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Stages of energy transfer in the FPU model

Pages: 113 - 122, Issue Special, July 2003

 Abstract        Full Text (219.3K)              

Joseph A. Biello - Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 301 Amos Eaton Hall, 110 8th Street, Troy, NY 12180, United States (email)
Peter R. Kramer - Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 301 Amos Eaton Hall, 110 8th Street, Troy, NY 12180, United States (email)
Yuri Lvov - Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 301 Amos Eaton Hall, 110 8th Street, Troy, NY 12180, United States (email)

Abstract: The (alpha) version of the Fermi-Pasta-Ulam is revisited through direct numerical simulations and an application of weak turbulence theory. The energy spectrum, initialized with a large scale excitation, is traced through a series of distinct qualitative phases en route to eventual equipartition. Weak turbulence theory is applied in an attempt to provide an effective quantitative description of the evolution of the energy spectrum. Some scaling predictions are well-confirmed by the numerical simulations.

Keywords:  Fermi-Pasta-Ulam model, weak turbulence, resonance broadening, equipartition.
Mathematics Subject Classification:  Primary: 41A60, 82C05, 82C28, Secondary: 34E13,37K60.

Received: September 2002;      Revised: April 2003;      Published: April 2003.