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From:
https://physics.aps.org/story/v27/st6
Physics Review Focus, February 11, 2011
David Harris writes:
The complex topography of a crumpled piece of paper has only two basic types of regions, and they can be combined to build up the whole surface, according to calculations.
The ridges and valleys on a crumpled piece of paper look complex. But there may be only two basic types of formations, which can be stitched together to make up the whole structure, according to the 18 February Physical Review Letters. A team of theorists modeled ripples on a thin sheet and found that a combination of sharp creases and gentle hills and valleys can solve the notoriously difficult equations that describe such sheets. Combining these two building blocks could help researchers study waves on biological cell membranes or the formation of scars on skin.
Robert Schroll of the University of Massachusetts in Amherst noticed that his shower curtain had numerous small ripples along the top, where it was constrained by curtain rings, but that it transitioned to a longer-wavelength ripple along the bottom. He realized that what determined the shape of the curtain over that transition was similar to another problem he was working on, so he and his colleagues built a theoretical model. But “we wouldn’t do all of this work just to explain a shower curtain,” he says. Thin sheets have a lot of industrial applications, such as creating masks for use in lithography or studying the stability of a submarine’s walls, and cell membranes act somewhat like thin sheets as well.
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