Anna Vainchtein

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 also will 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.”

Owing 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 because of 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. The formation and motion of the boundaries between phases are responsible for the material’s ability to dissipate a lot of energy.

Vainchtein’s research models 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.