en
Scientific article
Open access
English

On the energy distribution in Fermi-Pasta-Ulam lattices

Published inArchive for rational mechanics and analysis, vol. 205, no. 3, p. 993-1029
Publication date2012
Abstract

For FPU chains with large particle numbers, the formation of a packet of modes with geometrically decaying harmonic energies from an initially excited single low-frequency mode and the metastability of this packet over longer time scales are rigorously studied in this paper. The analysis uses modulated Fourier expansions in time of solutions to the FPU system and exploits the existence of almost-invariant energies in the modulation system. The results and techniques apply to the FPU alpha- and beta-models as well as to higher-order nonlinearities. They are valid in the regime of scaling between particle number and specific energy in which the FPU system can be viewed as a perturbation to a linear system, considered over time scales that go far beyond standard perturbation theory. Weak non-resonance estimates for the almost-resonant frequencies determine the time scales that can be covered by this analysis.

Keywords
  • Fermi-Pasta-Ulam lattice
  • Energy distribution
  • Modulated Fourier expansion
Citation (ISO format)
HAIRER, Ernst, LUBICH, Christian. On the energy distribution in Fermi-Pasta-Ulam lattices. In: Archive for rational mechanics and analysis, 2012, vol. 205, n° 3, p. 993–1029. doi: 10.1007/s00205-012-0526-3
Main files (1)
Article (Accepted version)
accessLevelPublic
Identifiers
ISSN of the journal0003-9527
540views
315downloads

Technical informations

Creation08/23/2012 7:44:00 AM
First validation08/23/2012 7:44:00 AM
Update time03/14/2023 5:39:37 PM
Status update03/14/2023 5:39:37 PM
Last indexation01/16/2024 12:08:34 AM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack