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Register a new userGeometry-driven folding of a floating annular sheet
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Predicting the large-amplitude deformations of thin elastic sheets is difficult due to the complications of self-contact, geometric nonlinearities, and a multitude of low-lying energy states. We study a simple two-dimensional setting where an annular polymer sheet floating on an air-water interface is subjected to different tensions on the inner and outer rims. The sheet folds and wrinkles into many distinct morphologies that break axisymmetry. These states can be understood within a recent geometric approach for determining the gross shape of extremely bendable yet inextensible sheets by extremizing an appropriate area functional. Our analysis explains the remarkable feature that the observed buckling transitions between wrinkled and folded shapes are insensitive to the bending rigidity of the sheet.
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An elastic sheet lying on the surface of a liquid, if axially compressed, shows a transition from a smooth sinusoidal pattern to a well localized fold. This wrinkle-to-fold transition is a manifestation of a localized buckling. The symmetric and antisymmetric shapes of the fold have recently been described by Diamant and Witten (2011), who found two exact solutions of the nonlinear equilibrium equations. In this Note, we show that these solutions can be generalized to a continuous family of solutions, which yields non symmetric shapes of the fold. We prove that non symmetric solutions also describe the shape of a soft strip withdrawn from a liquid bath, a physical problem that allows to easily observe portions of non symmetric profiles.
Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a fluid substrate. Floating shells spontaneously buckle to accommodate the natural excess of projected area and, depending on their intrinsic properties, structured wrinkling configurations emerge. We examine the mechanics of these instabilities and provide a theoretical framework to link the geometry of the shell with a space-dependent confinement. Finally, we discuss the potential of harnessing geometry and intrinsic curvature as new tools for controlled fabrication of patterns on thin surfaces.
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Controlling the phases of matter is a challenge that spans from condensed materials to biological systems. Here, by imposing a geometric boundary condition, we study controlled collective motion of Escherichia coli bacteria. A circular microwell isolates a rectified vortex from disordered vortices masked in bulk. For a doublet of microwells, two vortices emerge but their spinning directions show transition from parallel to anti-parallel. A Vicsek-like model for confined self-propelled particles gives the point where two spinning patterns occur in equal probability and one geometric quantity governs the transition as seen in experiments. This mechanism shapes rich patterns including chiral configurations in a quadruplet of microwells, thus revealing a design principle of active vortices.
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