Scaling, multiscaling, and nontrivial exponents in inelastic collision processes

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

Volumn 66, Issue 1, 2002, Pages

  Ben Naim, E ^a   Krapivsky, P L ^b  

^a CENTER FOR NONLINEAR STUDIES   (United States)

^b Boston University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION SCALING; GAUSSIAN RANDOM MATRICES; MATRIX STRUCTURES; ONE-DIMENSIONAL VICIOUS WALKER MODEL;

DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; SET THEORY; THERMODYNAMICS;

BROWNIAN MOVEMENT;

EID: 41349111246     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.011309     Document Type: Article

References (54)

1. Granular Gases, edited by T. Pöschel and S. Luding (Springer, Berlin, 2000).
2. H. J. Herrmann, in Disorder and Granular Media, edited by D. Bideau and A. Hansen (Elsevier Science, New York, 1993).
3. C. Bizon, M. D. Shattuck, J. B. Swift, W. D. McCormick, and H. L. Swinney, Phys. Rev. Lett. 80, 57 (1998).
4. E. L. Grossman, T. Zhou, and E. Ben-Naim, Phys. Rev. E 55, 4200 (1997).
5. A. Kudrolli, M. Wolpert, and J. P. Gollub, Phys. Rev. Lett. 78, 1383 (1997).
6. W. Losert, D. G. W. Cooper, J. Delour, A. Kudrolli, and J. P. Gollub, Chaos 9, 682 (1999).
7. J. S. Olafsen and J. S. Urbach, Phys. Rev. Lett. 81, 4369 (1998).
8. X. Nie, E. Ben-Naim, and S. Y. Chen, Europhys. Lett. 51, 679 (2000).
9. A. Samadani, L. Mahadevan, and A. Kudrolli, e-print cond-mat/0110427.
10. E. Rericha, C. Bizon, M. D. Shattuck, and H. L. Swinney, Phys. Rev. Lett. 88, 014302 (2002).
11. J. T. Jenkins and M. W. Richman, Phys. Fluids 28, 3485 (1985).
12. N. Sela and I. Goldhirsch, J. Fluid Mech. 361, 41 (1998).
13. A. Goldshtein and M. Shapiro, J. Fluid Mech. 282, 75 (1995).
14. P. K. Haff, J. Fluid Mech. 134, 401 (1983).
15. G. F. Carnevale, Y. Pomeau, and W. R. Young, Phys. Rev. Lett. 64, 2913 (1990).
16. B. Bernu and R. Mazighi, J. Phys. A 23, 5745 (1990).
17. S. McNamara and W. R. Young, Phys. Fluids A 4, 496 (1992).
18. Y. Du, H. Li, and L. P. Kadanoff, Phys. Rev. Lett. 74, 1268 (1995).
19. T. Zhou and L. P. Kadanoff, Phys. Rev. E 54, 623 (1996).
20. S. E. Esipov and T. Pöschel, J. Stat. Phys. 86, 1385 (1997).
21. P. Deltour and A. Barrat, J. Phys. I 7, 137 (1997).
22. T. P. C. van Noije and M. H. Ernst, Granular Matter 1, 57 (1998).
23. F. Rouyer and N. Menon, Phys. Rev. Lett. 85, 3676 (2000).
24. I. S. Aranson and J. S. Olafsen, e-print cond-mat/0110697.
25. A. Puglisi, V. Loreto, U. Marini Bettolo Marconi, and A. Vulpiani, Phys. Rev. E 59, 5582 (1999).
26. P. Résibois and M. de Leener, Classical Kinetic Theory of Fluids (Wiley, New York, 1977).
27. R. Soto and M. Mareschal, Phys. Rev. E 63, 041303 (2001).
28. A. Barrat, T. Biben, Z. Rácz, E. Trizac, and F. van Wijland, J. Phys. A 35, 463 (2002).
29. I. Goldhirsch and G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993).
30. R. Brito and M. H. Ernst, Europhys. Lett. 43, 497 (1998).
31. E. Ben-Naim, S. Y. Chen, G. D. Doolen, and S. Redner, Phys. Rev. Lett. 83, 4069 (1999).
32. I. Goldhirsch, Granular Gases (Ref. 1).
33. J. C. Maxwell, Philos. Trans. R. Soc. London 157, 49 (1867).
34. C. Truesdell and R. G. Muncaster, Fundamentals of Maxwell’s Kinetic Theory of a Simple Monoatomic Gas (Academic Press, New York, 1980).
35. M. H. Ernst, Phys. Rep. 78, 1 (1981).
36. A. V. Bobylev, Sov. Sci. Rev. 7, 111 (1988).
37. L. Acedo, A. Santos, and A. V. Bobylev, e-print cond-mat/0109490.
38. H.-D. Kim and H. Hayakawa, e-print cond-mat/0202003.
39. E. Ben-Naim and P. L. Krapivsky, Phys. Rev. E 61, R5 (2000).
40. A. Baldassarri, U. Marini Bettolo Marconi, and A. Puglisi, Europhys. Lett. 58, 14 (2002).
41. P. L. Krapivsky and E. Ben-Naim, J. Phys. A 35L147 (2002).
42. M. H. Ernst and R. Brito, Europhys. Lett. 58, 182 (2002);
43. M. H. ErnstR. BritoPhys. Rev. E 65, 040301 (2002).
44. U. Marini Bettolo Marconi and A. Puglisi, Phys. Rev. E 65, 011301 (2002);
45. Phys. Rev. EU. Marini Bettolo MarconiA. Puglisi65, 051305 (2002).
46. Every initial velocity distribution evolves towards the Maxwellian distribution if (Formula presented) and (Formula presented); for (Formula presented), there is no relaxation in the elastic case.
47. G. E. Andrews, R. Askey, and R. Roy, Special Functions (Cambridge University Press, Cambridge, UK, 1999).
48. A. Baldassarri (private communication).
49. N. V. Brilliantov and T. Pöschel, Phys. Rev. E 61, 1716 (2000).
50. H.-D. Kim and H. Hayakawa, J. Phys. Soc. Jpn. 70, 1954 (2001).
51. J. A. Carrillo, C. Cercignani, and I. M. Gamba, Phys. Rev. E 62, 7700 (2000).
52. G. Giese and A. Zippelius, Phys. Rev. E 54, 4828 (1996).
53. T. Aspelmeier and A. Zippelius, Physica A 282, 450 (2000).
54. A. Barrat, E. Trizac, and J. H. Fuchs, Eur. Phys. J. E 5, 161 (2001).