Fig. 7. Characterization of the dynamic states.
(A) Rotational order parameter φR for gas, flocking, and vortex states as a function of time (normalized by the filed period). (B) Tangential velocity profile for the vortex state as a function of distance from the center. The velocity is scaled by the reduced single-particle velocity αsV0. (C) Spatial particle velocity correlation functions for the different dynamic states; dashed lines correspond to the results including hydrodynamic interactions. Data are shown for the following frequencies: gas (f = 6 Hz), flocking (f = 20 Hz), and vortex (f = 47 Hz). (D) Correlation length Cd as a function of frequency; open symbols denote the results considering hydrodynamic interactions.