Fig. 3: Dynamics and spatiotemporal scales.

a Mean square displacement (MSD) of droplets of different radii R with t_o = 300. b Variance of discrete step sizes taken by droplets of different radii. The variance decreases as the droplet radius increases. (b, inset) An analytical calculation of the MSD shows crossover from ballistic to diffusive regime for a particle under exponentially correlated random force. MSD is shown for different values of the mass m, which is varied by choosing five different inertial times τ_m( = m/α), in the limit τ_m ≪ τ_F (see Methods for details). The crossover depends on τ_F and also on the droplet size R. c Time averaged one-time two-point velocity correlation function C_vv(r) of the velocity field in the active nematic bath. The integral length scale \({\ell }_{v}\equiv \int\nolimits_{0}^{\infty }{C}_{vv}(r){{{{{\rm{d}}}}}}r\) is marked with a vertical dashed line; (c, inset) ℓ_v in the active bath changes negligibly upon changing the droplet radius. d Integral length scale with time during typical realizations. e VACF \({C}_{\tilde{v}\tilde{v}}(\tau )\) of the droplet trajectories with varying R, and (f) the same on a Semi-logarithmic scale resolving the presence of multiple time scales.