# When utility equals beauty

## That’s Michael Brenner’s idea of the perfect equation

Michael Brenner is one of those rare people who does something different almost every day, and has fun doing it.

He constantly looks for “things that appear to be more complicated than I can understand.” Then he uses mathematics to try to understand them. Such things include finding what shape falls fastest in a vat of honey, and studying the collapse of bubbles and breakup of falling drops.

“In my work, the direct motivation is not always to do something practical,” Brenner, 33, admits. “However, whenever one tries to understand something complicated carefully and completely, there are inevitably useful outcomes. At the end of the day, the best outcome would be to discover something both beautiful and useful. Whereas a pure mathematician focuses on the former and an engineer on the latter, I am somewhere in the middle. I try to chose problems where there is a real possibility of insight, practicality, and fun.”

The National Science Foundation thinks enough of this approach to support Brenner with a prestigious Career Award that runs from 1998 until 2003. Last year, Harvard granted him tenure as a Gordon McKay Professor of Applied Mathematics and Applied Physics.

Asked to describe his colleague, Howard Stone, Gordon McKay Professor of Chemical Engineering and Applied Mechanics, who has known Brenner since he was a graduate student, wondered if he knew enough superlatives. “Insightful, thoughtful, creative, incredibly energetic, a great guy,” Stone enthuses. “Mike makes everyone around him better.”

### Falling shapes and bursting bubbles

One thing that holds Brenner’s interest is an effort to find what shape falls fastest in a viscous or “thick,” honey-like fluid. In the early part of the last century, scientists concluded that an oval, or ellipsoid, with a length twice its width falls fastest. Later, French scientists added cones to the ends of the ellipsoid and it fell a little faster.

Brenner refers to finding the optimal shape as “a very difficult math problem.” Using a computer, he has explored a new twist – adding a spiral shape to the oval. Brenner ran a contest to find a winning shape at the Massachusetts Institute of Technology (M.I.T.), where he worked before coming to Harvard. Undergraduate students shaped balls of clay and dropped them into a tank of fluid. There was so little difference between falling times that the competition failed to produce a winner.

“Basically it didn’t work, but it was fun,” Brenner says. “This is a problem in optimal design that turns out to be much harder than it looks. It’s unclear how important the answer is. It may have some application to the way that cells move in our bodies. I strongly believe that if we had a mathematical method to answer such a question, there would be tons of practical uses in biology, technology, and other fields.”

For Brenner, the best days come when his mathematical conclusions match data from well-conducted experiments, or vice versa. “It’s a way to have your cake and eat it,” he remarks. “You get to the essence of a complicated thing. In many cases, the precise understanding that results is the first step toward something useful.”

Another effort of his involves bursting bubbles. Bubbles of air in water can collapse with enough force to damage the propellers of ships, a process called cavitation. Brenner collaborates with a number of colleagues who try to understand cavitation well enough to reverse it and avoid such damage.

Under the right conditions, cavitating bubbles generate a weird blue light, along with high temperatures. Chemists are excited by the possibility that this so-called sonoluminescence might provide a cheap and easy way to produce the heat needed for certain chemical reactions.

“I work on a lot of different things at the same time in collaboration with a lot of different groups at Harvard and M.I.T.,” Brenner says.

One such collaboration involves making new types of fabrics by spraying fluid through a nozzle in a strong electric field. The fibers created are thousands of times thinner than a human hair, and they form a fabric without the need for weaving. “We want to understand this process well enough to predict the properties of any fabric produced by this electrospinning method,” Brenner explains.

Fingering a thin square of material made in this way, he notes that such fabrics could be used as filters of all kinds and could be made impermeable to such biological and chemical threats as anthrax and saran nerve gas. “A new industry is starting to emerge around this technology,” Brenner notes.

### Going where life sent him

You’d expect that someone like Brenner would have grown up tinkering with things and trying to find out how they work. Not so. “I grew up in Lakeland, Florida,” he says. “Not much goes on there, but they do have a lot of public tennis courts and I spent most of my time playing tennis. I had no interest in math or physics.”

Brenner didn’t care where he went to college as long as it was not in Florida. His father, a physician, graduated from the University of Pennsylvania, so he enrolled there in 1986.

“For no specific reason, I got interested in physics,” Brenner recalls. “I kept taking physics courses. When you do that, after a while you become a physicist.”

Brenner coordinated his graduate school choices with his future wife, Tracey, whom he met at the University of Pennsylvania. They decided to go to the University of Chicago. Things just sort of continued to happen, and Michael became interested in situations in physics where mathematical equations that are developed to predict outcomes breakdown.

Such a situation applied to equations that described the breakup of falling droplets, so Brenner did his Ph.D. thesis on that subject. He concluded that bubbles do not break up abruptly, as everyone thought, but in a stepwise fashion. A group of experimenters took slow-motion films of falling drops, and found that they break up just as Brenner’s new equations predicted they would.

“It was a beautiful confirmation,” Brenner comments. The University of Chicago thought so, too. The university awarded him its Marc Perry Galler Prize for an outstanding Ph.D. thesis in 1994. “The research didn’t have any technological impact that I’m aware of,” he says. “But it wasn’t completely useless. We developed mathematical tools and a way of thinking that is potentially useful for solving other problems.”

Brenner came to M.I.T. in 1995, and has worked since in the M.I.T.-Harvard corridor. “A huge amount of science and engineering is localized in this small area,” he comments. “It’s a very collaborative environment.”

Brenner greatly admires the work of British physicist Geoffrey Ingram Taylor (1886-1975). “Taylor made many of the important discoveries underlying a wide range of topics in physics and engineering, from nuclear explosions and air turbulence to how snakes swim,” he says. “He captured the essence of what he worked on, and made a great impact on the way physics and engineering are done.” Brenner makes no secret of wanting to be like Taylor.

Two years ago, Brenner taught a course on Taylor’s work at M.I.T. He and Howard Stone plan to teach the same course this spring at Harvard. “I’m excited about incorporating Taylor’s way of thinking into Harvard’s curriculum,” Brenner says. “It’s a wonderful way to learn a lot of unrelated things, and have fun while you’re doing it.”