Abstract: The Fermi-Pasta-Ulam (FPU) pioneering numerical experiment played a major role in the history of computer simulation because it introduced this. Abstract: A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with its suggested resolutions and its relation to other. Abstract: The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition.

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One of the most controversial phenomena in nonlinear dynamics is the reappearance of initial conditions. Celebrated as the Fermi-Pasta-Ulam-Tsingou problem, the attempt to understand how these recurrences form during the complex evolution that leads to equilibrium has deeply influenced the entire development of nonlinear science.

The enigma is rendered even more intriguing by the fact that integrable models predict recurrence as exact solutions, but the difficulties involved in upholding integrability for a sufficiently long dynamic has not allowed a quantitative experimental validation. In natural processes, coupling with the environment rapidly leads to thermalization, and finding nonlinear multimodal systems presenting multiple returns is a long-standing open challenge.

Here, we report the observation of more than three Fermi-Pasta-Ulam-Tsingou recurrences for nonlinear optical spatial waves and demonstrate the control of the recurrent behavior through the phase and amplitude of the initial field. These results identify the origin of the recurrence in the integrability of the underlying dynamics and allow us to achieve one of the basic aspirations of nonlinear dynamics: Flammini 2L.


Zhang 1G. Marcucci 2,3A.

Mathematicians Partially Solve Fermi-Pasta-Ulam Problem

Agranat 4P. Grinevich 5,6P. Santini 2,6C. Conti 2,3and E.

Nonlinear Sciences > Pattern Formation and Solitons

Nonlinear systems can return to a previously experienced state during their complex evolution. How, after all, can a chaotic system exhibit apparent periodic behavior? Here, we experimentally demonstrate that the general phenomenon of recurrence in a system corresponds to a collective motion among the constituents that is closely determined by the initial state and described by exact solutions of the underlying model. Recurrences are believed to be extremely sensitive to any environmental perturbations that characterize a natural system.

For this reason, they have eluded in-depth experimental investigations, and hypotheses on their physical origin have eluded validation until now. Using a novel optical setup in which light waves propagate in a nonlinear medium, we report the record observation of more than three Fermi-Pasta-Ulam-Tsingou recurrences and their deterministic control through the initial optical field.

Our results represent an unprecedented test for statistical mechanics and nonlinear wave theory and establish a paradigm that could impact future developments in the control and forecasting of unstable nonlinear systems from hydrodynamics to nonlinear optics.

Properties of the recurrent behavior. White lines interpolate local maxima and serve as guides. Blue and magenta lines in panels a — d are fitting functions according to Eq. We show measured dots and retrieved line apsta fields for different initial phases: Dashed lines indicate the uncertainty of the retrieved condition. From the integrable to the nonintegrable regime.


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X 8— Published 29 October Abstract One of the most controversial phenomena in nonlinear ferni is the reappearance of initial conditions.

Nonequilibrium statistical mechanics Nonlinear beam dynamics Nonlinear optics Optical solitons Pattern formation Spatiotemporal chaos. Breathers Nonlinear waves Solitons.

Weyl fermions are observed in a solid. Figure 1 Experimental setup. Figure 3 Properties of the recurrent behavior.

Fermi–Pasta–Ulam–Tsingou problem – Wikipedia

Figure 4 Inverse problem. Figure 5 From the integrable to the nonintegrable regime. Sign up to receive regular ferni alerts from Physical Review X. Series I Physics Physique Fizika.

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