Investigation of energy relaxation in 1-D nonlinear lattices by wavelets

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Abstract

The movement and relaxation of the localized energy on FPU lattices have been studied by using Wavelet transforms methods. The energy relaxation mechanism for nonlinear chains involves the degradation of higher frequency excitations into lower frequencies. It is shown that low frequency modes decay more slowly in nonlinear chains. The wavelet spectrum exhibits a behavior involving the interplay of phonon modes and breather modes.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    T. Pullerits, V. Sundstrom, Acc. Chem. Res. 29, 381 (1996)CrossRefGoogle Scholar
  2. 2.
    X. Hu, K. Schulten, Phys. Today 50, 28 (1997)CrossRefGoogle Scholar
  3. 3.
    Davydov’s Soliton Revisited: Self-trapping of Vibrational Energy in Protein, edited by P.L. Christiansen, A.C. Scott, NATO ASI Series B: Physics (Plenum press, New York, 1990), Vol. 243Google Scholar
  4. 4.
    K. Bolton, S. Nordholm, H.W. Schranz, J. Phys. Chem. 99, 2477 (1995)CrossRefGoogle Scholar
  5. 5.
    L. Cruzeiro-Hansson, S. Takeno, Phys. Rev. B 56, 894 (1997)ADSCrossRefGoogle Scholar
  6. 6.
    M. Peyrard, J. Farago, Physica A 288, 199 (2000)ADSCrossRefGoogle Scholar
  7. 7.
    G. Kopidakis, S. Aubry, Physica B 296, 237 (2001)ADSCrossRefGoogle Scholar
  8. 8.
    T. Rössler, J.B. Page, Phys. Rev. B 62, 11460 (2000)ADSCrossRefGoogle Scholar
  9. 9.
    S. Lepri, R. Livi, A. Politi, Phys. Rep. 377, 1 (2003)MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    F. Piazza, S. Lepri, R. Livi, J. Phys. A: Math. Gen. 34, 9803 (2001)MathSciNetADSMATHCrossRefGoogle Scholar
  11. 11.
    T. Prosen, D.K. Campell, Phys. Rev. Lett. 84, 2857 (2000)ADSCrossRefGoogle Scholar
  12. 12.
    K. Aoki, D. Kusnezov, Phys. Rev. Lett. 86, 4029 (2001)ADSCrossRefGoogle Scholar
  13. 13.
    F. Zhang, D.J. Isbister, D.J. Evans, Phys. Rev. E 61, 3541 (2000)ADSCrossRefGoogle Scholar
  14. 14.
    V.M. Burlakov, S.A. Kiselev, V.N. Pyrkov, Phys. Rev. B 42, 4921 (1990)ADSCrossRefGoogle Scholar
  15. 15.
    Y.A. Kosevich, S. Lepri, Phys. Rev. B 61, 299 (2000)ADSCrossRefGoogle Scholar
  16. 16.
    N.J. Zabusky, M.D. Kruskal, Phys. Rev. Lett. 15, 240 (1965)ADSMATHCrossRefGoogle Scholar
  17. 17.
    R. Dusi, G. Viliani, M. Wagner, Phil. Mag. B 71, 597 (1995)CrossRefGoogle Scholar
  18. 18.
    R. Dusi, G. Viliani, M. Wagner, Phys. Rev. B 54, 9809 (1996)ADSCrossRefGoogle Scholar
  19. 19.
    Y.A. Kosevich, Phys. Rev. B 47, 3138 (1993)ADSCrossRefGoogle Scholar
  20. 20.
    S. Flach, C.R. Willis, Phys. Rep. 295, 181 (1998)MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    S. Aubry, K. Kopidakis arXiv:cond-mat/0102162v1 (2001)Google Scholar
  22. 22.
    T. Cretegny, T. Dauxois, S. Ruffo, A. Torcini, Physica D 121, 109 (1998)ADSCrossRefGoogle Scholar
  23. 23.
    A.J. Sievers, S. Takeno, Phys. Rev. Lett. 61, 970 (1988)ADSCrossRefGoogle Scholar
  24. 24.
    J.B. Page, Phys. Rev. B 41, 7835 (1990)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    K.W. Sandusky, J.B. Page, K.E. Schmidt, Phys. Rev. B 46, 6161 (1992)ADSCrossRefGoogle Scholar
  26. 26.
    T. Dauxois, M. Peyrard, Phys. Rev. Lett. 70, 3935 (1993)ADSCrossRefGoogle Scholar
  27. 27.
    S. Aubry, Physica D 71, 196 (1994)MathSciNetADSMATHCrossRefGoogle Scholar
  28. 28.
    R.S. MacKay, S. Aubry, Nonlinearity 7, 1623 (1994)MathSciNetADSMATHCrossRefGoogle Scholar
  29. 29.
    D. Cai, A.R. Bishop, N. Gronbech-Jensen, Phys. Rev. E 52, 5784 (1995)ADSCrossRefGoogle Scholar
  30. 30.
    S. Takeno, M. Peyrard, Physica D 92, 140 (1996)MATHCrossRefGoogle Scholar
  31. 31.
    M. Matsumoto, G. Yamada, K. Oguchi, H. Wakabayashi, T. Makino, Thermophys. Prop. 22, 181 (2001)Google Scholar
  32. 32.
    M. Matsumoto, H. Wakabayashi, T. Makino, Thermophys. Prop. 23, 346 (2002)Google Scholar
  33. 33.
    M. Matsumoto, H. Wakabayashi, T. Makino, Nippon Dennetsu Shinpojiumu Koen Ronbunshu 39, 683 (2002)Google Scholar
  34. 34.
    G.M. Chechin, N.V. Novikova, A.A. Abramenko, Physica D 166, 208 (2002)MathSciNetADSMATHCrossRefGoogle Scholar
  35. 35.
    R. Reigada, A. Sarmiento, K. Lindenberg, Phys. Rev. E 64, 66608 (2001)ADSCrossRefGoogle Scholar
  36. 36.
    A. Graps, IEEE Comput. Sci. Eng. 2, 50 (1995)CrossRefGoogle Scholar
  37. 37.
    Y. Laib dit leksir, H. Bendjama, A. Allag, Proceedings of the World Congress on Engineering I, 731 (2007)Google Scholar
  38. 38.
    C.S. Burrus, R.A. Gopinath, H. Guo, Introduction to Wavelet and Wavelet Transforms (Prentice Hall, New Jersey, 1998)Google Scholar
  39. 39.
    S. Mallat, A Wavelet Tour of Signal Processing (Academic Press, San Diego, 1998)Google Scholar
  40. 40.
    J.R. Romero-Arias, G.G. Naumis, Phys. Rev. E 77, 61504 (2008)ADSCrossRefGoogle Scholar
  41. 41.
    J.R. Romero-Arias, F. Salazar, G.G. Naumis, G. Fernandez-Anaya, Philos. Trans. A Math. Phys. Eng. Sci. 367, 3173 (2009)MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Dicle University, Faculty of Science, Physics DepartmentDiyarbakırTurkey
  2. 2.Adnan Menderes University, Faculty of Science and Literature, Physics DepartmentAydınTurkey

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