Campus & Community

Taking a closer look at the obvious

6 min read

How do skirts fold, worms wiggle

Lakshminarayanan Mahadevan, Gordon McKay Professor of Applied Mathematics and Mechanics, enjoys discovering the sublime in the obvious. He asks the kinds of questions children ask that no one can answer, such as, how do flies that stick to walls get unstuck? (Staff photo Stephanie Mitchell/Harvard News Office)

Lakshminarayanan Mahadevan (Maha for short) studies the obvious but ignored – how do flags flutter, worms wiggle, fabrics fold. “There’s a certain joy in trying to discover the sublime in the mundane,” says the Gordon McKay Professor of Applied Mathematics and Mechanics at Harvard University.

“What excites me are things so in your face that almost no one thinks about them. But if it’s in your face, it’s worth understanding. It may even be useful. For example, the details of how flies stick and unstick themselves to walls could lead to exotic new adhesives.”

Take that fly crawling across the wall or ceiling. Most people know that insects can do this neat thing because they have a natural adhesive on the bottoms of their feet. Mahadevan got interested in the problem of how they unglue themselves when they want off the wall.

By studying their feet, Mahadevan and his colleagues at Lehigh University and Harvard discovered that the bugs boast regularly spaced grooves in their sticky feet. When the team compared a simple theory of the best way to stick and unstick, it agreed with actual measurements of the spacing of the grooves. The bugs have known for millions of years what humans just discovered. A report describing the research will be published in an upcoming issue of the Proceedings of the Royal Society, a British scientific journal.

Bugs do plumbing

How does one get started in this kind of work? “You ask questions that children ask all the time,” Mahadevan answers. Like them, “you get answers to some questions but not to others. I studied engineering and found that partially, but not completely, satisfying for finding out how things work. Then I switched to applied mathematics.”

With the encouragement of mentors, especially Joseph Keller, his Ph.D. adviser at Stanford University, Mahadevan realized that, “you can look at anything, anywhere, and see a problem. The questions I ask are not important on a grand scale, but they’re interesting because they’re around us. I look for extremes – far-out behaviors – because they potentially can illuminate general principles about how many different things work.”

He recently looked into the habits of snug bugs, like aphids, that live their whole lives in galls, abnormal swellings in the tissues of plants. They survive by eating sap produced by their shelters. It’s a cozy life, but the sap-lovers face a life-threatening problem. They have to survive in a small cell that’s slowly filling up with liquid scat.

Mahadevan and his colleagues at Cambridge University in England realized that they use an “incredibly clever strategy” to stay dry. The bugs make a powdery wax with which they coat their excrement and the walls of their cells. This produces tiny liquid marbles that the bugs roll out of their galls much more readily than if the scat drops were uncoated.

Others might regard this process as just a natural curiosity, another intriguing tool in the big bag of evolution. Mahadevan sees it as a technique that engineers might borrow to solve problems that involve moving small amounts of liquid across various kinds of surfaces, which can be done more easily by rolling rather than sliding.

Getting the hang of it

Mahadevan is also fascinated with how fabrics fold. At Cambridge University, where he worked before coming to Harvard’s Division of Engineering and Applied Sciences, he and postdoctoral fellow Enrique Cerda developed a set of equations that nicely predict how fabrics fold and wrinkle. The formulas cover everything from a rippling gown to the surfaces of diseased body cells.

He has no illusions about these numbers revolutionizing haute couture. Fashion designers tend not to be interested in mathematical equations of any shape or form. However, the numbers might score with computer animators, whose action figures appear unrealistically rubbery because it’s difficult to program how the clothing of their villains and heroes will hang as they perform deeds of devilry and daring.

Another possibility might be virtual changing rooms. A 3-D scanner would create a model of your body, then computer software would wrap it in silk or trendy denim to form a custom fit. Software for soft wear.

But Mahadevan isn’t interested in such fitting but obvious applications. He sees the physics of fashion being used to predict the changes in thin sheets of plastic, metals, ice, etc. as they are warped by natural forces such as gravity, wind, and earthquakes. At present, Mahadevan collaborates with Woodford L. and Ann A. Flowers University Professor George Whitesides, who studies how electronic devices and wires can assemble themselves into useful circuits. The question to address is how much the efficiency of such circuits could be increased by folding or wrapping the sheets on which they grow in ways that bring different parts closer together than they otherwise would be.

Then there’s crumpling. Can the same numbers that describe the crumpling of a newspaper apply to the shriveling of the surface of a diseased body cell, or the global forces that push layers of rocks up to make mountains?

Flapping flag and snapping plants

There are no limits to the possibilities or problems if you look closely enough, Mahadevan believes. He and postdoc Mederic Argentina have just worked out numbers that describe how flags flutter. Watching the flag wave in the air reminds Mahadevan of how worms wiggle through the soil and how fish wave their bodies to move through water. Given the frequency at which body waves move along the fish, can you calculate the speed of the fish, he wonders.

Another project has taken root from a Venus’ flytrap given to him as a present. He is currently fascinated by the idea of a plant that eats animals, instead of the other way around. “I’m looking into the mechanisms by which plants, not typically distinguished by movement, can not only do so but do it rapidly,” Mahadevan says.

But aren’t there plenty of sources of information about how that plant catches its food? “Don’t,” he cautions, “confuse familiarity with knowledge.”