A multi-university research team led by Brown applied mathematics professor George Karniadakis will help the Air Force fine-tune the aerodynamics of fighter jets. Credit: Lab of Jan Hesthaven, Brown University

What are the chances?

A Brown-led team of scientists gets a $5 million grant to reduce performance uncertainty in military equipment.
By Richard C. Lewis  |  June 25, 2009  |  Email to a friend

The challenge: Deliver a missile from Point A to Point B.

The problem: While calculating a flight map may be straightforward, a host of variables can interfere with accurate delivery. For example: “You have wind that could change the trajectory,” explains George Karniadakis, professor of applied mathematics. “How do you take that into account? You do that by assuming wind velocity may change over time.”

George Karniadakis: George Karniadakis Armed with a $5.1 million grant from the Air Force Office of Scientific Research, Karniadakis is attempting to put parameters on such uncertainties by using mathematical equations in a process called stochastic modeling.

Versions of the concept are widely used already – by the airline industry to reposition fleets and rebook passengers when bad weather strikes, by government planners to respond to a natural disaster, and even by shipping companies to schedule pickups and deliveries more efficiently. At Brown, faculty in the computer science department also are working on stochastic models for companies and government agencies.

The Air Force hopes to use the models of uncertainty quantification (UQ) developed by Karniadakis and his research group to increase the aerodynamic capabilities of jets and weapons, to design surfaces that can elude detection, and to build so-called “smart materials” that are extremely flexible and can withstand high temperatures or other extreme environments.

“Incorporating UQ into the conceptual and preliminary design phases is particularly important for revolutionary vehicle concepts and new design paradigms,” the Air Force said in announcing the grant, which will be in effect for three years, with a possible two-year extension.

Karniadakis is the principal investigator of the team, which also includes Brown applied mathematics professors Jan Hesthaven and Boris Rozovsky. Researchers from three other institutions – the California Institute of Technology, Cornell University, and the Massachusetts Institute of Technology – complete the group.

“Simply put, we are trying to put ‘error bars’ ” – a general approximation or “spread’ in the data – “in the results of simulations that reflect various modeling uncertainties,” Karniadakis said.

“This approach will give us an envelope for all the possibilities” – possibilities that then can be tested,” he adds.