## The master of Monte Carlo

A well-known pragmatist among theoretical physicists, Berni Alder’s first thought after hearing last fall that he was to receive the National Medal of Science, the nation’s highest honor for scientific achievement, was that maybe this would attract more people to work on projects with him.

Although officially retired from Lawrence Livermore National Laboratory (LLNL), Alder has a laundry list of unsolved issues in molecular dynamics, the computational method he invented and which has garnered him international accolades. Molecular dynamics and Alder’s Monte Carlo methods are nearly ubiquitous, used to solve problems in physics, molecular biology and other diverse areas.

After such a distinguished career, Alder certainly could have retired with his place secure in the history of computational physics. But he still feels the same need to prove his methods as he did in the early 1950s, when the idea of using computational methods to model physical systems was controversial.

“Among theoretical physicists in the early days there was great bias against computational methods, because they are cumbersome,” Alder says. “You want a nice analytic solution. It took decades to get to computational methods accepted intellectually by the hard-nosed theoretical physicists.”

Alder began as one of those theoretical physicists, but the complexity of the problems he was trying to solve drove him to computational approaches. As a graduate student, Alder worked with theoretical chemist John Kirkwood at the California Institute of Technology on the fundamental question of whether “hard spheres,” an idealized representation of the atoms, could form a solid without attractive forces between the spheres. If you could pack molecules more efficiently in a solid than a fluid, would their atom-spheres condense into a solid? And what would that phase transition look like?

Kirkwood had been working on a theoretical answer to the question, but it required the solution of a nonlinear integro-partial differential equation – notoriously difficult equations for finding an analytical solution and determining whether it’s unique.

“We didn’t know whether a solution existed,” Alder says.

The problem required a large number of calculations repeated over and over. The year was 1948, and the U.S. nuclear arms race with the Soviets was reaching fever pitch. The Los Alamos and Lawrence Livermore weapons labs had developed computational methods to handle complex nuclear reactions and some of those chemists and physicists now were moving into academic roles. Alder asked one such physicist, Stan Frankel, then head of a new digital computing group at Caltech, to help him with his hard sphere problem.

The two pondered how to solve the integral equation before seeking a better way.

Frankel had encountered computational modeling techniques such as the Monte Carlo method at Los Alamos, where he worked on the Manhattan Project. Before long, he and Alder were applying the method to solve Alder’s problem. It soon became apparent that the large computers needed to solve these problems resided at the national labs, and Alder took a position at LLNL, teaming with physicist Thomas E. Wainwright to complete the hard sphere problem.

The hard-sphere transition still cannot be solved using theoretical methods. If Alder and colleagues had continued working the problem using the old methods, they would almost certainly have failed. Instead, they ushered in a technique scientists and engineers still use today to understand the atomic and molecular interactions in many chemical and biological systems.

The 1956 paper that emerged from these early forays, “Phase Transition for a Hard Sphere System,” is often marked as the birth of molecular dynamics as a field.

Molecular dynamics takes advantage of what computers are good at: solving a given calculation in repeating loops. Given the precise coordinates of every atom in a defined system, the effect of hard sphere collisions can be calculated over time. The genius of Alder’s method was circumventing uncertainty, the bugbear of partial differential equations, and finding a numerical solution with no approximations.

“Computational methods are like numerical experiments,” he says. They enable scientists to describe a system mathematically, then perturb it in some way and allow the numerical experiment the freedom to react to those perturbations.