Fig. 3: Comparison of C-particle networks in simulations with the ring CP model.
Filled markers: in-container networks; empty markers: lifted networks; black curves: ring CP model. N = 4000 for all systems. Data are ensemble-averaged except for (c). a Relative size of the largest in-container cluster, S1(〈k〉), matches the ring CP model (black curve) for various θ; S1(〈k〉) of the lifted networks shifts to larger 〈k〉 as θ increases. Inset: k1/2 of the lifted networks increases with θ. Black horizontal line represents k1/2 of the ring CP model. b Susceptibility χ(〈k〉) of the in-container networks closely follows the ring CP model; χ(〈k〉) of the lifted networks shifts to larger 〈k〉 as θ increases. Inset: Peak height of the lifted networks increases with θ at θ ≤ 72°. Raw data for (a and b) are in Supplementary Fig. 4a–d. c Vertical length, Lz /D, of the largest lifted cluster approximately equals its average eccentricity in each trial. d Lz /D peaks near k1/2 for all θ and closely resembles the average eccentricity of the ring CP model (black curve). Shaded areas in (a, b, and d) indicate standard error bands. e Mean clustering coefficients C(〈k〉) of in-container and lifted networks collapse onto a curve close to the ring CP model (black curve), but much lower than the sphere CP model (dotted curve). f Adjacency spectra for networks with the same 〈k〉: lifted C-particles (θ = 20°, blue area), ring CP model (black outline), and ER random network (red outline). More spectra are compared in Supplementary Fig. 9, with discussions in Supplementary Information. g Cluster size distribution follows ns ~ s−τ near percolation at 〈k〉 ≈ 2.1 for lifted C-particles in simulation (θ = 20°, maroon circles) and experiment (θ = 25°, blue circles), and for the ring CP model (black line). Blue line indicates the slope of the standard 3D percolation (τ = 2.19). More ns data are in Supplementary Fig. 6.
