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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Figure 4 displays the full evolution, from the initial state to the generation of the moving chaotic breather.

Breathers Nonlinear waves Solitons. However, by accident, one day, they let the program run longer. When they realized their oversight and came back to the computer room, they noticed that the system, after remaining in the near equipartition state for a while, had then departed from it.

Views Read Edit View history. Inusing the so-called continuum limitZabusky and Kruskal were able to relate the periodic behavior observed in Figure 2 to the dynamics of localized excitations, nowadays known as solitons.

## Mathematicians Partially Solve Fermi-Pasta-Ulam Problem

A partial success was obtained using an adapted Krylov-Bogoliubov averaging method, which provided an estimate of the recurrence time Jackson, How, after all, can a chaotic system exhibit apparent periodic behavior?

This theoretical prediction was successfully tested numerically Izrailev et al.

Using the resonance overlap criterion, Izrailev and Chirikov predicted ferrmi, as the nonlinearity of the FPU model is increased, by e. Dashed lines indicate the uncertainty of the retrieved condition.

Weyl fermions are observed in a solid. This behavior is generic, because it is intimately related to modulational instabilitya self-induced modulation of the steady state resulting from a balance between nonlinear and dispersive effects. Mary Tsingou ‘s contributions to the FPUT problem were largely ignored by the community until Dauxois published additional information regarding the development and called for the problem to be renamed to grant proper attribution.

If instead of preparing a long wavelength low-frequency initial state, one now puts the energy in the short wavelength high-frequency part of the normal mode spectrum Zabusky and Deemthe pathway to equipartition may lead to the creation of highly localized excitations that have an oscillating amplitude and bear most of the energy: Blue and magenta lines in panels a — d are fitting functions according to Eq. Here results are scarce due to the numerical difficulty to simulate large lattices.

The solution of the paradox is two-fold.

### [] Propagation dynamics on the Fermi-Pasta-Ulam lattices

By using this site, you agree to the Terms of Use and Privacy Policy. Comparison of theory with computer solutions. The strong stochasticity threshold a term first used in Pettini and Landolfi exhibited in the numerical experiments of Livi and coworkers Livi et al. It is your responsibility to obtain pzsta proper permission from the rights holder directly for these figures.

### [nlin/] The Fermi-Pasta-Ulam “numerical experiment”: history and pedagogical perspectives

Grinevich 5,6P. Santini 2,6Pawta. It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4. An important open question is what remains of the FPU phenomenology in two-dimensional and three-dimensional lattices.

pasga During its motion the chaotic breather collects energy and its amplitude increases. This page was last edited on 19 Septemberat From the integrable to the nonintegrable regime. Nauk, N 3pp. Independendly, Bocchieri and collaborators Bocchieri et al.

## Fermi–Pasta–Ulam–Tsingou problem

Another may be that ergodic behavior may depend on the initial energy of the system. Zabusky and Kruskal argued that it was the fact that soliton solutions of the KdV equation can pass through one another without affecting the asymptotic shapes that patsa the quasi-periodicity of the waves in the FPUT experiment. White lines interpolate local maxima and serve as guides. Under this change of coordinates, the equation becomes:.