• Number 321  |
• September 27, 2010

Chorin and Sethian Team Up in Applied Math

Alexandre Chorin and James Sethian of the Computational Research Division at DOE’s Lawrence Berkeley National Laboratory have been described as shining examples of “what applied mathematics can accomplish to benefit science as a whole.”

It’s a judgment recently reconfirmed when the International Council for Industrial and Applied Mathematics (ICIAM) awarded Chorin the Lagrange Prize for his “fundamental and original contributions to applied mathematics, fluid mechanics, statistical mechanics, and turbulence modeling” and simultaneously gave Sethian the Pioneer Prize for work in the new field of imaging and shape recovery. These are two of the five prestigious math prizes ICIAM hands out just once every four years.

The problems Alexandre Chorin tackles aren’t political, and the attempted solutions certainly aren’t military, but it may be no accident that a man born in Warsaw, Poland, in 1938 has devoted much of his life’s work to understanding turbulence — essential for understanding combustion, energy efficiency, and fusion energy, among other subjects of interest to DOE.

"Turbulence is a very hard field,” Chorin says. "You really have to have knowledge in lots of other fields, and you have to do other things also if you ever are going to get satisfaction."

Some of his earliest work tackled airflow over an aircraft wing. The result was the overthrow of the Law of the Wall, a mathematical formulation virtually taken for granted since its first publication in, ironically, 1938. Chorin showed that the solutions to seemingly simple basic equations may be so complex, and the necessary computing power so vast, that precise solutions are unreachable. So he developed techniques like the Random Vortex Method, which approximates actual physical behavior in a way Chorin compares to impressionist painting: "Sometimes a Monet can capture nature more accurately than a photograph."

Chorin grew up in Israel and Switzerland and obtained his Ph.D. from New York University in 1966. After research at NYU’s Courant Institute he came to UC Berkeley, where he is a professor of mathematics. At Berkeley Lab he is a principal investigator with CRD’s Mathematics Department. 

James Sethian was born in Washington D.C. in 1954, received his B.A. from Princeton in 1976, and his Ph.D. from UC Berkeley in 1982. His graduate advisor was none other than Alexandre Chorin, “a wise and skilled thesis advisor: I am fortunate to be in the large community of his former students,” Sethian says.

He credits his early interest in the analysis of flame fronts to Chorin’s suggestions. “He artfully led me toward unanswered questions about interface evolution” and related puzzles, which eventually guided Sethian and his colleagues to methods for describing front propagation by solving equations on fixed grids — an approach now known as the Level Set Method.

“As first laid out, that version of the Level Set Method was mathematically appealing, numerically robust — and unnecessarily slow,” Sethian says, mostly because of the need to work in higher dimensions. With the help of his colleagues he tamed the cost by reducing the problem to its original dimensionality — at once a major mathematical development and a powerful computational tool with an astonishing array of applications.

The problems Sethian has attacked include inkjet design for high-speed printers; crystal growth; designing optimal structures under loads; etching and deposition in computer chip manufacture; shape-based image analysis in medicine and biomedicine; and seismic imaging for the petroleum industry.

Sethian was a postdoc at NYU’s Courant Institute, courtesy of the National Science Foundation, before joining the faculty of UC Berkeley in 1985, where he is a professor of mathematics. At Berkeley Lab he heads CRD’s Mathematics Department.

Submitted by DOE's Lawrence Berkeley National Laboratory