On the rigidity of amorphous solids

Annales de Physique

Volumn 30, Issue 3, 2005, Pages 1-96

  Wyart, M ^a  

^a SERVICE DE PHYSIQUE DE L ETAT CONDENSÉ   (France)

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EID: 33646390110     PISSN: 00034169     EISSN: 12864838     Source Type: Journal    
DOI: 10.1051/anphys:2006003     Document Type: Review

References (124)

1. Amorphous solids, Low temperature properties, edited by W. A. Phillips (Springer, Berlin, 1981).
2. P.W. Anderson, B.I. Halperin, C.M. Varma, Philos. Mag. 25, 1 (1972).
3. J.J. Freeman, A.C. Anderson, Phys. Rev. B 34, 5684 (1986).
4. S. Ludwig, C. Enss, P. Strhlow, S Hunklinger, Phys. Rev. Lett. 88, 075501 (2002).
5. R. Berman, Proc. R. Soc. A 280, 90 (1950).
6. A. Tanguy, J.P. Wittmer, F. Leonforte, J.L. Barrat. Phys. Rev. B 66, 174205 (2002).
7. J.P. Wittmer, A. Tanguy, J.L. Barrat, L. Lewis, Europhys. Lett. 57, 423 (2002).
8. F. Leonforte, A. Tanguy, J. P. Wittmer, J.-L. Barrat, Phys. Rev. B 70, 014203 (2004).
9. F. Leonforte, R. Boissiere, A. Tanguy, J.P. Wittmer, J.-L. Barrat, e-print arXiv:cond-mat/0505610.
10. R. Brockbank, J.M. Huntley, R.C. Ball, J. Phys. II 7, 1521 (1997); and references therein.
11. J.P. Wittmer, P. Claudin, M.E. Cates, J.P. Bouchaud, Nature 382, 336 (1996).
12. M.E. Cates, J.P. Wittmer, J.P. Bouchaud, P. Claudin, Phys. Rev. Lett. 81, 1841 (1998).
13. E. Clement, G. Reydellet, L. Vanel, D.W. Howell, J. Geng, R.P. Behringer, XIII international congress on rheology, Cambridge (UK) (British Society of Rheology, Glasgow, 2000), Vol. 2, p. 426.
14. G. Reydellet, E. Clement, Phys. Rev. Lett. 86, 3308 (2001) and references therein.
15. J.-P. Bouchaud, P. Claudin, D. Levine, M. Otto, Eur. Phys. J. E 4, 451 (2001).
16. E.R. Nowak, J.B. Knight, E. Ben-Naim, H.M. Jaeger, S.R. Nagel, Phys. Rev. E 57, 1971 (1998);
17. P. Philippe, thesis, Univ. Rennes I (2002);
18. C. Josserand, A.V. Tkachenko, D.M. Mueth, H.M. Jaeger, Phys. Rev. Lett. 85, 3632 (2000).
19. O. Pouliquen, Phys. Rev. Lett. 93, 248001 (2004).
20. A.J. Liu, S. Nagel, Nature 396, 21 (1998).
21. C.A. Angell, in Relaxation in complex systems, edited by K.L. Ngai, G.B. Wright (Office of Naval Research, Washington DC, 1985).
22. E. Weeks, D.A. Weitz, Chem. Phys. 284, 361 (2002).
23. See e.g. M.D. Ediger, Ann. Rev. Phys. Chem. 51, 99 (2000).
24. C. Toninelli, M. Wyart, L. Berthier, G. Biroli, J.-P. Bouchaud, Phys. Rev. E 71, 041505 (2005).
25. W. Kob, H.C. Anderson, Phys. Rev. E 48, 4364 (1993).
