Continuing the previous work on the same subject, we study here different two-dimensional Fermi– Pasta–Ulam FPU-like models, namely, planar models with a triangular cell, molecular-type potential and different boundary conditions, and perform on them both traditional FPU-like numerical experiments, i.e., experiments in which energy is initially concentrated on a small subset of normal modes, and other experiments, in which we test the time scale for the decay of a large fluctuation when all modes are excited almost to the same extent. For each experiment, we observe the behavior of the different two-dimensional systems and also make an accurate comparison with the behavior of a one-dimensional model with an identical potential. We assume the thermodynamic point of view and try to understand the behavior of the system for large n the number of degrees of freedom at fixed specific energy =E/n. As a result, it turns out that: i The difference between dimension one and two, if n is large, is substantial. In particular making reference to FPU-like initial conditions the “one-dimensional scenario,” in which the dynamics is dominated for a long time scale by a weakly chaotic metastable situation, in dimension two is absent; moreover in dimension two, for large n, the time scale for energy sharing among normal modes is drastically shorter than in dimension one. ii The boundary conditions in dimension two play a relevant role. Indeed, models with fixed or open boundary conditions give fast equipartition, on a rather short time scale of order −1, while a periodic model gives longer equilibrium times although much shorter than in dimension one.

A study of the FermiPasta–Ulam problem in dimension two

Gradenigo G
2008

Abstract

Continuing the previous work on the same subject, we study here different two-dimensional Fermi– Pasta–Ulam FPU-like models, namely, planar models with a triangular cell, molecular-type potential and different boundary conditions, and perform on them both traditional FPU-like numerical experiments, i.e., experiments in which energy is initially concentrated on a small subset of normal modes, and other experiments, in which we test the time scale for the decay of a large fluctuation when all modes are excited almost to the same extent. For each experiment, we observe the behavior of the different two-dimensional systems and also make an accurate comparison with the behavior of a one-dimensional model with an identical potential. We assume the thermodynamic point of view and try to understand the behavior of the system for large n the number of degrees of freedom at fixed specific energy =E/n. As a result, it turns out that: i The difference between dimension one and two, if n is large, is substantial. In particular making reference to FPU-like initial conditions the “one-dimensional scenario,” in which the dynamics is dominated for a long time scale by a weakly chaotic metastable situation, in dimension two is absent; moreover in dimension two, for large n, the time scale for energy sharing among normal modes is drastically shorter than in dimension one. ii The boundary conditions in dimension two play a relevant role. Indeed, models with fixed or open boundary conditions give fast equipartition, on a rather short time scale of order −1, while a periodic model gives longer equilibrium times although much shorter than in dimension one.
File in questo prodotto:
File Dimensione Formato  
2008_Chaos_18_Benettin.pdf

non disponibili

Licenza: Non pubblico
1.75 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12571/7917
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact