Jianfeng Lu: The Mathematics of Materials and of the Body

New faculty member applies math to solve some of the hardest questions in science

Jianfeng Lu's mathematical studies put numbers to work for researchers in materials science, physics, chemistry and other fields. Photo by Les Todd/Duke University Photography

As a mathematician, Jianfeng Lu appreciates the abstract beauty of theories and proofs. But he also sees his craft as a powerful, pragmatic tool for helping researchers solve their greatest scientific challenges.

Lu, 29, joined Duke in the summer of 2012 as an assistant professor in the mathematics department. Trained as an applied mathematician, he helps scientists in chemistry, materials science and biology develop mathematical descriptions of their observations. With his broad interests but focused expertise, he can probe far into materials to explore their electron structure or deep within the body to explain the fleeting molecular-level interactions that make life possible.

In materials science, Lu's work helps researchers simulate the electron structure in new substances. Scientists want to understand electron structure to measure how materials will handle different conditions. Algorithms to calculate materials' electron structures exist now, and scientists can run these formulas on supercomputers to determine the total energy, atomic forces and charge density of about ten thousand electrons in a system.

But many systems in materials science have more than a million atoms, requiring simulations far beyond the reach of current technology. "I try to understand and design fast algorithms, so that the simulations can be done for larger systems incorporating more atoms. I also work on coupling electronic structure models with atomistic and continuum models to get a more efficient and accurate description for large systems," Lu said.

His mathematical work within the body provides a different challenge. Certain chemical reactions "happen so rarely that they are hard to simulate," Lu said, explaining that scientists want to understand these fleeting biochemical reactions because they are "essential to everyday life." With researchers in biology and chemistry, Lu works to develop techniques to reconstruct the body's reactions and better analyze their physical chemistry.

Lu's work fits into a wide spectrum of applied mathematics, including applied analysis, probability and scientific computing, said Harold Layton, the chair of Duke's mathematics department. "Jianfeng's broad expertise in applied mathematics, and his interest in the natural sciences will provide opportunities to interact and collaborate with a number of Duke faculty in the natural sciences and also faculty in the Pratt School of Engineering," Layton said.

A native of Hangzhou, China, Lu said he was interested in math from an early age. But he didn’t decide to make it his career until he was an undergraduate student at Peking University in Beijing. During his second year there, Lu said he "saw how powerful mathematics was to model situations, and how it could help others solve their problems." Then, he realized he wanted to be a mathematician. He graduated with a bachelor's degree in math in 2005.

Later that year, Lu came to the U.S. to begin graduate work at Princeton. "The U.S. offered a more active research environment and more opportunities to work in applied mathematics, which I liked because of its interdisciplinary nature," he said. At Princeton, he worked with mathematician Weinan E on electron structure problems and also collaborated with mathematician Ingrid Daubechies, who came to Duke in 2010.

Lu earned his Ph.D. from Princeton in 2009 and then worked at New York University before heading south to Durham. "Duke has a nice environment to do research. We're encouraged to talk to people and to have interactions between disciplines, which fits well with my research and makes me happy to be here," he said.

Lu, who is teaching Elementary Differential Equations during the fall 2012 semester, is married and lives in Durham. When he's not working on algorithms and other mathematical tools, he enjoys listening to music, reading and playing table tennis.