26. J.C. Maxwell, Philos. Mag. 27, 294 (1864).
27. C. Kittel, Introduction to solid state physics (John Willey and son Inc., 1996).
28. S.N. Taraskin, S.R. Elliot, Phys. Rev. B 59, 8572 (1999).
29. A.P. Sokolov, U. Buchenau, W. Steffen, B. Frick, A. Wischnewski, Phys. Rev. 652, 9815 (1995).
30. N.J. Tao, G. Li, X. Chen, W.M. Du, H.Z. Cummins, Phys. Rev. A 44, 6665 (1991).
31. D. Engberg, A. Wischnewski, U. Buchenau, L. Brjesson, A.J. Dianoux, A.P. Sokolov, L.M. Torell, Phys. Rev. B 59, 4053 (1999).
32. A.I. Chumakov, I. Sergueev, U. van Burck, W. Schirmacher, T. Asthalter, R. Ruffer, O. Leupold, W. Petry, Phys. Rev. Lett. 92, 245508 (2004).
33. A. Wischnewski, U. Buchenau, A.J. Dianoux, W.A. Kamitakahara, J.L. Zarettky, Phys. Rev. B 57, 2663 (1998).
34. J. Horbach, W. Kob, K. Binder, Eur. Phys. J. B 19, 531 (2001).
35. G. Parisi, Eur. Phys. J. E 9, 213 (2002).
36. T.S. Grigera, A. Cavagna, I. Giardina, G. Parisi, Phys. Rev. Lett. 88, 055502 (2002).
37. U. Buchenau, Yu.M. Galperin, V.L. Gurevich, H.R. Scober, Phys. Rev. B 43, 5039 (1991).
38. S. Alexander, Phys. Rep. 296, 65 (1998).
39. V.G. Karpov, M.I. Klinger, F.N. Ignatiev, Zh. Sov. Phys. JETP 57, 439 (1987).
40. V.L. Gurevich, D.A. Parshin, J. Pelous, H.R. Schober, Phys. Rev. B 48, 16318 (1993).
41. W. Schirmacher, G. Diezmann, C. Ganter, Phys. Rev. Lett. 81, 136 (1998).
42. S.N. Taraskin, Y.L. Loh, G. Natarajan, S.R. Elliot, Phys. Rev. Lett. 86, 1255 (2001).
43. E. Maurer, W. Schirmacher, J. Low Temp. Phys. 137, 453 (2004).
44. S. Ciliberti, T.S. Grigera, V. Martin-Mayor, G. Parisi, P. Verrocchio, AIP Conf. Proc. 708, 565 (2004).
45. T.S. Grigera, V. Martin-Mayor, G.Parisi, P. Verrocchio, Phys. Rev. Lett. 8, 085502 (2001).
46. M. Mezard, G. Parisi, A. Zee, Nucl. Phys. B 559, 689 (1999).
47. W. Gotze, M.R. Mayr, Phys. Rev. E 61, 587 (2000).
48. T. Nakayama, Rep. Prog. Phys. 65, 1195 (2002).
49. A.J. Leadbetter, J. Chem. Phys. 51, 779 (1969).
50. D. Caplin, G. Gruener, J.B. Dunlop, Phys. Rev. Lett. 30, 1138 (1973).
51. Bilar, W.A. Phillips, Philos. Mag. 32, 113 (1975).
52. C.S. O'Hern, L.E. Silbert, A.J. Liu, S.R. Nagel, Phys. Rev. E 68, 011306 (2003).
53. C.S. O'Hern, S.A. Langer, A.J. Liu, S.R. Nagel, Phys. Rev. Lett. 88, 075507 (2002).
54. D.J. Durian, Phys. Rev. Lett. 75, 4780 (1995).
55. L.E. Silbert, D. Ertas, G.S. Grest, T.C. Hasley, D. Levine, Phys. Rev. E 65, 031304 (2002).
56. T.G. Mason, J. Bibette, D.A. Weitz, Phys. Rev. Lett. 75, 2051 (1995).
57. J.C. Phillips, J. Non-Cryst. Sol. 43, 37 (1981).
