Ponno, A., Christodoulidi, Helen, Skokos, Ch. and Flach, S. (2011) The twostage dynamics in the FermiPastaUlam problem: From regular to diffusive behavior. Chaos: An Interdisciplinary Journal of Nonlinear Science, 21 (4). 043127. ISSN 10541500
Full content URL: http://doi.org/10.1063/1.3658620
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Item Type:  Article 

Item Status:  Live Archive 
Abstract
A numerical and analytical study of the relaxation to equilibrium of both the FermiPastaUlam (FPU) αmodel 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 progression with time, through a secular avalanche process. At the end of this first stage of the dynamics, the timeaveraged modal energy spectrum of the Toda system stabilizes to its final profile, well described, at low energy, by the spectrum of a qbreather. The Toda equilibrium state is clearly shown to describe well the longliving quasistate of the FPU system. On the long term, the modal energy spectrum of the FPU system slowly detaches from the Toda one by a diffusivelike rising of the tail modes, and eventually reaches the equilibrium flat shape. We find a simple law describing the growth of tail modes, which enables us to estimate the timescale to equipartition of the FPU system, even when, at small energies, it becomes unobservable.
Keywords:  FermiPastaUlam, qbreathers, Energy localization 

Subjects:  G Mathematical and Computer Sciences > G121 Mechanics (Mathematical) F Physical Sciences > F340 Mathematical & Theoretical Physics G Mathematical and Computer Sciences > G120 Applied Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
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ID Code:  37110 
Deposited On:  16 Sep 2019 10:14 
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