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Press Release

Susan Peich

For immediate release:
May 28, 2003

Carnegie Mellon University Hosts Conference For Advances in Nonlinear Analysis

PITTSBURGH—Some of the brightest minds in applied mathematics will gather at Carnegie Mellon University for a conference in Advances in Nonlinear Analysis. The conference will run from Friday, May 30, until Sunday, June 1, with the first lecture starting at 9 a.m. Friday in the Giant Eagle Auditorium, A-51 Baker Hall. The conference concludes at 4 p.m. Sunday.

Mathematicians are coming from as far away as Italy and the Czech Republic to speak about their research in applied mathematics and how it supports new developments in the material sciences. The relationship between applied mathematics and materials science research is cooperative. "Materials science relies on mathematical theory," states Mellon College of Science Professor Irene Fonseca. "Conversely, we look at mathematical theories based on what's up and coming in materials science research." Fonseca also directs Carnegie Mellon's Center for Nonlinear Analysis (CNA).

One of the CNA's main research areas is how applied mathematics supports materials science research. It is a center funded by the National Science Foundation specifically to develop and study mathematical models that, in turn, help materials science researchers study behaviors in both natural and synthetic materials. Studies of behaviors range from how these materials react under stress to how and when these stresses occur. The practical application of mathematical models in materials science research promotes better structures in industries such as construction, medicine, electronics and aviation.

Mathematical studies are invaluable to the field of materials science, according to David Kinderlehrer, Ph.D., a professor of mathematics at Carnegie Mellon who applies mathematical approaches in support of materials research. Kinderlehrer studies microstructures in relation to metallurgical grain-growth. He states, "We are constantly developing new mathematical models to help us calculate microscopic grain [structural] behavior in materials. Understanding grain growth allows us to tailor grain behavior, thus improving the performance of various materials."

Some of these approaches incorporate nonlinear analysis, which evaluates phenomena that aren't linear — rather they are unpredictable in practice, or "bumpy." For example, Kinderlehrer employs nonlinear analysis in understanding the way materials behave at the microscopic level. This information is critical when trying to improve upon materials such as shape-memory alloys. One of the speakers at the conference, Kaushik Battacharya, a professor from California Institute of Technology, will discuss shape-memory alloys and their practical application in small medical devices. His research seeks to understand these microstructures and how it changes as a result of forces and deformation. Battacharya has collaborated with both Fonseca and Kinderlehrer on such research. "To make the microstructure work for us, we have to take advantage of the bumpiness in this [microstructure] energy," states Kinderlehrer. "That requires new developments in applied math. That's our job; it's why we get out of bed in the morning."

Most of the speakers at the conference will address issues in applied mathematics as it pertains to materials science. For a complete list of speakers, a lecture schedule and registration information, go to the ANA Conference Web site at or contact Giovanni Leoni, associate professor in mathematics and a conference organizer, at 412-268-2557.


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