58. M.F. Thorpe, J. Non-Cryst. Sol. 57, 355 (1983).
59. A.V. Tkachenko, T.A. Witten, Phys. Rev. E 60, 687 (1999).
60. A.V. Tkachenko, T.A. Witten, Phys. Rev. E 62, 2510 (2000).
61. D.A. Head, A.V. Tkachenko, T.A. Witten, Eur. Phys. J. E 6, 99 (2001).
62. C.F. Moukarzel, Phys. Rev. Lett. 81, 1634 (1998).
63. P.M. Duxbury, D.J. Jacobs, M.F Thorpe, C. Moukarzel, Phys. Rev. E 59, 2084 (1999).
64. N.W. Aschcroft, N.D. Mermin, Solid State Physic, HWR International.
65. Y. Cai, M.F. Thorpe, Phys. Rev. B 40, 10535 (1989).
66. M. Tatsumisago, B.L. Halfpapa, J.L. Green, S.M. Lindsay, C.A. Angell, Phys. Rev. Lett. 64, 1549 (1990).
67. J.-N. Roux, Phys. Rev. E 61, 6802 (2000).
68. L. Silbert, A.J. Liu, S. Nagel, e-print arXiv: cond-mat/8581616.
69. M. Wyart, L.E. Silbert, S.R. Nagel, T.A. Witten, e-print arXiv:cond-mat/8588415, Phys. Rev. E (submitted).
70. K.O. Trachenko, M.T. Dove, M.J. Harris, V. Heine, J. Phys.: Condens. Matter 12, 8041 (2000).
71. K.D. Hammonds, A. Bosenick, M.D. Dove, V. Heine, Amer. Mineral. 83, 476 (1998).
72. M.T. Dove, V. Heine, K.D. Hammonds, Mineralog. Mag. 59, 629 (1995).
73. K. Trachenko, M. Dove, V. Brazhkin, F.S. El'kin, Phys. Rev. Lett. 93, 135502 (2004).
74. M.D. Newton, M. O'Keeffe, G.V. Gibbs, Phys. Chem. Miner. 6, 305 (1980).
75. B.B. Karki, M.C. Warren, L. Stixrude, G.J. Ackland, J. Grain, Phys. Rev. B 55, 3465 (1997).
76. D.A. Head, Phys. Rev. E 72, 021303 (2005).
77. R.B. Griffiths, Phys. Rev. Lett. 23, 17crossed D sign19 (1969).
78. C.A. Angell, Y. Yue, L.-M. Wang, J.R.D. Copley, S. Borick, S. Mossa, J. Phys.: Condens. Matter 15, 1051 (2003).
79. E. Duval, L. Saviot, L. David, S. Etienne, J.F. Jal, Europhys. Lett. 63, 778 (2003).
80. C.S. O'Hern, S.A. Langer, A.J. Liu, S.R. Nagel., Phys. Rev. Lett. 86, 111 (2001).
81. A. Donev, S. Torquato, F.H. Stillinger, Phys. Rev. E 71, 011105 (2005).
82. G. Parisi, F. Zamponi, e-print arXiv:cond-mat/8586445.
83. H.A. Makse, N. Gland, D.L. Johnson, L. Schwartz, Phys. Rev. E 70, 061302 (2004).
84. C. Maloney, A. Lemaitre, Phys. Rev. Lett. 93, 195501 (2004).
85. B.A. DiDonna, T.C. Lubensky, e-print arXiv : cond-mat/0506456.
86. J.H. Snoeijer, J.M. van Leeuwen, Phys. Rev. E 65, 051306 (2002).
87. J.H. Snoeijer, T.J.H. Vlugt, M. Van Hecke, W. van Saarloos, Phys. Rev. Lett. 92, 054302 (2004).
88. J.H. Snoeijer, private communication.
89. J.D. Goddard, Proc. R. Soc. Lond. Ser. A 430, 105 (1990).
90. H.P. Zhang, H.A. Makse, e-print arXiv: cond-mat/05013370.
91. R.D. Mindlin, J. App. Math. (ASME) 71, 259 (1949).
