Continuum limit of amorphous elastic bodies: A finite-size study of low-frequency harmonic vibrations

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 17, 2002, Pages 1742051-17420517

  Tanguy, A ^a   Wittmer, J P ^a   Leonforte, F ^a   Barrat, J L ^a  

^a UNIVERSITÉ LYON 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CHEMICAL STRUCTURE; DYNAMICS; ELASTICITY; MOLECULAR SIZE; PARTICLE SIZE; SPECTRUM; VIBRATION;

EID: 0036871473     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (50)

1. A.C. Eringen and E.S. Suhubi, Elastodynamics (Academic, New York, 1975).
2. L.D Landau and E.M. Lifshitz, Theory of Elasticity (Butterworth-Heinemann, London, 1995).
3. P.M. Chaikin and T. C. Lubensky, Principles of Condensed Matter (Cambridge University Press, Cambridge, 1995).
4. S. Alexander, Phys. Rep. 296, 65 (1998).
5. N.D. Fatti, C. Voisin, F. Chevy, F. Vallée, and C. Flytzanis, J. Chem. Phys. 110, 11 484 (1999).
6. M. Nisoli, S. De Silvestri, A. Cavalleri, A.M. Malvezzi, A. Stella, G. Lanzani, P. Cheyssac, and R. Kofman, Phys. Rev. B 55, R13 424 (1997).
7. J.H. Hodak, I. Martini, and G.V. Hartland, J. Phys. Chem. 108, 9210 (1998); J. H. Hodak, A. Henglein, and J. V. Hartland, ibid. 112, 5942 (2000).
8. J.H. Hodak, I. Martini, and G.V. Hartland, J. Phys. Chem. 108, 9210 (1998); J. H. Hodak, A. Henglein, and J. V. Hartland, ibid. 112, 5942 (2000).
9. L. Saviot, B. Champagnon, E. Duval, and A.I. Ekimov, Phys. Rev. B 57, 341 (1998); B. Palpant, H. Portales, L. Saviot, J. Lermé, B. Prével, M. Pellarin, E. Duval, A. Perez, and M. Broyer, ibid. 60, 17 107 (1999); H. Portales, L. Saviot, E. Duval, M. Fujii, S. Hayashi, N. Del Fatti, and F. Vallée, J. Chem. Phys. 115, 3444 (2001).
10. L. Saviot, B. Champagnon, E. Duval, and A.I. Ekimov, Phys. Rev. B 57, 341 (1998); B. Palpant, H. Portales, L. Saviot, J. Lermé, B. Prével, M. Pellarin, E. Duval, A. Perez, and M. Broyer, ibid. 60, 17 107 (1999); H. Portales, L. Saviot, E. Duval, M. Fujii, S. Hayashi, N. Del Fatti, and F. Vallée, J. Chem. Phys. 115, 3444 (2001).
11. L. Saviot, B. Champagnon, E. Duval, and A.I. Ekimov, Phys. Rev. B 57, 341 (1998); B. Palpant, H. Portales, L. Saviot, J. Lermé, B. Prével, M. Pellarin, E. Duval, A. Perez, and M. Broyer, ibid. 60, 17 107 (1999); H. Portales, L. Saviot, E. Duval, M. Fujii, S. Hayashi, N. Del Fatti, and F. Vallée, J. Chem. Phys. 115, 3444 (2001).
12. E. Duval, L. Saviot, A. Mermet, L. David, S. Etienne, V. Bershtein, and A.J. Dianoux (unpublished); G. Viliani, E. Duval, and L. Angelani (unpublished); E. Duval and I. Mermet, Phys. Rev. B 58, 8159 (1998).
13. E. Duval, L. Saviot, A. Mermet, L. David, S. Etienne, V. Bershtein, and A.J. Dianoux (unpublished); G. Viliani, E. Duval, and L. Angelani (unpublished); E. Duval and I. Mermet, Phys. Rev. B 58, 8159 (1998).
14. E. Duval, L. Saviot, A. Mermet, L. David, S. Etienne, V. Bershtein, and A.J. Dianoux (unpublished); G. Viliani, E. Duval, and L. Angelani (unpublished); E. Duval and I. Mermet, Phys. Rev. B 58, 8159 (1998).
15. A.J. Dianoux, W. Petry, and D. Richter, Dynamics of Disordered Materials (North-Holland, Amsterdam, 1993).
16. W. Schirmacher, G. Diezemann, and C. Ganter, Phys. Rev. Lett. 81, 136 (1998).
17. L. Angelani et al., Phys. Rev. Lett. 84, 4874 (2000).
18. J.P. Wittmer, A. Tanguy, J.-L. Barrat, and L. Lewis, Europhys. Lett. 57, 423 (2002).
