Advancing the science
of advancing interfaces
Posted Dec 5, 2008
Mathematician James Sethian works on the edge. He confronts one of the most challenging problems in physics: capturing the behavior of moving interfaces, the edges where one material pushes into or retreats from another – where a gas mixes and burns, where metals or coatings meet silicon chips, even where ink meets air.
Sethian, a Lawrence Berkeley National Laboratory (LBNL) senior scientist and University of California at Berkeley mathematics professor, has led a three-decade effort to build computer codes that model combustion, that reconstruct the delicate structures hidden in the human body and that improve the analysis of everything from seismic waves to noisy images. The results have, among other practical applications, improved computer chip manufacturing and medical images and helped in oil discovery.
Although most of the applications have moving interfaces in common, their underlying physics and chemistry can vary widely. Sethian has pushed to come up with the right equations to depict those physical and chemical processes, then couple these processes to numerical algorithms that track interfaces.
When he started at Berkeley and LBNL (and for a period at the Courant Institute of Mathematics before returning) in the late 1970s, Sethian focused on building accurate codes to numerically simulate combustion. “The real dynamics of flame fronts are challenging: the geometry of the advancing flame, the local chemistry and complex breaking and merging all factor into determining the efficiency of the burning process,” he says. “I was trying to track the geometry advancing combustion zones, but there weren’t good algorithms to track moving flame fronts in even two dimensions, let alone three dimensions.”
Most numerical models of moving interfaces tracked connected “markers” placed along the interface, an arrangement Sethian compares to buoys linked with ropes. The methods either failed or became very difficult if the markers crossed over themselves or the boundary broke up. “That led to trying to build better numerical algorithms to track moving fronts in general,” he says.