Maximum particle density, relative to the mid-plane gas density, as a function of scale, for simulations with NS collisions (top panel) and simulations with no collisions (bottom panel). Diamonds indicate the maximum density over a given scale, while pluses indicate the mean of the time-dependent maximum density. Simulations with NS collisions display good convergence in the maximum density, following closely a max(ρ_p) ∝ L^-2 law (thin black line), while the mean of the maximum density increases from 64³ to 128³, due to a higher temporal filling factor of major concentration events at higher resolution (see Fig. 7). The dashed line shows the maximum density for a uniform razor-thin mid-plane layer for comparison. Blue dotted lines show the Roche density for the minimum mass solar nebula at 3 AU from the central star, and for five times less and more massive nebulae. The red dotted line indicates the characteristic length scale of the streaming instability, L = ηr. Particle densities above 10³ times the gas density are reached in regions smaller than  ≈ 0.003H, equivalent of L ≈ 50   000 km at 3 AU.