L_{\rm V}(t,\Delta) \sim (\ln t)^{1/\varphi}$, where
$\varphi$ is a disorder independent exponent. Two-point correlation functions
for the velocity shows dynamical scaling, but the density does not.