Fig. 1.

A concrete example of particle tracking, with N = 400 particles moving from their original positions (red circles) to new ones (blue diamonds). (Left) Two consecutive images are superimposed to facilitate comparison of the successive positions. Particles are transported by a turbulent fluid flow with local stretching, shear, vorticity and diffusivity parameters a^∗ = 0.28, b^∗ = 0.54, c^∗ = 0.24, and κ^∗ = 1.05 (see Eq. 9). We focus on turbulent transport because of the challenges it poses, yet the methods we develop are quite general. (Right) Actual motion of each particle. Evidently, the simple criterion of particle proximity fails to pick the actual trajectories, and the mapping of the particles between the two images is intrinsically uncertain. Nevertheless, the inference algorithms described here rapidly yield excellent predictions (a = 0.32, b = 0.55, c = 0.19, and κ = 1.00) for the parameters of the flow.