Fig. 3.

The quarter rotational pattern. a Schematic showing the rotational pattern under alternating magnetic field with $\alpha =6.0$ and $\beta =0.3$. b The rotational parameter $R$ of each rotor for a 4 × 4 rotor array. The dots depicts a single rotor, with blue meaning clockwise ($R=-1$) and yellow meaning counter-clockwise rotation ($R=1$). The observation is based on 25 cycles. c, d Time-averaged flow field generated by the rotors in c experiment ($\alpha =6.0$ and $\beta =0.3$) and d simulation ($\alpha =6.0$ and $\beta =0.03$). The contour shows the vorticity $\omega$ strength, the black arrows visualize the local flow field and the large gray arrows show net flow field created by the system. Symbols indicate the rotor position. e Time history of the vortex strength $\mid \omega \mid$ for three categories of rotors, in experiment and simulation. Note $T=1∕f$ is the period. f Rotational pattern with a grid that has a Gaussian noise $\sigma$ in the rotor position. The simulation is for $\alpha =50.0$ and $\beta =0.1$