Spontaneous formation of density waves in granular matter under swirling excitation

We study here the spontaneous clustering of a submonolayer of grains under horizontal circular shaking. The clustering of grains occurs when increasing the oscillation amplitude beyond a threshold. The dense area travels in a circular fashion at the driving frequency, which even exceeds the speed of driving. It turns out that the observed clustering is due to the formation of density waves. The analysis of a phenomenological model shows that the instability of the uniform density profile arises by increasing the oscillation amplitude and captures the non-monotonic dependence of the transition amplitude of the clustering on the global density of the system. Here, the key ingredient is that the velocity of individual grains increases with the local density. The interplay of the dissipative particle-particle interaction and frictional driving of the substrate results in this dependence, which is tested with discrete element method simulations.