Randomly driven granular fluids: Large-scale structure

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 59, Issue 4, 1999, Pages 4326-4341

  van Noije, T P C ^a   Ernst, M H ^a   Trizac, E ^b   Pagonabarraga, I ^b  

^a UTRECHT UNIVERSITY   (Netherlands)

^b FOM INSTITUTE AMOLF   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001398820     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.4326     Document Type: Article

References (49)

1. H. M. Jaeger, S. R. Nagel, and R. P. Behringer, Rev. Mod. Phys. 68, 1259 (1996).
2. R. A. Bagnold, Proc. R. Soc. London, Ser. A 225, 49 (1954).
3. S. B. Savage and M. Sayed, J. Fluid Mech. 142, 391 (1984).
4. P. C. Johnson, P. Nott, and R. Jackson, J. Fluid Mech. 210, 501 (1990).
5. S. Warr, J. M. Huntley, and G. T. H. Jacques, Phys. Rev. E 52, 5583 (1995).
6. F. Melo, P. B. Umbanhowar, and H. L. Swinney, Phys. Rev. Lett. 75, 3838 (1995).
7. L. S. Tsimring and I. S. Aranson, Phys. Rev. Lett. 79, 213 (1997)
8. D. H. Rothman, Phys. Rev. E 57, R1239 (1998)
9. S. C. Venkataramani and E. Ott, Phys. Rev. Lett. 80, 3495 (1998).
10. M. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
11. A. Kudrolli, M. Wolpert, and J. P. Gollub, Phys. Rev. Lett. 78, 1383 (1997).
12. J. S. Olafsen and J. S. Urbach, Phys. Rev. Lett. 81, 4369 (1998).
13. J. T. Jenkins and M. W. Richman, Arch. Ration. Mech. Anal. 87, 355 (1985)
14. J. J. Brey, J. W. Dufty, and A. Santos, J. Stat. Phys. 87, 1051 (1997)
15. N. Sela and I. Goldhirsch, J. Fluid Mech. 361, 41 (1998).
16. D. R. Williams and F. C. MacKintosh, Phys. Rev. E 54, R9 (1996).
17. G. Peng and T. Ohta, Phys. Rev. E 58, 4737 (1998).
18. L. Oger, C. Annic, D. Bideau, R. Dai, and S. B. Savage, J. Stat. Phys. 82, 1047 (1996).
19. R. Jackson, in Fluidization, edited by J. F. Davidson, R. Clift, and D. Harrison (Academic Press, London, 1985).
20. C. Bizon and H. L. Swinney (private communication).
21. T. P. C. van Noije and M. H. Ernst, Granular Matter 1, 57 (1998).
22. M. R. Swift, M. Boamfǎ, S. J. Cornell, and A. Maritan, Phys. Rev. Lett. 80, 4410 (1998).
23. J. R. Dorfman, T. R. Kirkpatrick, and J. Sengers, Annu. Rev. Phys. Chem. 45, 213 (1994).
24. R. Brito and M. H. Ernst, Europhys. Lett. 43, 497 (1998).
25. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic Press, London, 1986).
26. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases (Cambridge University Press, Cambridge, 1970).
27. T. P. C. van Noije, M. H. Ernst, R. Brito, and J. A. G. Orza, Phys. Rev. Lett. 79, 411 (1997)
28. T. P. C. van Noije, R. Brito, and M. H. Ernst, Phys. Rev. E 57, R4891 (1998).
29. U. Frisch, B. Hasslacher, and Y. Pomeau, Phys. Rev. Lett. 56, 1505 (1986).
30. D. H. Rothman and S. Zaleski, Rev. Mod. Phys. 66, 1417 (1994).
31. S. McNamara, Phys. Fluids A 5, 3056 (1993).
32. L. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, New York, 1959), Chap. 17.
33. I. Goldhirsch and G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993).
34. S. McNamara and W. R. Young, Phys. Fluids A 4, 496 (1992)
35. S. McNamaraW. R. YoungPhys. Rev. E 50, R28 (1994)
36. Phys. Rev. ES. McNamaraW. R. Young53, 5089 (1996).
37. P. Deltour and J.-L. Barrat, J. Phys. I 7, 137 (1997).
38. A. Puglisi, V. Loreto, U. Marini Bettolo Marconi, A. Petri, and A. Vulpiani, Phys. Rev. Lett. 81, 3848 (1998).
39. M. P. Allen and D. J. Tildesley, Computer Simulations of Liquids (Clarendon Press, Oxford, 1987).
40. S. Jasty, M. Al-Naghy, and M. de Llano, Phys. Rev. A 35, 1376 (1987).
41. G. Grinstein, D.-H. Lee, and S. Sachdev, Phys. Rev. Lett. 64, 1927 (1990).
42. S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London, Ser. A 381, 17 (1982).
43. M. H. Ernst, E. H. Hauge, and J. M. J. van Leeuwen, Phys. Rev. Lett. 25, 1245 (1970)
44. M. H. ErnstE. H. HaugeJ. M. J. van LeeuwenPhys. Rev. A 4, 2055 (1971).
45. J. R. Dorfman and E. G. D. Cohen, Phys. Rev. Lett. 25, 1257 (1970)
46. M. H. Ernst and J. R. Dorfman, Physica (Amsterdam) 61, 157 (1972).
47. T. P. C. van Noije, M. H. Ernst, and R. Brito, Physica A 251, 266 (1998).
48. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1965).
49. J. R. Dorfman and H. van Beijeren, in Statistical Mechanics, Part B: Time-Dependent Processes, edited by B. J. Berne (Plenum Press, New York, 1977), Chap. 3.