19. V.A. Luchnikov, N.M. Medvedev, Yu.I. Naberukhin, and H.R. Schober, Phys. Rev. B 62, 3181 (2000); H.R. Schober and C. Oligschleger, ibid. 53, 11 469 (1996); H.R. Schober and B.B. Laird, ibid. 44, 6746 (1991).
20. V.A. Luchnikov, N.M. Medvedev, Yu.I. Naberukhin, and H.R. Schober, Phys. Rev. B 62, 3181 (2000); H.R. Schober and C. Oligschleger, ibid. 53, 11 469 (1996); H.R. Schober and B.B. Laird, ibid. 44, 6746 (1991).
21. V.A. Luchnikov, N.M. Medvedev, Yu.I. Naberukhin, and H.R. Schober, Phys. Rev. B 62, 3181 (2000); H.R. Schober and C. Oligschleger, ibid. 53, 11 469 (1996); H.R. Schober and B.B. Laird, ibid. 44, 6746 (1991).
22. V. Mazzacurati, G. Ruocco, and M. Sampoli, Europhys. Lett. 34, 681 (1996).
23. S.N. Taraskin and S.R. Elliott, in Physics of Glasses, edited by Jund and Jullien, AIP Conf. Proc. No. 489 (AIP, New York, 1999).
24. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, San Diego, 1995).
25. M. Leibig, Phys. Rev. E 49, 1647 (1994).
26. S. Melin, Phys. Rev. E 49, 2353 (1994).
27. F. Radjai and S. Roux, cond-mat/0205618 (unpublished).
28. M.E. Cates, J.P. Wittmer, J.P. Bouchaud, and P. Claudin, Phys. Rev. Lett. 81, 1841 (1998).
29. M.E. Cates, J.P. Wittmer, J.P. Bouchaud, and P. Claudin, Chaos 9, 511 (1999).
30. A.J. Liu and S.R. Nagel, Nature (London) 396, 21 (1998).
31. S.A. Langer and A.J. Liu, J. Phys. Chem. B 101, 8667 (1997).
32. G. Debrégeas, H. Tabuteau, and J.-M. di Meglio, Phys. Rev. Lett. 87, 178305 (2001).
33. Ph. Claudin and E. Clément (unpublished).
34. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1995).
35. J. Salençon, Handbook of Mechanics (Springer-Verlag, Berlin, 2001).
36. cont for the wavelength where necessary.
37. Note that in 2D, the upper bound for the Poisson ratio is 1 and not 1/2 as in 3D.
38. D.R. Squire, A.C. Holt, and W.G. Hoover, Physica (Amsterdam) 42, 388 (1969).
39. l〉. This is due to the fact that the tension along the chain is constant but not the displacement field. Hence, Eqs. (9) are in general only good approximations if the dispersion of the effective spring constants is small and an external macroscopic strain is locally transmitted in an affine way. (λ is then indeed given by the mean coupling constant with a negative quadratic dispersion correction in leading order.)
40. I. Goldhirsch and C. Goldenberg, cond-mat/0203360 (unpublished).
41. M.P. Allen and D.J. Tildesley, Computer Simulations of Liquids (Oxford Science, Oxford, 1987).
42. J.M. Thijssen, Computational Physics (Cambridge University Press, Cambridge, 1999).
43. W. H. Press et al., Numerical Recipes (Cambridge University Press, 1982).
44. S. Pinker, How the Mind Works (Penguin, New York, 1999).
45. J.Y. Choi, J.J. Dongarra, R. Pozo, D.C. Sorensen, and D.W. Walker, Int. J. Supercomput. Appl. 8, 99 (1994).
46. A. Tanguy and J. Wittmer (unpublished).
47. A. Tanguy and P. Nozières, J. Phys. 16, 1251 (1996).
48. J.R. Williams and N. Rege, Powder Technol. 90, 187 (1997); M.R. Kuhn, Mech. Mater. 31, 407 (1999); J-N. Roux and G. Combe, C.R. Phys. 3, 131 (2002).
49. J.R. Williams and N. Rege, Powder Technol. 90, 187 (1997); M.R. Kuhn, Mech. Mater. 31, 407 (1999); J-N. Roux and G. Combe, C.R. Phys. 3, 131 (2002).
50. J.R. Williams and N. Rege, Powder Technol. 90, 187 (1997); M.R. Kuhn, Mech. Mater. 31, 407 (1999); J-N. Roux and G. Combe, C.R. Phys. 3, 131 (2002).