The Fermi-Pasta-Ulam problem: Scaling laws vs. initial conditions

Journal of Statistical Physics

Volumn 135, Issue 5-6, 2009, Pages 873-893

  Benettin, G ^a   Livi, R ^b   Ponno, A ^a  

^a UNIVERSITY OF PADOVA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Energy transfer; Fermi Pasta Ulam problem; Scaling laws

Indexed keywords

EID: 67650717503     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-008-9660-6     Document Type: Article

References (26)

1. Fermi, E., Pasta, J., Ulam, S.: Studies of non linear problems, Los-Alamos internal report, document LA-1940 (1955). In: Enrico Fermi Collected Papers, vol. II, pp. 977-988. University of Chicago Press/Accad. Naz. Lincei, Chicago/Roma (1965). (Also reproduced in [3])
2. G.P. Berman F.M. Izrailev 2005 The "Fermi-Pasta-Ulam" problem-the first 50 years Chaos 15 015104
3. Gallavotti, G. (ed.): The Fermi-Pasta-Ulam Problem: A Status Report. Lect. Notes Phys., vol. 728. Springer, Berlin (2008)
4. R. Livi M. Pettini S. Ruffo M. Sparpaglione A. Vulpiani 1985 Equipartition threshold in nonlinear large Hamiltonian systems: the Fermi-Pasta-Ulam model Phys. Rev. A 31 1039 1045
5. C.G. Goedde A.J. Lichtenberg M.A. Lieberman 1992 Chaos and the approach to equilibrium in a discrete Sine-Gordon equation Physica D 59 200 225
6. J. De Luca A.J. Lichtenberg S. Ruffo 1995 Energy transition and time scales to equipartition in the Fermi-Pasta-Ulam oscillator chain Phys. Rev. E 51 2877 2885
7. E. Fucito F. Marchesoni E. Marinari G. Parisi L. Peliti S. Ruffo A. Vulpiani 1982 Approach to equilibrium in a chain of nonlinear oscillators J. Phys. 43 707 713
8. R. Livi M. Pettini S. Ruffo M. Sparpaglione A. Vulpiani 1983 Relaxation to different stationary states in the Fermi-Pasta-Ulam model Phys. Rev. A 28 3544 3552
9. M. Pettini M. Landolfi 1990 Relaxation properties and ergodicity breaking in nonlinear Hamiltonian dynamics Phys. Rev. A 41 768 783
10. L. Berchialla A. Giorgilli S. Paleari 2004 Esponentially long times to equipartition in the thermodynamic limit Phys. Lett. A 321 167 172
11. L. Berchialla L. Galgani A. Giorgilli 2004 Localization of energy in FPU chains Discrete Contin. Dyn. Syst. Ser. A 11 855 866
12. J.A. Biello P.R. Kramer Y.V. L'vov 2003 Stages of energy transfer in the FPU model Discrete Contin. Dyn. Syst. 2003 Suppl. 113 122 (Special number devoted to the Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, 24-27 May 2002, Wilmington, NC)
13. Benettin, G., Carati, A., Galgani, L., Giorgilli, A.: The Fermi-Pasta-Ulam problem and the metastability perspective. In: Gallavotti, G. (ed.) The Fermi-Pasta-Ulam Problem: A Status Report. Lect. Notes Phys., vol. 728, pp. 151-189. Springer, Berlin (2008)
14. F.M. Izrailev B.V. Chirikov 1966 Statistical properties of a nonlinear string Sov. Phys. Dokl. 11 30 32
15. H. Kantz R. Livi S. Ruffo 1994 Equipartition thresholds in chains of anharmonic oscillators J. Stat. Phys. 76 627 643
16. Lichtenberg, A.J., Livi, R., Pettini, M., Ruffo, S.: Dynamics of oscillator chains. In: Gallavotti, G. (ed.) The Fermi-Pasta-Ulam Problem: A Status Report. Lect. Notes Phys., vol. 728, pp. 21-121. Springer, Berlin (2008)
17. D.L. Shepelyansky 1997 Low-energy chaos in the Fermi-Pasta-Ulam problem Nonlinearity 10 1331 1338 (Pubitemid 127431086)
18. Ponno, A.: A theory of the energy cascade in FPU models. Preprint (2008)
19. N.J. Zabusky M.D. Kruskal 1965 Interaction of "Solitons" in a collisionless plasma and the recurrence of initial states Phys. Rev. Lett. 15 240 243
20. D. Bambusi A. Ponno 2006 On metastability in FPU Commun. Math. Phys. 264 539 561
21. Bambusi, D., Ponno, A.: Resonance, metastability and blow-up in FPU. In: Gallavotti, G. (ed.) The Fermi-Pasta-Ulam Problem: A Status Report. Lect. Notes Phys., vol. 728, pp. 191-205. Springer, Berlin (2008)
22. A. Ponno 2003 Soliton theory and the Fermi-Pasta-Ulam problem in the thermodynamic limit Europhys. Lett. 64 606 612 (Pubitemid 37469971)
23. Ponno, A.: The Fermi-Pasta-Ulam problem in the thermodynamic limit: scaling laws of the energy cascade. In: Collet, P., et al. (eds.) Proceedings of the Cargèse Summer School 2003 on Chaotic Dynamics and Transport in Classical and Quantum Systems, pp. 431-440. Kluwer Academic, Dordrecht (2005)
24. S. Flach A. Ponno 2008 The Fermi-Pasta-Ulam problem: Periodic orbits, normal forms and resonance overlap criteria Physica D 237 908 917
25. J. Ford 1961 Equipartition of energy for nonlinear systems J. Math. Phys. 2 387 393
26. S. Venakides 1987 The zero dispersion limit of the Korteweg-de Vries equation with periodic initial data Trans. Am. Math. Soc. 301 189 226