Stress and fold localization in thin elastic membranes. Finite deformation mechanics in buckled thin films on compliant supports. Smart morphable surfaces for aerodynamic drag control. Fabricating microlens arrays by surface wrinkling. Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer. Mechanical model of brain convolutional development. Nested self-similar wrinkling patterns in skins. Introduction to Applied Nonlinear Dynamical Systems and Chaos Vol. Swarming ring patterns in bacterial colonies exposed to ultraviolet radiation. Landau theory of the crumpling transition. Hydrodynamic fluctuations at the convective instability. Transition from a uniform state to hexagonal and striped Turing patterns. Patterns and collective behavior in granular media: Theoretical concepts. Mechanical basis of morphogenesis and convergent evolution of spiny seashells. Symmetry breaking and the evolution of development. Phase Transition Dynamics (Cambridge Univ. Parteli, E., Durán, O., Tsoar, H., Schwämmle, V. How filaments of galaxies are woven into the cosmic web. Our approach builds on general differential-geometry principles and can thus be extended to arbitrarily shaped surfaces.īond, J. Furthermore, a comparison to earlier experiments suggests that the theory is universally applicable to macroscopic and microscopic systems. By testing the theory against experiments on spherically shaped surfaces, we find quantitative agreement with analytical predictions for the critical curves separating labyrinth, hybrid and hexagonal phases. Here, we report a generalized Swift–Hohenberg theory that describes wrinkling morphology and pattern selection in curved elastic bilayer materials. Yet owing to the nonlinearity of the underlying stretching and bending forces, the transitions cannot be reliably predicted by current theoretical models.
Symmetry-breaking transitions associated with the buckling and folding of curved multilayered surfaces-which are common to a wide range of systems and processes such as embryogenesis, tissue differentiation and structure formation in heterogeneous thin films or on planetary surfaces-have been characterized experimentally.
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