Fig. 1: Droplet size dependence and deformation fluctuations.

a, b Typical absolute velocity field scaled by its root mean square value for system size 200 × 200 and 400 × 400, respectively at t = 500. The interface between the passive nematic droplet and the outer active bath is shown with a solid yellow line. c, d Typical vorticity field for system size 200 × 200 and 400 × 400 respectively at t = 500. The length and times scales are expressed in units of \({x}_{o}=\sqrt{\frac{{K}_{o}}{{\Gamma }_{o}{C}_{o}{\eta }_{o}}}\) and \({t}_{o}=\frac{1}{{\Gamma }_{o}{C}_{o}}\) respectively, where K_o is the elastic constant, Γ_o is the molecular relaxation parameter, C_o is a material constant, and η_o is the viscosity in the outer active nematic phase (see Methods). e Individual trajectories of the geometric center r(t) of passive nematic droplet of radius R = 15 and R = 45, and (f) droplet interface during typical realizations for R = 15 and R = 45. g Typical realizations of the position of the droplet center relative to the initial position, ∣r(t)∣, exhibiting periods of “run" and “stay". h Ratio of the horizontal to the vertical span of the droplet for R = 15, 30, and 45. The dynamics of translations as well as the aspect ratio slow down as the radius is increased. i Probability distribution function of the translational steps taken by the geometric center of the droplet. PDF(Δr) narrows down upon increasing the radius of the droplet. j PDF of discrete changes in the direction of motion of the droplet. PDF(Δθ) scales nearly exponentially for intermediate range of angles (Δθ ≈ 25^o to 65^o) with heavy-tailed rare events for > 90^o or close to complete reversal. The quantities Δr and Δθ are calculated over a fixed time step of 10^–3 measured in units of t_o.