The Fermi–Pasta–Ulam ‘numerical experiment’: history and pedagogical perspectives

The pioneering Fermi–Pasta–Ulam (FPU) numerical experiment played a major role in the history of computer simulation because it introduced this concept for the first time. Moreover, it raised a puzzling question which was answered more than 10 years later. After an introduction to this problem, we briefly review its history and then suggest some simple numerical experiments, with the Matlab© code provided, to study various aspects of the ‘FPU’ problem. 1. The physical question The ‘FPU problem’, as it is known presently, bears the name of the three scientists3 who wanted to study the thermalization process of a solid [1]. As revealed by Ulam later [2], these authors were looking for a theoretical physics problem suitable for an investigation with one of the very first computers, the MANIAC (Mathematical Analyzer, Numerical Integrator and Computer). Their work, published in 1955 in a classified Los Alamos National Laboratory report, had been completed shortly before the death of Enrico Fermi in 1954. Ulam told later that Fermi did not suspect the importance of this discovery and considered this work as ‘minor’. He nevertheless intended to talk about it at the conference of the American Mathematical Society where he had been invited just before he became seriously ill. Fermi, Pasta and Ulam decided to study how a crystal evolves towards thermal equilibrium by simulating a chain of particles of unitary mass, linked by a quadratic interaction potential, 3 Ms Mary Tsingou, who took part in the numerical study with Fermi, Pasta and Ulam is not an author of the report, however, her contribution is recognized in two lines of the acknowledgment section of the FPU report. 0143-0807/05/050003+09$30.00 c © 2005 IOP Publishing Ltd Printed in the UK S3