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Physics 6720 Fermi-Pasta-Ulam Experiment

In the early 1950's electronic computers were in their infancy. Los Alamos National Laboratory acquired a MANIAC I, one of the first such computers. The new tools made it possible to explore problems that could not be solved with pencil and paper, leading to the creation of a new subdiscipline: computational physics. This was the setting for a landmark study in nonlinear mechanics by Enrico Fermi, J. Pasta, and Stanislaw Ulam (FPU) [1].

The FPU experiment was designed to investigate the process of thermalization in a complex mechanical system. The system they chose was a vibrating string with a weakly anharmonic (nonlinear) force law. The string was represented as a chain of masses connected with springs, making the number of degrees of freedom finite. The anharmonic force law is conservative (i.e. energy is conserved). The motion of a perfectly harmonic (linear) chain can be described in terms of normal modes. If such an harmonic chain is set into motion with only one normal mode excited, it continues to vibrate in only that mode. Thus the energy of motion is concentrated in one mode and remains so forever. Anharmonic terms in the force law induce coupling among the normal modes. So if a slightly anharmonic chain is set into motion in one of the harmonic modes, one expects that with time, other modes will be excited and the initial energy of motion will be redistributed among them. The motion is quite complex and one might ask whether such a system is complex enough that the laws of statistical mechanics apply, namely, that with time the energy of motion will be distributed uniformly among all the degrees of freedom -- i.e. normal modes. They were surprised at what they found. You will be, too.

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Carleton DeTar 2005-11-07