Parallel computers ‘evolutionize’ research (continued)

“Coefficients for reactions involving simple chemical species—such as oxygen reacting with hydrogen—can be calculated precisely on a desktop PC,” Minkoff said. But as molecular size increases, the calculations rapidly outstrip the capabilities of most massively parallel computers.

Minkoff and Wagner use a matrix-based approach that allows parallel computers to calculate systems involving molecules containing many atoms. The elements of the matrix are combinations of kinetic and potential energy associated with the molecules’ relative proximity and orientation. The computations involve multidimensional space and identify the most stable energy states among the molecules. Key to their research is PETSc, the “Portable, Extensible Toolkit for Scientific computation” developed by Argonne’s Mathematics and Computer Science Division to solve large-scale, specialized problems.

Minkoff and Wagner start by modeling reactions of simple, two-atom molecules and test their results against the precise mathematical solution. They then expand their model to include more complex molecules containing many atoms and compare their results with those from the traditional approach, which uses statistical methods to estimate the coefficients. Their work is funded by the U.S. Department of Energy’s (DOE) Office of Basic Energy Science and Office of Advanced Scientific Computing Research.

Diving into the nucleus
Argonne physicists Steve Pieper and Bob Wiringa work deeper inside the atom. They use parallel supercomputers to calculate the forces that bind together nucleons—protons and neutrons—to form atomic nuclei. Their goal is to develop theory that matches observation.

“Good theory has to explain, for example, why there’s no stable eight-body nucleus,” Wiringa said. “This imposes a limit on the nuclei created in the earliest moments of the Big Bang. In the beginning, there were no nuclei with more than seven nucleons.”

A key challenge is to find models that work for both neutron-rich nuclei—those with a high ratio of neutrons to protons—and for those with equal numbers.

“If we want to compute the forces in neutron stars, which are essentially all neutrons,” Wiringa said, “we need to understand neutron-rich nuclei like helium-10, which is unstable.” With two protons and eight neutrons, helium-10 is the most neutron-rich nucleus known.

Pieper and Wiringa study nuclei with five to 10 nucleons. Their work begins with a model that calculates the binding energies for two-body nuclei.

Known from thousands of experiments involving collisions, binding energies are the precise energies required to break a nucleus apart. Each nucleus has more than one binding energy, depending on whether it is at its “ground” or most stable state, or whether it has been excited to an intermediate state by an interaction that imparted some energy but not enough to break it apart.

Pieper and Wiringa’s two-body model is the “Argonne potential,” published in 1995 by Wiringa and colleagues from Flinders University, South Australia, and Old Dominion University, Va. In 2000, their paper was the world’s most cited theoretical nuclear physics publication.

To study nuclei with more than two nucleons, Pieper and Wiringa extend the two-body model by adding the “Illinois family,” a collection of three-body models they developed with Vijay Pandharipande of the University of Illinois at Urbana-Champaign.

“The required computing power,” explained Pieper, “increases exponentially with the number of nucleons. Calculations for up to six bodies can be done on a modern PC. For seven or eight, we can use Chiba City comfortably, but it’s a stretch for nine. For 10, we use the National Energy Research Scientific Computing Center at Lawrence Berkeley National Laboratory.”

To compute a single 10-body energy state, 500 processors work in parallel at 250 million operations a second for eight to 15 hours. “And,” said Pieper, “we have to test a whole family of energy states.”

Their recent work, funded by DOE’s Nuclear Physics Division, provides a fairly consistent picture of binding in nuclei with up to 10 nucleons. Their next step, as computing power continues to expand, will be to extend their work to larger nuclei.

For more information, please contact David Baurac.

Return to beginning of this story

Next: New section - World-Class Research Facilities

Back to top