Qiang Du | Developing New Mathematical and Computational Tools for Science and Engineering

Oct 21 2014 | As an applied and computational mathematician, Du is internationally recognized as one of the world's leading researchers in the study of Ginzburg-Landau theory.

More and more researchers are using computational analysis to understand data and effectively model scientific solutions for needs that range from designing safer airplanes to understanding molecular structures and predicting social behavior. Key to a computer’s capability in solving complex, real-world problems are mathematical models and numerical algorithms.

Qiang Du
Qiang Du
Fu Foundation Professor of Applied Mathematics
—Photo by Jeffrey Schifman

“We live in an age where computational science is becoming a nascent interdisciplinary field and the advent of computing technology is rapidly transforming how mathematics get used in applications. What has intrigued me the most in my research are the challenging questions that have strong practical motivations and demand new mathematical and computational tools for their solutions,” says Qiang Du, the Fu Foundation Professor of Applied Mathematics.

As an applied and computational mathematician, Du is internationally recognized as one of the world's leading researchers in the study of Ginzburg-Landau theory, the mathematical theory used to describe phase transitions and the captivating phenomena of superconductivity. His research in this area gives a better understanding of how superconductors work, and helps scientists leverage superconductors’ unique capabilities most effectively.

He has also developed approaches to mathematically model and simulate other defects and interfaces in nature—in essence, portraying physical reality using equations, computer codes, and pictures that help explain complex systems. Some of those systems include materials phase boundaries, biological membranes, and quantized vortices in Bose-Einstein condensates—a type of flow pattern exhibited by certain collections of confined atoms at extremely cold temperatures. He has also contributed to the design of space tessellation and mesh generation strategies, and developed mathematical models to explore hidden structure and information in images and data.

“I am very proud to have worked with mathematicians to make advances in theory, and at the same time, to have teamed up with scientists in various disciplines to perform numerical simulations for challenging problems, validate theoretical findings, and provide practical solutions,” he says.

Du is continuing his research with a focus on developing mathematical tools and numerical algorithms for applications in physical, biological, materials, data, and information science. In the last few years he has become particularly interested in the mathematical and computational study of nonlocal models. Physical and biological interactions frequently involve the redistribution of organisms or molecules in space. It is difficult to collect data and pass through information over numerous time and spatial scales. Nonlocal mathematical models may be an effective alternative to bridge the different scales and help scientists make more accurate predictions and explore new questions.

“These new mathematical models, along with improved simulation techniques, have begun to populate in research areas like the study of materials damage, anomalous diffusion, and collective dynamics, and have great potential to help scientists and engineers,” says Du. His work in this direction is now partially supported through the newly funded Air Force Office of Scientific Research Multidisciplinary University Research Initiative (AFOSR MURI) center for Material Failure Prediction through Peridynamics.

Prior to joining Columbia Engineering, Du was the Verne M. Willaman Professor of mathematics and also a professor of materials science and engineering at Pennsylvania State University. He is a faculty affiliate of Columbia’s Data Science Institute. In 2013, he was selected as a Society for Industrial and Applied mathematics (SIAM) Fellow for contributions to applied and computational mathematics with applications in materials science, computational geometry, and biology.

BS, University of Science and Technology of China, 1983; PhD, Carnegie Mellon University, 1988

—by Amy Biemiller