The FPU Model and Simulation: “A Little Discovery”

Abstract

In the Spring of 1952, the MANIAC-I computing machine came on line at Los Alamos. One of the first digital computers, it filled a large room, used vast arrays of large, hot, glowing vacuum tubes for computation, and processed box after box of permanently inscribed, single-command, disposable, punched cards. That summer, in a professional configuration foreshadowing the disciplinary alliance of the future, physicist Enrico Fermi, computer scientist John Pasta, and mathematician Stanislaw Ulam, gathered together to discuss the computation potential presented by the speed, accuracy, and relentless automation of these new electronic marvels. Although these machines were quite a bit slower than even the first personal computers of the 1970s, to say nothing of the workstations most physicists use routinely today, they could provide access to some of those physical problems that had remained marginalized for 50 years because it took so long to laboriously carry out numerical methods by hand. Fermi wanted to develop new heuristic techniques for investigating nonlinear dynamical problems “experimentally” by beginning with the simplest possible nonlinear problem, solving it, and moving on to successively more complex problems, perhaps even making an approach to one of the most difficult nonlinear problems of all—turbulence.

. . . it makes an enormous difference how the atoms are placed, and in what position they are brought together, and what movements they give each other and receive, and how the same atoms, with only a little change, can make both “flames” and “firs,“ just as these two words have similar elements, but differently arranged, and so we speak of flames and firs by different names.

Lucretius (Book I, lines 908–914)

Let us say here that the results of our computations show features which were, from the beginning, surprising to us.

Fermi, Pasta and Ulam (1955, p. 981