Today at Brown

Ask Konstantinos Spiliopoulos about his research, and he gives you an example:

Take a flame flickering in a tube, he says. Contrary to what you may believe, the tongue of a flame doesn’t necessarily pass uniformly through the tube. It hugs the boundary, the degree of which is determined in part on the tube’s shape.

“The flame propagates through the boundary (of the tube), not through the interior,” Spiliopoulos explained.

Scientists are unsure why this occurs, although some theorize it may be related to heat. It’s this uncertainty that fascinates Spiliopoulos, an incoming Prager Assistant Professor of Applied Mathematics.

Spiliopoulos delves into what he terms “wave guides.” His goals are to draw up equations that can accurately reflect unexplained phenomena in nature. The tools being used generally fall within fields known as the Feynman-Kac formula and large deviation principle, which is a bridge of sorts between stochastic mathematics and deterministic mathematics, he said. More and more, he added, such techniques are used in the financial world to price derivative products and to gauge how likely companies are to default.

The Athens, Greece, native takes a special interest in seeing how waves move through tubes and layers. And if that’s not enough, he wants the extra challenge of figuring out what happens when the boundaries of those media are not smooth.

“This is much more mathematically and physically involved,” he says.

The research is not simply theoretical. Understanding the behavior of a flame in a tube is crucially important in building better casings for jet engines, for instance. Just recently, Spiliopoulos said, an aerospace design engineer approached him and asked him if there were any equations that could support the construction of parts that bend and wave. “They do the measurements, and they take that into manufacturing,” Spiliopoulos said.

Spiliopoulos’ studies also can be applied in the life sciences. Take a cell, for instance. Divide the cell’s surface area by its volume, and “this can tell you the properties of the cell,” such as what it might contain, how much it can hold, and how it might react in certain situations.

“So, there is a connection there,” Spiliopoulos said.

Spiliopoulos, 29, earned his Ph.D. in mathematical statistics at the University of Maryland. This fall, he will teach a graduate class for the first time, called “Asymptotic Problems for Stochastic Processes and Differential Equations.”

“It will be an adventure for me,” he said.