On the door of James Anderson’s office, you’ll
find no name plate, just a large illustration of a mathematical
methodology called Direct Simulation Monte Carlo. Tacked to a nearby
bulletin board, a tiny tag that looks like it came from the back
of a soda bottle: “Sorry, you are not an instant winner.”
The self-effacing Anderson pioneered the application of the Monte
Carlo method to the calculation of the energies of atomic interactions.
His work has helped him come part of the way toward a life-long
goal: solving one of mathematics’ Grand Challenges—the
sign problem.
“We can solve very small problems exactly—which is
something new and different in quantum mechanics—but that
Grand-Challenge problem is still out there for large systems,”
he explains.
Anderson, an Evan Pugh Professor of Chemistry
and Physics, brings complex
information home to his students the old-fashioned way: visual aids.
He proudly shows off his notebook of class notes, complete with
color transparencies of drunken sailors (the Random Walk), error
bars reduced to nothing but a + sign, but magnified to fill the
page (“you still can’t see the error”), and the
old Johnny Mercer lyrics, “You’ve got to accentuate
the positive, eliminate the negative” (the sign problem).
Anderson also finds time to direct the Penn
State Consortium for Education in Many-Body Applications supported
by the National Science Foundation’s
Integrated Graduate Education and Research Training (IGERT) program.
Its goal is to expand and improve the work of graduate students
and faculty across multiple disciplines.
“It’s interesting the things you have to do to force
people to get together!” he says, laughing. “What the
NSF is looking for is trendsetters with ideas that will spread—and
this could spread.”
Anderson’s latest prediction is that a detonation can go
much faster than prev-iously thought (see pg 13). Thanks to faster
computers combined with the Monte Carlo method, Anderson was able
to predict some-thing never before imagined to be true. “Simplified
models, in which the shock wave is assumed to precede the reaction,
are incomplete,” Anderson writes in his paper on the discovery.
“We find that the reaction and the shock regions may overlap
and ‘ultrafast’ detonations may occur.” While
he down-plays the effect of this discovery, he admits that it could
affect how scientists respond to some observations they have been
making.
Anderson’s life is full of predictions. That may be why he
enjoys scuba diving, a totally unpredictable sport he jumped into
only five years ago. He now travels to Grand Cayman or Bonaire for
some of the best diving in the world.
But his mind is always working on the sign problem somehow. “The
beauty of working on that particular problem is that you could hit
it at any time. The solution could be just around the corner.”
Suzan Erem
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