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March-April 2008
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< previous | 1 | 2 | 3 | 4 Paint often wrinkles—but sometimes it cracks. This seems odd, he points out, because in wrinkling, things are pushed together, whereas cracks form when things are pulled apart. What accounts for these antithetical behaviors? The answer, he explains, depends on whether and how the drop is attached to the surface. “For example, if I have sliced the grape in half and stuck it down on a surface,” then it can’t shrink easily because it is stuck to the substrate, and it will rip. “On the other hand, if the drying grape is not attached,” removing liquid from the inside will cause it to wrinkle as it shrinks. Changing one little parameter changes the outcome. Using this knowledge, Mahadevan points out, “You could learn to engineer materials cleverly.” The roughness imparted by wrinkles might prevent things from getting stuck to a surface, so that it becomes self-cleaning (like a ridged Circulon skillet). Or a lifesaving drug could be hidden in a crack of material engineered so that, whenever it shrinks or swells, the drug is exposed.
Photographs by Jim Harrison The same rules of geometry and physics can govern wrinkling in objects as small as carbon nanotubes and as large as an elephant’s trunk. Mahadevan makes the point with a tube of rolled rubber. (See a video demonstration.) But the applications are not Mahadevan’s main focus. He is seeking a general understanding of how things are ordered and shaped in space and time, and strives for simple answers. “The simplest answers often are very powerful,” he points out, “since they allow one to move from one problem to another, often via analogy.” For example, “If you get an idea looking at a particular system on a particular scale,” can it be used to explain other things that initially seem very different, but are not? “We have wrinkles on our skin,” he points out, “but, on a grander scale, wrinkles on the earth are called mountains. We have made a little bit of progress explaining their shape and size by doing experiments with balloons, which are very, very naively like the earth’s crust.” The crust moves, he explains; it floats on a hot mantle of molten iron and silicate rock. Along the mid-Atlantic ridge, the mantle wells up and new crustal material is formed; in other places the crust falls back into the mantle. “If you look at the globe, you have seen perhaps that subduction zones [where two tectonic plates meet and one is forced beneath the other] are never, or very rarely, straight lines.” Think of the islands of Japan or the Aleutians off the coast of Alaska. “They are almost always along arcs,” he notes. “Why? What sets the size of the arc? And why is the arc cuspate—not one uniform arc, but many little arcs?” Mahadevan suggests an answer based on very simple ideas. Newly formed hot crust is buoyant, which is why it rises. As it surfaces, it begins to cool and becomes heavier, even as it continues to be pushed up by new molten material beneath. Eventually, however, the newly formed crust’s weight causes it to fall back. “That much is known,” says Mahadevan. “The question is, does it fall down smoothly, gently, or does it fall down suddenly? If suddenly, does it fall along a straight line or does it fall along an arc? And very, very naively,” he says, answering his own question, “it must fall along an arc.” As the hardened rim of the crust collapses, it is moving toward a smaller diameter, which means the perimeter has to shrink. But “the perimeter can’t shrink very quickly, so instead, what will happen is, it will buckle.” He is currently working with postdoctoral fellow Haiyi Liang and geophysicist Rebecca Bendick of the University of Montana to test some of these ideas using real geological data. The work builds on subjects Mahadevan has studied in the past, like wrinkles in human skin—or on the surface of a drop of paint. 1 | 2 | 3 | 4 | continued >  
 
 
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