American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 113-122. doi: 10.3934/proc.2003.2003.113

Stages of energy transfer in the FPU model

Joseph A. Biello 1, , Peter R. Kramer 1, and  Yuri Lvov 1,

1. 

Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 301 Amos Eaton Hall, 110 8th Street, Troy, NY 12180, United States, United States, United States

Received  September 2002 Revised  April 2003 Published  April 2003

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: equipartition., weak turbulence, resonance broadening, Fermi-Pasta-Ulam model.
Mathematics Subject Classification: Primary: 41A60, 82C05, 82C28, Secondary: 34E13,37K6.
Citation: Joseph A. Biello, Peter R. Kramer, Yuri Lvov. Stages of energy transfer in the FPU model. Conference Publications, 2003, 2003 (Special) : 113-122. doi: 10.3934/proc.2003.2003.113
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