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We focus on two approaches that have been proposed in recent years for the explanation of the so-called Fermi-Pasta-Ulam (FPU) paradox, i.e., the persistence of energy localization in the "low-q " Fourier modes of Fermi-Pasta-Ulam nonlinear lattices, preventing equipartition among all modes at low energies. In the first approach, a low-frequency fraction of(More)
A numerical and analytical study of the relaxation to equilibrium of both the Fermi-Pasta-Ulam (FPU) α-model and the integrable Toda model, when the fundamental mode is initially excited, is reported. We show that the dynamics of both systems is almost identical on the short term, when the energies of the initially unexcited modes grow in geometric(More)
– We study a long-range–interaction generalisation of the one-dimensional Fermi-Pasta-Ulam (FPU) β-model, by introducing a quartic interaction coupling constant that decays as 1/r α (α ≥ 0) (with strength characterised by b > 0). In the α → ∞ limit we recover the original FPU model. Through molecular dynamics we show that i) for α ≥ 1 the maximal Lyapunov(More)
We study numerically statistical distributions of sums of orbit coordinates, viewed as independent random variables in the spirit of the Central Limit Theorem, in weakly chaotic regimes associated with the excitation of the first (k = 1) and last (k = N) linear normal modes of the Fermi-Pasta-Ulam-α system under fixed boundary conditions. We show that at(More)
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