Fig. 37

Theoretical predictions (lines) and numerical simulation (markers) are shown. A1 Classification of line segments. (Solid) lines embedded in the margin, (dotted) lines touching the margin, (striped) interior lines .A2 Capacity α = P/N of a network N = 200 as a function of R (line length) with margins κ = 0, 0.5. A3 Fraction of configurations at capacity with κ = 0. (red) lines in the margin, (blue) touching the margin, (black) interior lines. B1 D2 balls, B2 capacity α = P/N for κ = 0 for large D = 50 and R \( \propto \) D^−1/2 as a function of \( {\text{R}}\sqrt {\text{D}} \). (Blue solid) α_D(0, R) compared with α₀(\( {\text{R}}\sqrt {\text{D}} \)) (red square). (Inset) capacity α at κ = 0 for 0.35 ≤ R ≤ 20 and D = 20: (blue) theoretical α compared with approximate form (1 + R⁻²)/D (red dashed). C1 2D L1 balls. C2 Fraction of configurations as a function of radius R at capacity with κ = 0. (red) entire manifold embedded, (blue) touching margin at a single vertex, (gray) touching with two corners (one side), (purple) interior manifold