Cambridge, Mass. November 23, 2009 Applied mathematicians dissected the morphology of the plantain lily (Hosta lancifolia), a characteristic long leaf with a saddle-like arc midsection and closely packed ripples along the edges. The simple cause of the lily's fan-like shapeelastic relaxation resulting from bending during differential growthwas revealed by using an equally simple technique, stretching foam ribbons.
Haiyi Liang, a postdoctoral student at Harvard's School of Engineering and Applied Sciences (SEAS), and L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics at SEAS and a core faculty member of the Wyss Institute for Biologically Inspired Engineering, were inspired to study the formation of laminae (thin leaf-like structures) because they are so commonplace in biology.
The work had its origins in conversations that Mahadevan had with experimental biologists Mimi Koehl at the University of California, Berkeley and Wendy Silk from the University of California, Davis, who showed him examples of such morphologies in long submarine algal blades.
"These blades have rippled edges when they grow in slowly moving water. When they are transplanted to environments that have rapidly moving water, they generate new blades which are much narrower," says Mahadevan. "This example of phenotypic plasticity, or the ability of the algae to change their shape in response to environmental forces, led to a paper co-authored with Koehl and Silk last year that focused primarily on the experimental findings."
Inspired by this, Mahadevan and Liang developed an analog model to understand how a long leaf is formed by pulling flat, foam ribbons, measuring approximately 4.3" x 1.5" (about the size of a large bookmark), beyond their elastic limit and then letting them go. These stretching strains were applied preferentially to the horizontal edges so that the foam ribbon naturally forms a saddle-like shape when i
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