Fermi Pasta Ulam Tsingou Experiment

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The Fermi-Pasta-Ulam-Tsingou-Experiment (often also called Fermi-Pasta-Ulam-Experiment ) investigates the vibrational behavior of complex systems . The surprising result of this experiment is one of the essential contributions of chaos research .

As one of the first computer experiments, it also had a significant influence on the simulation process as an experimental technique .

Experimental set-up

In the case of a linear oscillator (purple), the entire amplitude remains in one oscillation mode. With quadratic non-linear coupling, the energy is distributed to all vibration modes. But after a while the entire amplitude returns to the original mode of vibration.

This experiment was carried out in the summer of 1953 by Enrico Fermi , John R. Pasta , Stanislaw Ulam and Mary Tsingou and published in a 1955 report by the Los Alamos National Laboratory . It was one of the first computer experiments; The experimental setup was in the computer , the MANIAC I , simulated model . Analyzes was energy of a vibrating string whose behavior with a non-linear portion of term ( quadratic and cubic will be described).

Expectation

In the case of a linear oscillator , the same states are set up again after the same time (or local) intervals; individual frequencies ( oscillation modes ) can be determined.

In the case of non-linear coupling , Fermi expected an ergodic behavior: the determining frequency weakens in its effect, all modes can be excited equally → the arrangement behaves randomly.

Results

Instead of the random, an almost periodic (quasi-periodic) behavior occurs. From this it is concluded:

  • many non-linear equations can be solved exactly
  • Ergodic behavior can depend on the initial energy

In 1965, Norman Zabusky and Martin Kruskal were able to show that the Korteweg-de-Vries equation represents the continuous borderline case and thus provide an initial explanation for the quasi-periodic behavior.

In addition to these findings on the complexity of non-linear systems, the use of a computer to investigate mechanical and physical processes is a pioneering achievement .

See also

literature

  • E. Fermi, J. Pasta, S. Ulam: Studies of Nonlinear Problems (PDF; 595 kB) . Document LA-1940 (May 1955)
  • Thomas P. Weissert: The Genesis of Simulation in Dynamics: Pursuing the Fermi-Pasta-Ulam Problem. New York [u. a.], Springer, 1997
  • Thierry Dauxois: Fermi, Pasta, Ulam and a mysterious lady. Physics Today (January 2008)
  • NJ Zabusky and MD Kruskal: Interaction of solitons in a collisionless plasma and the recurrence of initial states . Phys. Rev. Lett. 15 (1965), pp. 240-243
  • Mason A. Porter, Norman J. Zabusky, Bambi Hu and David K. Campell: Fermi, Pasta, Ulam and the Birth of Experimental Mathematics . Spectrum of Science 11/2010, pp. 70–77