Coarsening dynamics of aster defects in model polar active matter†

Abstract

We numerically study the dynamics of topological defects in 2D polar active matter coupled to a conserved density field, which shows anomalous kinetics and defect distribution. The initial many-defect state relaxes by pair-annihilation of defects, which behave like Ostwald ripening on short timescales. However, defect coarsening is arrested at long timescales, and the relaxation kinetics becomes anomalously slow compared to the equilibrium state. Specifically, the number of defects in the active system approaches a steady state, following a power-law dependence in the rate of change of the inverse density. In contrast, in thermal equilibrium, the decay is exponential. Finally, we show that the anomalous coarsening of defects leads to unique patterns in the coupled density field, which is consistent with patterns observed in experiments on the actin cytoskeleton. These patterns can act as cell signaling platforms and may have important biological consequences.