Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition.

@article{Penati2007TailRO,
  title={Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition.},
  author={Tiziano Penati and Sergej Flach},
  journal={Chaos},
  year={2007},
  volume={17 2},
  pages={
          023102
        }
}
Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time, resonant anomalies (peaks) are observed in its weakly excited tail for long times preceding equipartition. We observe a similar resonant tail structure also for exact time-periodic Lyapunov orbits, coined q-breathers due to their exponential localization in modal space. We give a… 

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References

SHOWING 1-10 OF 35 REFERENCES
q-Breathers and the Fermi-Pasta-Ulam problem.
TLDR
Normal modes from the harmonic limit into the FPU parameter regime are continued and persistence of these periodic orbits are obtained, termed here q-breathers (QB), characterized by time periodicity, exponential localization in the q-space of normal modes and linear stability up to a size-dependent threshold amplitude.
q-breathers in Fermi-Pasta-Ulam chains: existence, localization, and stability.
TLDR
This work continues normal modes from the harmonic limit into the FPU parameter regime and gets persistence of these periodic orbits, termed here q-breathers (QB), characterized by time periodicity, exponential localization in the q-space of normal modes, and linear stability up to a size-dependent threshold amplitude.
Time scale to ergodicity in the Fermi-Pasta-Ulam system.
TLDR
A theory to determine the time evolution and the excitation of the nonlinear modes based on a resonant normal form treatment of the resonances among the oscillators is developed, which predicts the critical energy for equipartition, the time scale to equipartsition, and the form of theNonlinear modes below equipartitions in qualitative agreement with the numerical results.
Discrete breathers in Fermi-Pasta-Ulam lattices.
TLDR
The interplay between energy thresholds for breathers in the presence of strongly asymmetric FPU potentials and the corresponding profiles of the low-frequency limit of breather families are analyzed.
Localization of energy in FPU chains
We revisit the celebrated model of Fermi, Pasta and Ulam with the aim of investigating, by numerical computations, the trend towards equipartition in the thermodynamic limit. We concentrate our
Equipartition times in a Fermi-Pasta-Ulam system
We investigate with numerical methods the celebrated Fermi-Pasta- Ulam model, a chain of non-linearly coupled oscillators with identical masses. We are interested in the evolution towards
Exact solutions in the FPU oscillator chain
q-Breathers in finite two- and three-dimensional nonlinear acoustic lattices.
TLDR
By use of perturbation theory and numerical calculations, it is obtained that the localization and stability of QBs are enhanced with increasing system size in higher lattice dimensions opposite to their one-dimensional analogues.
On Metastability in FPU
We present an analytical study of the Fermi–Pasta–Ulam (FPU) α–model with periodic boundary conditions. We analyze the dynamics corresponding to initial data with one low frequency Fourier mode
The Fermi-Pasta-Ulam Problem in the Thermodynamic Limit
In the present contribution we justify and discuss the scaling laws characterizing the first phase of the energy transfer from large to small spatial scales in a chain of nonlinear oscillators (the
...
...