Scales and kinetics of granular flows

Chaos

Volumn 9, Issue 3, 1999, Pages 659-672

  Goldhirsch, I ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

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EID: 0033196588     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166440     Document Type: Article

References (76)

1. A. Coulomb, Memoires de Mathematiques et de Physique Presentes a l'Academie Royale des Sciences par Divers Savants et lus dans les Assemblees, L'Imprimerie Royale, Paris, 1776.
2. G. Hagen, Berlin Monatsberichte Akad. Wis. 35, 442 (1852).
3. O. Reynolds, Philos. Mag. 20, 469-481 (1885).
4. cf., e.g., Physics of Dry Granular Media, edited by H. J. Herrmann, J.-P. Hovi, and S. Luding, NATO ASI Series E: Applied Sciences, Vol. 350, 1998;
5. also some recent reviews (a) R. P. Behringer, Nonlinear Sci. Today 3, 1 (1993);
6. (b) J. M. Jaeger and S. R. Nagel, Rev. Mod. Phys. 68, 1259-1273 (1996).
7. P. B. Umbanhowar, F. Melo, and H. L. Swinney, Nature (London) 382, 793 (1996).
8. An old reference proposing an explanation for the normal stress differences is M. W. Richman, J. Rheol. 33, 1293 (1989), and references therein. See also other references on this topic in the review paper by Campbell, Ref. 10 below.
9. I. Goldhirsch, N. Sela, and S. H. Noskowicz, Phys. Fluids 8, 2337 (1996).
10. I. Goldhirsch and N. Sela, Phys. Rev. E 54, 4458 (1996).
11. N. Sela and I. Goldhirsch, J. Fluid Mech. 361, 41 (1998), and references therein.
12. Review on rapid granular flows: C. S. Campbell, Annu. Rev. Fluid Mech. 22, 57 (1990).
13. M. Hopkins and H. Shen, J. Fluid Mech. 244, 477-491 (1992).
14. D. Burnett, Proc. London Math. Soc. 40, 382 (1935).
15. M. K. Kogan, Rarefied Gas Dynamics (Plenum, New York, 1969).
16. S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases (Cambridge Univ. Press, Cambridge, 1970).
17. For example, (a) L. C. Woods, J. Fluid Mech. 93, 585 (1979);
18. (b) K. Fiscko and D. Chapman, AIAA J. 118, 374 (1989).
19. M. A. Hopkins and M. Y. Louge, Phys. Fluids A 3, 47 (1991).
20. (a) I. Goldhirsch and G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993);
21. (b) I. Goldhirsch, M-L. Tan, and G. Zanetti, J. Sci. Comput. 8, 1 (1993);
22. (c) M-L. Tan and I. Goldhirsch, Phys. Fluids 9, 856 (1997).
23. (a) I. Goldhirsch and M-L. Tan, Phys. Fluids 8, 1752-1763 (1996);
24. (b) M-L. Tan and I. Goldhirsch, Phys. Fluids 9, 856-869 (1997).
25. S. McNamara and W. R. Young, Phys. Fluids A 4, 496 (1992).
26. S. McNamara and W. R. Young, Phys. Fluids A 5, 34 (1993).
27. S. McNamara and W. R. Young, Phys. Rev. E 50, R28-R31 (1994).
28. P. K. Haff, J. Fluid Mech. 134, 401-948 (1983).
29. M-L. Tan and I. Goldhirsch, Phys. Rev. Lett. 81, 3022-3025 (1998).
30. cf. e.g., (a) A. V. Bobylev, Theor. Math. Phys. 60, 280-310 (1984);
31. (b) A. N. Gorban and I. V. Karlin, Transp. Theory Stat. Phys. 21. 101-117 (1992).
32. P. Rosenau, Phys. Rev. A 40, 7193-7196 (1989); see also M. Slemrod, Arch. Ration. Mech. Anal. 146, 73 (1999).
33. P. Rosenau, Phys. Rev. A 40, 7193-7196 (1989); see also M. Slemrod, Arch. Ration. Mech. Anal. 146, 73 (1999).
34. M. H. Ernst and J. R. Dorfman, J. Stat. Phys. 12, 311 (1976).
35. I. Oppenheim, in Correlation Functions and Quasiparticle Interactions in Condensed Matter, edited by J. Woods Halley (Plenum, 1978), and references therein; D. Ronis, Physica A 99, 403 (1979).
