Fig. 2: Diffusion driven by an active carpet.

For a–d the surface is covered with sessile perpendicular Stokeslets with independent random forces. Also see Supplementary Movie 1. For e–h the surface is covered by parallel Stokeslets moving along a surface with a constant velocity V and rotational diffusion D_r. For both cases we simulate the motion of tracer particles subject to these active fluctuations, ensemble-averaged over N_e = 100 independent tracer trajectories, as a function of their initial distance from the surface, z₀. a Diagram and typical time course of a random force f(t) described by an Ornstein–Uhlenbeck process. b Velocity correlation function (VCF) of the tracer velocity over time. Blue lines show different values of z₀, each ensemble-averaged, and the red dashed line is the prediction of Eq. (48). The inset shows that the resulting correlation time τ is independent of z₀. c Mean-squared displacement (MSD) for different values of z₀, each ensemble-averaged, transitioning from ballistic to diffusive motion. The red dashed lines show the theoretical approximation of Eq. (3) for z₀ = 2, 20. d Anisotropic diffusivity in the directions parallel (blue, green) and perpendicular (purple) to the surface. The solid lines show the prediction of Eq. (4). e Diagram and typical time course of the orientation angle ϕ_a(t) described by rotational diffusion. f–h are equivalent to b–d for moving actuators.