Figure 3: The width of domain walls.
(a,b) Equilibrium wrinkle patterns in a square section of a spherical shell on liquid substrate (simulation). Vertical displacement z (top-left) and mean curvature H (bottom-right) clearly indicate splitting of the patterns into four domains divided by domain walls of varying widths. (a) η≈2.4 × 10−4, all domain walls are of the ‘Chevron’ type, that is, wrinkle angle changes monotonically when moving along the wrinkle across a domain wall. (b) η≈5.7 × 10−5, domain walls in the high-amplitude wrinkles become Ω-shaped through the formation of localized d-cones (cusp is well seen in the mean curvature map). (c) The width of Chevron-shaped domain walls is proportional to the penetration length (equation (18)), hence to the amplitude. Ω-shaped walls have widths proportional to the wrinkle wavelength, regardless of the amplitude. Widths are extracted from simulations by fitting wrinkle angle to an arctangent, in compliance with19. Penetration lengths are calculated from system parameters and the measured amplitude of each wrinkle.
