**Contact:**

Lauren Ward

412-268-7761

Carnegie Mellon Receives $2.1 Million

For Center for Nonlinear Analysis

## NSF Grant Supports Interdisciplinary Studies in Mathematics, Materials Science, Biotechnology

PITTSBURGH—The Center for Nonlinear Analysis (CNA) at Carnegie Mellon University has received a five-year, $2.1 million grant from the National Science Foundation to renew its research to identify and address cutting-edge mathematical questions in diverse fields.

"This research is important for highlighting emerging areas that nonlinear analysis should address. Deriving new mathematical applications is critical to solving everyday problems in materials design and testing, biotechnology and engineering," said Irene Fonseca, the Mellon College of Science (MCS) Professor of Mathematical Sciences and principal investigator on the grant. "Investigators with the CNA have been in the front ranks in integrating the discovery of new mathematics and mathematical ways of understanding with other modes of scientific investigation, particularly in materials science."

Established in 1991, the CNA is one of a select number of centers nationwide supported to conduct work in computation, mechanics, calculus of variations, partial differential equations and numerical equations. Applications of nonlinear analytical tools include understanding problems associated with materials such as the liquid crystals used in electronic devices. Applied analysis can also help determine the best ways to create stable foams for use in automotive lubricants, ceramics and tissue engineering.

"Our center combines new science and new mathematics. Applied analysis and scientific computation are pillars in this linkage," Fonseca said. "The CNA combines expertise in both these fields. Starting with a practical application, such as making a material that can withstand certain conditions, is what motivates mathematicians to develop a model and then perform an analysis. Ultimately, we want to close the loop with engineers to see whether our model can predict how a material will behave."

The center will continue developing international partnerships and cooperation agreements with collaborators, including experimentalists, theorists, physical scientists and bioscientists, according to Fonseca. The center currently has collaborations with universities and research institutions in the U.S., Canada, Chile, France, Germany, Italy, Portugal, and the U.K., and is a U.S. node of a large European Training and Mobility in Research network.

"The imprint of the CNA is large and growing," said Fonseca, who noted that more than 50 postdoctoral fellows have been trained there and several are now scientific leaders at research institutions in the U.S. and abroad. "The CNA is a worldwide asset in educating young investigators in research opportunities at the broad interface between mathematics and other sciences."

These young investigators include postdoctoral fellows and graduate students, most of whom work with Carnegie Mellon scientists on interdisciplinary research projects.

Since 1992, the CNA has also participated in the annual Summer Undergraduate Applied Mathematics Institute, a highly successful program that recruits minorities and women to pursue graduate studies in applied mathematics.

For more information about the CNA, visit www.math.cmu.edu/cna. For more information about the Mellon College of Science, which maintains innovative research and educational programs in biological sciences, chemistry, physics, mathematics and several interdisciplinary areas, see www.cmu.edu/mcs.

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