92. E. Somfai, M. van Hecke, W.G. Ellenbroek, W. van Saarloos, e-print arXiv:cond-mat/0510506.
93. T.C. Choy, Effective Medium Theory, Principles and Applications (Oxford University press, 1999).
94. D.A. Keen, M.T. Dove, J. Phys.: Condens. Matter 11, 9263 (1999).
95. B. Hehlen, E. Courtens, A. Yamanaka, K. Inoue, J. Non-Cryst. Sol. 307, 87 (2002).
96. K. Vollmayr, W. Kob, K. Binder, Phys. Rev. B 54, 15808 (1996).
97. M.T. Dove, M.J. Harris, A.C. Hannon, J.M. Parker, I.P. Swainson, M. Gambhir, Phys. Rev. Lett. 78, 1070 (1997).
98. W.A. Kamitakahara, R.L. Cappelletti, P. Boochland, F. Gompf, Bull. Am. Phys. Soc. 32, 812 (1987).
99. Y. Cai, M.F. Thorpe, Phys. Rev. B 40, 15535 (1989).
100. J.-L. Barrat, W. Gotze, A. Latz, J. Phys.: Cond. Matter 1, 7163 (1989).
101. W. Gotze, L. Sjorgen, Rep. Prog. Phys. 55, 241 (1992).
102. A. Ferguson, B. Fisher, B. Chakraborty, Europhys. Lett. 66, 277 (2004).
103. A. Donev, S. Torquato, F.H. Stillinger, R. Connelly, J. Compt. Phys. 197, 139 (2004).
104. W. Kob, J.L. Barrat, F. Sciortino, P. Tartaglia, J. Phys.: Condens. Matter 12, 6385 (2000).
105. A. Duri, P. Ballesta, L. Cipelletti, H. Bissig, V. Trappe, Fluct. Noise Lett. 5, 1 (2005).
106. L. Buisson, L. Bellon, S. Ciliberto, J. Phys.: Condens. Matter 15, S1163 (2003).
107. E. Somfai, J.-N. Roux, J. Snoejer, M. Van Hecke, W. van Saarloos, e-print arXiv:cond-mat/0408128.
108. Ch. Liu, S.R. Nagel, J. Phys.: Condens. Matter 6, 433 (1994).
109. M. Foret, E. Courtens, R. Vacher, J.-B. Suck, Phys. Rev. Lett. 77, 3835 (1996).
110. D.J. Lacks, Phys. Rev. Lett. 84, 4629 (2000).
111. J. Kurchan, L. Laloux, J. Phys. A: Math Gen. 29, 1929 (1996).
112. T.R. Kirkpatrick, D. Thirumalai, P.G. Wolynes, Phys. Rev. A 40, 1045 (1989).
113. L.F. Cugliandolo, J. Kurchan, Phys. Rev. Lett. 71, 173 (1993).
114. L.V. Woodcock, C.A. Angell, P. Cheeseman, J. Chem. Phys. 65, 1565 (1976);
115. S.A. Brawer, Phys. Rev. Lett. 46, 778 (1981);
116. S.A. Brawer, J. Chem. Phys. 75, 3516 (1981);
117. D.A. Litton, S.H. Garofalini, J. Non-Cryst. Sol. 217, 250 (1997).
118. Y. Guissani, B. Guillot, J. Chem. Phys. 104, 7633 (1996).
119. A. Cavagna, Europhys. Lett. 53, 490 (2001).
120. J.-L. Barrat, J. Badro, Ph. Gillet, J. Comp. Simul. 20, 17 (1997).
121. L. Berthier, Phys. Rev. E 69, 020201 (2004).
122. B. Bernu et al., Phys. Rev. A 36, 4891 (1987).
123. E. Kolb, J. Cviklinski, J. Lanuza, P. Claudin, E. Clement, Phys. Rev. E 69, 031306 (2004).
124. J.-P. Bouchaud, G. Biroli, J. Chem. Phys. 121, 7347 (2004).