36. I. Oppenheim, in Correlation Functions and Quasiparticle Interactions in Condensed Matter, edited by J. Woods Halley (Plenum, 1978), and references therein; D. Ronis, Physica A 99, 403 (1979).
37. (a) H. Mori, Phys. Rev. 111, 694 (1958);
38. (b) H. Mori, ibid. 112, 1829 (1958).
39. I. Goldhirsch and T. P. C. van Noije, "Green-Kubo relations for granular fluids," preprint, 1998.
40. S. Harris, Introduction to the Theory of the Boltzmann Equation (Holt, Reinhart, and Winston, New York, 1971).
41. C. Cercignani, Theory and Application of the Boltzmann Equation (Scottish Academic, Edinburgh and London, 1975).
42. T. P. C. van Noije, M. H. Ernst, R. Brito, and J. A. G. Orza, Phys. Rev. Lett. 79, 411 (1997).
43. J. F. Lutsko, Phys. Rev. Lett. 77, 2225 (1996), and references therein.
44. A. I. Murdoch, Arch. Mech. 50, 531 (1998), and references therein.
45. M. Babic, Int. J. Eng. Sci. 35, 523 (1997).
46. B. J. Glasser and I. Goldhirsch, preprint, 1998.
47. S. B. Savage, in Disorder, Diffusion and Structure Formation in Granular Flows, edited by D. Bideau and A. Hansen [Random Materials and Processes Ser., edited by H. E. Stanley and E. Guyon (North Holland, Amsterdam, 1993)].
48. C. O'Hern, B. Miller, and R. P. Behringer, Phys. Rev. E 54, 4458 (1996).
49. J. J. Brey, F. Moreno, and J. W. Dufty, Phys. Rev. E 54, 1270 (1996).
50. J. J. Brey, J. W. Dufty, C. S. Kim, and A. Santos, Phys. Rev. E 58, 4638 (1998).
51. S. H. Noskowicz, O. Bar-Lev, and I. Goldhirsch (unpublished).
52. (a) I. Kuscer and M. M. R. Williams, Phys. Fluids 10, 1922 (1967);
53. (b) F. Schurrer and G. Kugerl, Phys. Fluids A 2, 609 (1990).
54. (a) S. E. Esipov and T. Poschel, J. Stat. Phys. 86, 1385 (1997);
55. (b) J. J. Brey, D. Cubero, and M. J. Ruiz-Montero, Phys. Rev. E 59, 1256 (1999).
56. (a) J. T. Jenkins and S. B. Savage, J. Fluid Mech. 130, 187 (1983);
57. (b) C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy, ibid. 140, 223-256 (1984);
58. (c) J. T. Jenkins and M. W. Richman, Phys. Fluids 28, 3485 (1985);
59. (d) C. K. K. Lun and S. B. Savage, J. Appl. Mech. 154, 47 (1987);
60. (e) J. T. Jenkins and M. W. Richman, J. Fluid Mech. 192, 313-328 (1988).
61. J. T. Jenkins and M. W. Richman, Arch. Ration. Mech. Anal. 87, 355-377 (1985).
62. C. K. K. Lun, J. Fluid Mech. 223, 539 (1991).
63. E. J. Boyle and M. Massoudi, Int. J. Eng. Sci. 28, 1261-1275 (1990).
64. (a) O. R. Walton and R. L. Braun, Acta Mech. 63, 73-86 (1986).
65. (b) O. R. Walton and R. L. Braun, J. Rheol. 30, 949-980 (1986).
66. H. Grad, Commun. Pure Appl. Math. 2, 331-407 (1949).
67. N. Sela and I. Goldhirsch, "Boundary Conditions for Granular and Molecular Gases: a Systematic Approach" (unpublished).
68. Some previous work on boundary conditions for granular gases: (a) J. T. Jenkins and M. W. Richman, J. Fluid Mech. 171, 53-69 (1986);
69. (b) M. W. Richman, Acta Mech. 75, 227-240 (1988);
70. J. T. Jenkins, J. Appl. Mech. 59, 120-127 (1992);
71. J. T. Jenkins and E. Askari, J. Fluid Mech. 223, 497-508 (1991).
72. C. L. Pekeris, Proc. Natl. Acad. Sci. USA 41, 661-664 (1955).
73. N. Sela and I. Goldhirsch, Phys. Fluids 7, 507-525 (1995).
74. Advances in Thermodynamics, edited by S. Salomon and S. Sienintycz (Francis and Taylor, New York, 1991), and numerous references therein.
75. L. P. Kadanoff, Rev. Mod. Phys. 71, 435-444 (1999).
76. J. J. Brey, M. J. Ruiz-Montero, and D. Cubero (unpublished).