FOR RELEASE FRIDAY, MAY 10, 2002
CONTACT: Luca Capogna, assistant professor, mathematics, Fulbright College(479) 575-3351, [email protected]
Melissa Blouin, science and research communications manager(479) 575-5555, [email protected]
Editor's note: For the solution to an equation describing spilt milk, please log on to: http://www.pigtrail.uark.edu/news
MATHEMATICIAN RECEIVES NSF CAREER GRANT TO CONTINUE STUDIES OF EQUATIONS USED TO MODEL REAL-LIFE SITUATIONS
FAYETTEVILLE, Ark. -- The movement of a robot's arm, the pattern of spilt milk on a table and the act of parallel parking share something in common--they can all be described by mathematical equations. Mathematicians use these equations to explain why things happen and why they don't happen--for instance, how it is possible to parallel park a car even if the car can't be shoved sideways.
University of Arkansas mathematics professor Luca Capogna studies equations like these, focusing on geometric models in which there are "forbidden" parameters--directions in which a robot arm or a car cannot move. His research has won the attention of the National Science Foundation, which recently awarded him a Career Award for $355,000 dollars.
The equations Capogna studies interest engineers, physicists and chemists, who use them to model real-life situations. An example might be looking at how a substance spreads: It may take the shape of a sphere at first, but impurities and irregularities can cause changes in its geometry--and also change the equation that describes its movement.
The equations can be used to reflect changes in a situation and also to mirror its constraints. Scientists use computers to calculate complex equations, but computers have their own constraints when it comes to solving these equations. Capogna looks at ways to show that the solutions to certain differential equations are as "regular" as possible. For instance, the solution could be continuous, or its derivatives might be continuous. Once one knows that a certain equation yields "regular" solutions, then it becomes feasible to use computers and numerical methods to explicitly evaluate such solutions.
In addition to furthering his research, the funds from the career award will provide stipends for graduate and undergraduate research positions, allowing students to study the same problems that Capogna examines in his research and work under his supervision on original research projects.
Capogna has been working with groups of undergraduate and graduate students, having them work on research projects that require them to learn something new and tackle unsolved problems. Tackling equations together works for both groups of students, Capogna said. The undergraduate students benefit from the stimulation of working with graduate students on research projects. Graduate students have to explain complex subjects to the undergraduates and test their knowledge.
"There are many very talented undergraduate students here who could be involved in this kind of work," he said.
NSF program title: Integration of Research and Education in the Study of Analysis and Partial Differential Equations in Carnot-Caratheodory Spaces.
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