Propagation of mechanical waves in a one-dimensional nonlinear disordered lattice

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 2, 2006, Pages

  Richoux, O ^a   Depollier, C ^a   Hardy, J ^a  

^a UNIVERSITÉ DU MAINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC WAVE PROPAGATION; CRYSTAL LATTICES; GREEN'S FUNCTION; PERTURBATION TECHNIQUES; QUADRATIC PROGRAMMING;

LOCALIZATION LENGTH; NONLINEAR LATTICE; PROPAGATIVE REGIME; TRANSMISSION COEFFICIENT;

ACOUSTIC WAVES;

EID: 33344461456     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.026611     Document Type: Article

References (36)

1. P. W. Anderson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.109.1492 109, 1492 (1958).
2. P. Sheng, Scattering and Localization of Classical Waves in Random Media (Singapore, World Scientific, 1990).
3. A. Sànchez, E. Macià, and F. Dominguez Adame, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.49.15428.2 49, 15428 (1994).
4. A. Sanchez, F. Dominguez Adame, G. Berman, and F. Izrailev, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.51.6769 51, 6769 (1995).
5. C. M. Soukoulis, S. Datta, and E. N. Economou, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.49.3800 49, 3800 (1994).
6. Yu S. Kivshar, S. A. Gredeskul, A. Sanchez, and L. Vasquez, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.1693 64, 1693 (1990).
7. E. Cota, J. V. Jose, J. Maytorena, and G. Monsivais, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.3302 74, 3302 (1995).
8. P. Devillard and B. Souillard, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01020646 43, 423 (1986).
9. M. Sayar, M. C. Demirel, and A. R. Atilgan, J. Sound Vib. JSVIAG 0022-460X 10.1006/jsvi.1997.0984 205, 372 (1997).
10. M. J. McKenna, J. Keat, J. Wang, and J. D. Maynard, Physica B PHYBE3 0921-4526 10.1016/0921-4526(94)90849-4 194, 1039 (1994).
11. M. J. McKenna, R. L. Stanley, and J. D. Maynard, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.1807 69, 1807 (1992).
12. D. L. Shepelyansky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1787 70, 1787 (1993).
13. A. A. Zevin, J. Sound Vib. JSVIAG 0022-460X 10.1006/jsvi.1996.0318 193, 847 (1996).
14. R. Spigler, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.527042 27, 1760 (1996).
15. D. J. Mead and S. M. Lee, J. Sound Vib. JSVIAG 0022-460X 10.1016/0022-460X(84)90390-0 92, 427 (1984).
16. R. Knapp, G. Papanicolaou, and B. White, Nonlinearity and Localization in One-dimensional Random Media, edited by, A. R. Bishop, D. K. Campbell, and, St. Pnevmatikos, Disorder and nonlinearity, Springer Series in Solid State Science (Springer, Berlin 1989).
17. R. Knapp, G. Papanicolaou, and B. White, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01029200 63, 567 (1991).
18. C. M. Soukoulis, Jorge V. José, E. N. Economou, and P. Sheng, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50.764 50, 764 (1983).
19. M. Luban and J. H. Luscombe, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.34.3674 34, 3674 (1986).
20. S. A. Gredeskul and Y. S. Kivshar, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(92)90023-S 216, 1 (1992).
21. V. V. Beloshapkin, A. G. Tretyakov, and G. M. Zaslavsky, Commun. Pure Appl. Math. CPMAMV 0010-3640 47, 39 (1994).
22. C. W. Cai, H. C. Chan, and Y. K. Cheung, Trans. ASME, J. Appl. Mech. JAMCAV 0021-8936 64, 940 (1997).
23. D. Hennig, H. Gabriel, and G. P. Tsironis, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(98)00025-8 307, 333 (1999).
24. R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1983).
25. O. Richoux, C. Depollier, and J. Hardy, Acta. Acust. Acust. AAACDB 1610-1928 88, 934 (2002).
26. G. Gonon, O. Richoux, and C. Depollier, Signal Process. SPRODR 0165-1684 10.1016/j.sigpro.2003.05.001
27. J. M. Luck, Systèmes Désordonnés Unidimensionnels (Collection Alea Saclay, 1992).
28. Y. Wan and C. M. Soukoulis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.41.800 41, 800 (1990).
29. Y. Wan and C. M. Soukoulis, in Wave Transmission in a One-Dimensional Nonlinear Lattice: Multistability and Noise, edited by, A. R. Bishop, Springer Proceedings in Physics: Disorder and Nonlinearity Vol. 39 (Springer-Verlag, Berlin, 1989).
30. M. Grabowski and P. Hawrylak, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.41.5783 41, 5783 (1990).
31. P. Hawrylak, M. Grabowski, and P. Wilson, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.6398 40, 6398 (1989).
32. P. Hawrylak and M. Grabowski, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.8013 40, 8013 (1989).
33. F. Delion, Y. E. Levy, and B. Souillard, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.57.2010 57, 2010 (1986).
34. D. Hennig, H. Gabriel, G. P. Tsironis, and M. Molina, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.111416 64, 2934 (1994).
35. Q. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.53.15577 53, 15577 (1996).
36. L. Brillouin and P. Parodi, Propagation dans les Milieux Périodiques (Masson-Dunod, Paris, 1956).