Fig. 3. Collective particle dynamics.

(A) Spatial particle velocity correlation functions for different frequencies; here, a is the particle radius. Inset: Correlation length versus frequency f. When the correlation length becomes comparable to the system size for the frequency f ≈ 40 Hz, the particle motion is self-organized into a large vortex. The dashed line serves as a guide to the eyes. (B) Rotational order parameter φ_R for gas, flocking, and vortex states. (C) Vortex velocity profile versus distance from the center.