Fermi–Pasta–Ulam problem

The Fermi - Pasta - Ulam experiment investigates the vibration behavior of complex systems. The surprising result of this experiment is one of the major contributions of the research on chaos. As one of the first computer experiments it influenced the process of the simulation as an experimental technique significantly.

Experimental arrangement

This experiment was conducted in summer 1953 by Enrico Fermi, John R. Pasta, Stanislaw Ulam and Mary Tsingou and published in 1955 in a report by the Los Alamos National Laboratory. It was one of the first computer experiments; the experimental arrangement was a computer, the MANIAC I, simulated model. We investigated the energy of a vibrating string, whose behavior is described by a nonlinear partial term ( quadratic and cubic).

Expectation

For a linear oscillator to the same conditions after the same time (or local ) basis set again, there are individual frequencies ( oscillation modes ) can be determined. Expected for non-linear coupling Fermi an ergodic behavior: the dominant frequency is weakening in its effects, all modes can be excited equally → the arrangement behaves randomly.

Results

Instead of random raises an almost periodic (quasi- periodic ) behavior. It is concluded:

• Many non- linear equations are solved exactly
• Ergodic behavior may be dependent on the initial energy

1965 could Norman Zabusky and Martin Kruskal show that the Korteweg -de Vries equation is the continuous limit case, and thus give a first explanation for the quasi- periodic behavior.

In addition to these findings on the complexity of nonlinear systems using a computer to study mechanical and physical processes is a pioneering venture.