Pitt Math Researcher Wins Prestigious NSF CAREER Award

PITTSBURGH—University of Pittsburgh assistant professor of mathematics Anna Vainchtein has been awarded the National Science Foundation (NSF) Faculty Early Career Development (CAREER) Award.

The prestigious five-year, $400,000 award will fund Vainchtein's work on materials with "shape memory." The project will also involve training graduate and undergraduate students in an interdisciplinary research program, mentoring female graduate students, and outreach activities for middle and high school students.

Materials with shape memory are flexible and can sustain unusually large deformations. "Take a straight piece of wire made out of nickel-titanium alloy, and bend it in half," said Vainchtein. "The wire will stay bent, but as soon as you put it into a cup of hot water, it will snap back to its straight form, as if it suddenly 'remembered' its previous shape."

Due to their remarkable properties, shape memory materials are used in a variety of ways: from cell phone antennas, eyeglass frames, and orthodontic braces to medical guide wires and cardiac stents. In addition, the materials are able to absorb large amounts of energy, a property that can be used to lessen earthquake and wind-induced vibrations of buildings and structures.

Both energy dissipation and shape memory effect are due to a transformation from one solid state, or phase, to another. The two phases correspond to two different configurations of the material's crystal lattice—an orderly pattern of atoms. At higher temperatures, the material exists in a stronger parent phase, but either mechanical loading or lower temperatures can change its crystal structure to another, more flexible, phase. The resulting formation and motion of the boundaries between phases are responsible for the material's ability to dissipate a lot of energy.

"But how does a new phase nucleate?" asked Vainchtein. "How fast do the phase boundaries move? What controls the rate of energy dissipation? These are important open problems in modeling shape memory and other active materials." Her research addresses such questions through modeling phenomena on the level of lattices.

The resulting mathematical problems, involving nonlinear dynamics of discrete systems, are similar to those that arise in such fields as biology, image recognition, and numerical analysis.

The NSF CAREER Award supports the early career-development activities of those teacher-scholars who most effectively integrate research and education within the context of the mission of their organization.

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