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L. Mahadevan

The Physics of Everyday Life

L. Mahadevan

Like a slow-motion release of a firework, a flower’s bud bursts forth into a delicate display. Looking at a bouquet at the florist, you might never ask how the intricate petals, stems, and stigmas, each contained in a green orb the size of a gobstopper, emerged perfectly unfolded without the slightest rip.

SEAS's Lakshminarayanan Mahadevan (Maha for short), Gordon McKay Professor of Applied Mathematics and Mechanics, has not only posed the question, but is trying to solve countless others like it. Using mathematics to understand how materials move and behave, he places particular emphasis on phenomena visible to the naked eye and closely tied to experiments or experience.

He’s explored the way honey coils (important for geologists who study the flow of molten rock within the Earth), why insects can adhere to surfaces (leading to the creation of new types of adhesives), how hair coils on water (helpful in understanding the principles of self-assembly), and the way fabrics fold and wrinkle (providing insight about the spiky surface of a diseased red blood cell).

“I find joy in discovering the sublime in the mundane,” says Maha, who recently relocated from one Cambridge (England) to another (Massachusetts). “I try to uncover explanations for everyday events that are easily seen but not well understood.

They typically turn out to be more relevant than I first imagined.” Think again about the complexity of the flower as you recall how you’ve struggled to fold a map without tearing, or at least swearing. Within the blooming process lies what Maha calls a theory for “self-assembled origami.”

The bud can unpack its suitcase and iron its clothes without the help of even a finger. “Natural systems offer a rich arena to learn about the interplay between geometry and physics in the real world. Folding is not just for flowers, but critical to our very existence. It happens in our tightly bound-up DNA,” Maha points out.

Moreover, stopping to smell (and study) the roses might someday help with creating self-assembling nanostructures, one of the most critical components of the emerging field of nanotechnology. Maha’s dark, vibrant eyes flit behind large round glasses that reflect the light in his sizable, but test tube–free third floor office of Pierce Hall. In his experience, you don’t necessarily need a lab or complicated devices to do meaningful experiments and research.

“Why struggle to find something worth studying when you have quick access to rich events, like how a flag flutters, that you can easily play with? Being able to radically change parameters – a light breeze versus a strong wind – without losing the effect is ideal for experimentation.”

With today’s emphasis on rapid innovation, supermarket science (creating volcanoes with baking soda) and everyday experimentation (looking out the window rather than at an LCD monitor) may seem passé. Yet Maha’s hands-on experimentation, most of which could have been done by true renaissance engineers, does not imply that such research is any less difficult or fruitful. Rather, he acknowledges that good science can arise from simple observation.

Not surprisingly, Maha’s “mundane” investigations cross – if not leap – over traditional boundaries in physics, math, engineering, and biology. In fact, figuring out what comes naturally requires continuous collaboration with scientists from many disciplines at Harvard, MIT, and throughout the world. Maha emphasizes that his dedicated students – “the lifeblood of my enterprise” – deserve as much credit as he does for illuminating the physics of everyday life.

“Ultimately, any robust event is likely to be interesting for its own sake, since it explains something essential about how the world works,” observes Maha. And he’s not alone in appreciating such rough magic. In regard to Maha and his colleagues’ celebrated theory of how wrinkles form, Nature editor Philip Ball wrote, “It is humbling to find in a high-powered journal like Physical Review Letters that we have limped along for years without an understanding of what controls the wavelength and amplitude of wrinkling in a sheet. There’s plenty still to be learned from the $20 experiment.”

Maha explains his passion for research by referencing a classic tale about the young Krishna, from the Bhagavata Purana. The child, an incarnation of the Hindu god Vishnu but brought up incognito by foster parents, had a reputation for mischief.

One day, friends accused Krishna of eating dirt. Dismayed, his mother demanded an explanation. Krishna denied the charge, saying “I have not eaten dirt. They are all lying!” To force a confession, his mother told him to open wide. But Krishna, to avoid being caught in a lie, played a trick.

Instead of muddy teeth, he revealed the entire universe to her – the earth, the stars, and the elements of all creation. And then, to
keep his cover, Krishna quickly cast a spell of forgetfulness over her to clear her memory.

“One way to look at the story,” Maha explains, “is to understand that meaning and the answers to the deepest questions can be found in the stuff all around us. Science is about looking for connections and finding joy in discovery itself.”

Lucky for us, Maha – unlike Krishna’s mother – has not forgotten where the universe lies, but continues to look deep inside simple things, like flowers or dirt, to pull out the profound.

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Ordinary Beauty

Since all the world’s his lab, Mahadevan studies a wide variety of problems using lessons from every discipline at his disposal.

Françoise Brochard-Wyart and Nobel laureate Pierre-Gilles de Gennes captured the interdisciplinary spirit that pervades all his work when discussing his and E. Cerda’s groundbreaking research on the geometry and physics of wrinkling.

They said, “The paper provides a beautiful and simple understanding of many natural phenomena – bridging geometry, mechanics, physics, and even biology.”

Plumbing for pests

Some sap-loving aphids live their entire lives deep inside galls, or the abnormal swellings of plant tissue. Since what goes in (what they eat) must go out (as waste), these aphids could easily drown inside the enclosed spaces. Mahadevan and his colleagues discovered that these snug bugs secrete powdery water-repellent wax on the surface of their homes and on their waste products.

The wax-on-wax formula turns the excrement droplets into “liquid marbles” that the critters can then roll clean away. Mahadevan hopes to learn from these tiny engineers how to improve attempts at efficiently manipulating minute volumes of liquid on small surfaces.

Getting gell-o to jog

One of Mahadevan’s research teams has created an “artificial animal” from a filament of cylindrical hydrogel (cut with small scales on the bottom) that, when vibrated atop a sheet of glass, can mimic – and
hence, help explain – the movement of snakes, snails, and other creatures.

By varying the angle, scales, and direction of the vibration, the team derived different patterns of motion.

“A simple experiment can explain a wide range of locomotion for radically different animals,” says Mahadevan, “and also hints that there’s an underlying, similar process for how all of them move.” This discovery might lead to new motion techniques for tiny machines, robots, or for use in manufacturing processes that involve moving substances across surfaces.

Uncovering wrinkles

Mahadevan and his colleagues from Cambridge, England, proposed a now-famous general theory about an everyday bother that keeps dry cleaners happy – the wrinkling of fabrics and other materials.

When you press down on a spring you crush it, and in so doing, the spring stores elastic energy. Likewise, a sheet can either stretch or bend; the resulting deformed sheet adopts the shape that minimizes its total bending energy.

Mahadevan’s laws of wrinkling predict the amplitude and wavelength of the resulting wrinkles, and work for a variety of materials – plastics, fabrics, and even human skin. Understanding how a cape falls over you or how our sheets look after a restless sleep could lead to more realistic computer animations or better-fitting clothes.