Spontaneous formation of density waves in granular matter under swirling excitation

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