Data di Pubblicazione:
2004
Citazione:
Localization of energy in FPU chains / L. Berchialla, L. Galgani, A. Giorgilli. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 11:4(2004), pp. 855-866. [10.3934/dcds.2004.11.855]
Abstract:
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 attention on a particular class of initial
conditions, namely, with all the energy on the first mode or the first few modes. We
observe that the approach to equipartition occurs on two different time scales: in a
short time the energy spreads up by forming a packet involving all low–frequency
modes up to a cutoff frequency ωc, while a much longer time is required in order to
reach equipartition, if any. In this sense one has an energy localization with respect
to frequency. The crucial point is that our numerical computations suggest that this
phenomenon of a fast formation of a natural packet survives in the thermodynamic
limit. More precisely we conjecture that the cutoff frequency ωc is a function of the
specific energy ε = E/N, where E and N are the total energy and the number of
particles, respectively. Equivalently, there should exist a function εc(ω), representing
the minimal specific energy at which the natural packet extends up to frequency ω.
The time required for the fast formation of the natural packet is also investigated.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
FPU model ; nonlinear systems
Elenco autori:
L. Berchialla, L. Galgani, A. Giorgilli
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