Mathematical Biology and Ecology Seminar
Wednesday, September 30, 2015 - 11:05am
1 hour (actually 50 minutes)
Morphogenesis of curved bilayer membranes Buckling of curved membranes plays a prominent role in the morphogenesis of multilayered soft tissue, with examples ranging from tissue differentiation, the wrinkling of skin, or villi formation in the gut, to the development of brain convolutions. In addition to their biological relevance, buckling and wrinkling processes are attracting considerable interest as promising techniques for nanoscale surface patterning, microlens array fabrication, and adaptive aerodynamic drag control. Yet, owing to the nonlinearity of the underlying mechanical forces, current theoretical models cannot reliably predict the experimentally observed symmetry-breaking transitions in such systems. Here, we derive a generalized Swift-Hohenberg theory capable of describing the wrinkling morphology and pattern selection in curved elastic bilayer materials. Testing the theory against experiments on spherically shaped surfaces, we find quantitative agreement with analytical predictions separating distinct phases of labyrinthine and hexagonal wrinkling patterns. We highlight the applicability of the theory to arbitrarily shaped surfaces and discuss theoretical implications for the dynamics and evolution of wrinkling patterns.