Don Estep, a mathematics professor at Colorado State University, is part of a team of researchers that won a three-year, $2.3 million grant from the U.S. Department of Energy to develop new mathematical equations that model physical phenomena important to the country’s energy problems.

The grant was one of 13 awarded after an intensely competitive review of more than 300 proposals. Estep’s group also includes researchers from the Sandia National Laboratories, Florida State University and Rensselaer Polytechnic Institute.

The DOE needs new mathematical equations for further research on such complex matters as fusion reactors, nanoscale devices such as molecule-scale transistors and micro-gears, nanoscale fibrous materials used in new kinds of protective clothing and the molecular-scale water shell that forms around medical implants.

Estep’s team’s project goal is to develop a mathematical theory for coupling atomistic physics to continuum physics. Atomistic physics describes situations like a very sparse gas, in which the behavior of individual atoms and molecules has to be considered. Mathematically, this often involves probability and statistics. In continuum physics, used for dense fluids and solids, the atoms and molecules are grouped together in the mathematical description, which often involves differential equations. Modern engineering requires coupling of these two regimes.

"Our project team includes leading engineers and mathematicians from both the academic and national lab communities," Estep said. "The project has very much to do with teamwork and interdisciplinary science and mathematics."

The research is funded under the Department of Energy’s Office of Science "Multiscale Mathematics" program. The Department of Energy wants scientists to study how different physical processes work together and then develop mathematical equations that describe those processes and their interactions.

"Brute force computational simulation, even on the most powerful present-day computers, cannot handle these ranges, so new mathematics is needed," said Raymond L. Orbach, director of the Office of Science for the Department of Energy. "This initiative is meant to surmount this barrier to our understanding of nature."

Estep has taught in the College of Natural Sciences at Colorado State since 2000. He received his bachelor’s from Columbia University and his master’s and doctoral degrees from the University of Michigan.

His research involves development of new numerical techniques, new and interesting mathematical analysis, computational investigations of specific problems and software development. He is the co-director of PRIMES, an interdisciplinary graduate training program in quantitative ecology supported by an Integrative Graduate Education and Research Traineeship grant from the National Science Foundation. He is also the faculty advisor for the Rams Cycling Team.

This summer, he received an international award, the 2005 Mid Career Prize from Computational and Mathematical Methods in Science and Engineering. The prize is given every year to researchers who make exceptional contributions in the areas of applied and computational mathematics.

"Professor Estep’s ground-breaking work has been recognized worldwide for some time, and this award is further evidence for both the quality of his mathematics and the impact of his research," said Rick Miranda, dean of the College of Natural Sciences at Colorado State. "On our campus he has been a vigorous leader in applied mathematics, serving as co-director of the Program for Interdisciplinary Mathematics, Ecology, and Statistics (PRIMES), being heavily involved in the formation of the Information Science and Technology Center, and having substantive collaborations with colleagues across campus, especially in Natural Resources and in Engineering. These accolades are well deserved."

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