FIG. 2.

Time-dependent diffusion coefficient D(t) for the two-dimensional random medium of Fig. 1. a, Comparison of the RG solution (6), red, with the Monte Carlo simulations, blue, for the set of decreasing permeabilities, corresponding to ζ = 0.5, 1, 2, 4, 10, 20, 40, 100, 200, 400 (top to bottom). The diffusion time τ_D is marked by blue circles. b, Scaling behavior of D(t). As the strength ζ of the restrictions increases from bottom to top, the numerical curves begin to collapse as a signature of the universal behavior (10). Dashed lines show the ζ → ∞ limits from our RG solution: the “impermeable” limit D(t)/D_∞ = 2d τ_r/t and the scaling limit (10) with $C_2(\infty )=4/\sqrt{\pi }$. c, Parameters of the scaling limit (10), C₂(ζ) (filled circles) and D_∞(ζ) (open circles), determined from the fit of the simulations in b to equation (10), compared with the RG predictions (solid and dashed red lines). Thin solid line is the RG limit $C_2(\infty )=4/\sqrt{\pi }$.