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 density and polarisation 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 polarisation field grows algebraically as . The density field does not show clean power-law growth; however, it follows approximately. In the inhomogeneous system, we find a disorder-dependent growth. For both the density and the polarisation, growth slows down with increasing strength of disorder. The polarisation shows a disorder-dependent power-law growth for intermediate times. At late times, there is a crossover to logarithmic growth , where φ is a disorder-independent exponent. Two-point correlation functions for the polarisation show dynamical scaling, but the density does not.