2005, 2005(Special): 710-719. doi: 10.3934/proc.2005.2005.710

Equipartition times in a Fermi-Pasta-Ulam system

1. 

Dipartimento di Matematica “F. Enriques”, Universita di Milano, Via Saldini 50, 20133 Milano

2. 

Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via R. Cozzi 53, 20125 - Milano

Received  September 2004 Revised  March 2005 Published  September 2005

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 equipartition when energy is initially given to one or a few modes. In previous works we considered the initial energy being given on the lower part of the spectrum. Using the spectral entropy as a numerical indicator we obtained a strong indication that the relaxation time to equipartition increases exponentially with an inverse power of the specific energy. Such a scaling appears to remain valid in the thermodynamic limit. In this paper we explore the dynamics obtained with the initial excitation on the high frequency modes, and we obtain also in this case indication of exponentially long times to equipartition.
Citation: Simone Paleari, Tiziano Penati. Equipartition times in a Fermi-Pasta-Ulam system. Conference Publications, 2005, 2005 (Special) : 710-719. doi: 10.3934/proc.2005.2005.710
[1]

Gisèle Ruiz Goldstein, Jerome A. Goldstein, Fabiana Travessini De Cezaro. Equipartition of energy for nonautonomous wave equations. Discrete & Continuous Dynamical Systems - S, 2017, 10 (1) : 75-85. doi: 10.3934/dcdss.2017004

[2]

Luisa Berchialla, Luigi Galgani, Antonio Giorgilli. Localization of energy in FPU chains. Discrete & Continuous Dynamical Systems - A, 2004, 11 (4) : 855-866. doi: 10.3934/dcds.2004.11.855

[3]

Dmitry Treschev. Travelling waves in FPU lattices. Discrete & Continuous Dynamical Systems - A, 2004, 11 (4) : 867-880. doi: 10.3934/dcds.2004.11.867

[4]

Joseph A. Biello, Peter R. Kramer, Yuri Lvov. Stages of energy transfer in the FPU model. Conference Publications, 2003, 2003 (Special) : 113-122. doi: 10.3934/proc.2003.2003.113

[5]

Vaughn Climenhaga. A note on two approaches to the thermodynamic formalism. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 995-1005. doi: 10.3934/dcds.2010.27.995

[6]

Yong Fang. Thermodynamic invariants of Anosov flows and rigidity. Discrete & Continuous Dynamical Systems - A, 2009, 24 (4) : 1185-1204. doi: 10.3934/dcds.2009.24.1185

[7]

Peter R. Kramer, Joseph A. Biello, Yuri Lvov. Application of weak turbulence theory to FPU model. Conference Publications, 2003, 2003 (Special) : 482-491. doi: 10.3934/proc.2003.2003.482

[8]

Michael Kastner, Jacques-Alexandre Sepulchre. Effective Hamiltonian for traveling discrete breathers in the FPU chain. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 719-734. doi: 10.3934/dcdsb.2005.5.719

[9]

Yakov Pesin. On the work of Sarig on countable Markov chains and thermodynamic formalism. Journal of Modern Dynamics, 2014, 8 (1) : 1-14. doi: 10.3934/jmd.2014.8.1

[10]

Manfred Denker, Yuri Kifer, Manuel Stadlbauer. Thermodynamic formalism for random countable Markov shifts. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 131-164. doi: 10.3934/dcds.2008.22.131

[11]

Yongluo Cao, De-Jun Feng, Wen Huang. The thermodynamic formalism for sub-additive potentials. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 639-657. doi: 10.3934/dcds.2008.20.639

[12]

Anna Mummert. The thermodynamic formalism for almost-additive sequences. Discrete & Continuous Dynamical Systems - A, 2006, 16 (2) : 435-454. doi: 10.3934/dcds.2006.16.435

[13]

Luis Barreira. Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures. Discrete & Continuous Dynamical Systems - A, 2006, 16 (2) : 279-305. doi: 10.3934/dcds.2006.16.279

[14]

Manfred Denker, Yuri Kifer, Manuel Stadlbauer. Corrigendum to: Thermodynamic formalism for random countable Markov shifts. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 593-594. doi: 10.3934/dcds.2015.35.593

[15]

Amjad Khan, Dmitry E. Pelinovsky. Long-time stability of small FPU solitary waves. Discrete & Continuous Dynamical Systems - A, 2017, 37 (4) : 2065-2075. doi: 10.3934/dcds.2017088

[16]

Renaud Leplaideur. From local to global equilibrium states: Thermodynamic formalism via an inducing scheme. Electronic Research Announcements, 2014, 21: 72-79. doi: 10.3934/era.2014.21.72

[17]

Eugen Mihailescu. Applications of thermodynamic formalism in complex dynamics on $\mathbb{P}^2$. Discrete & Continuous Dynamical Systems - A, 2001, 7 (4) : 821-836. doi: 10.3934/dcds.2001.7.821

[18]

Robert A. Gatenby, B. Roy Frieden. The Role of Non-Genomic Information in Maintaining Thermodynamic Stability in Living Systems. Mathematical Biosciences & Engineering, 2005, 2 (1) : 43-51. doi: 10.3934/mbe.2005.2.43

[19]

Weinan E, Jianchun Wang. A thermodynamic study of the two-dimensional pressure-driven channel flow. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4349-4366. doi: 10.3934/dcds.2016.36.4349

[20]

Wei Lv, Ruirui Sui. Optimality of piecewise thermal conductivity in a snow-ice thermodynamic system. Numerical Algebra, Control & Optimization, 2015, 5 (1) : 47-57. doi: 10.3934/naco.2015.5.47

 Impact Factor: 

Metrics

  • PDF downloads (1)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]