Modulational instability in isolated and driven Fermi–Pasta–Ulam lattices |
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Authors: | T Dauxois R Khomeriki S Ruffo |
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Institution: | (1) Laboratoire de Physique, UMR-CNRS 5672, ENS Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France;(2) Dipartimento di Energetica, “S. Stecco” and CSDC, Università di Firenze and INFN, via S. Marta 3, 50139 Firenze, Italy;(3) Department of Exact and Natural Sciences, Tbilisi State University, 3 Chavchavadze Avenue, Tbilisi, 0128, Georgia |
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Abstract: | We present a detailed analysis of the modulational
instability of the zone-boundary mode for one and higher-dimensional
Fermi–Pasta–Ulam (FPU) lattices. The growth of the instability is followed by
a process of relaxation to equipartition, which we have
called the Anti-FPU problem because the energy is initially
fed into the highest frequency part of the spectrum, while in the
original FPU problem low frequency excitations of the
lattice were considered. This relaxation process leads to the formation of chaotic
breathers in both one and two space dimensions. The system then relaxes to
energy equipartition, on time scales that increase as the energy
density is decreased. We supplement this study by considering the
nonconservative case, where the FPU lattice is homogeneously driven at
high frequencies. Standing and travelling nonlinear waves and
solitonic patterns are detected in this case. Finally we investigate
the dynamics of the FPU chain when one end is driven at a frequency located
above the zone boundary. We show that this excitation stimulates
nonlinear bandgap transmission effects. |
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Keywords: | |
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