Collision properties of one-dimensional granular particles with internal degrees of freedom

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

Volumn 54, Issue 5, 1996, Pages 4828-4837

  Giese, Götz ^a   Zippelius, Annette ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000227879     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.54.4828     Document Type: Article

References (38)

1. See, for example, J.A.C. Gallas, H.J. Herrmann, and S. Sokolowski, Phys. Rev. Lett. 69, 1371 (1992); Physica A 189, 437 (1992); T. Pöschel, J. Phys. (Paris) II 3, 27 (1993); Y-h. Taguchi, Phys. Rev. Lett. 69, 1367 (1992); J. Phys. (France) II 2, 2103 (1992); Int. J. Mod. Phys. B 7, 1839 (1993); J.A.C. Gallas et al., J. Stat. Phys. 82, 443 (1996).
2. See, for example, J.A.C. Gallas, H.J. Herrmann, and S. Sokolowski, Phys. Rev. Lett. 69, 1371 (1992); Physica A 189, 437 (1992); T. Pöschel, J. Phys. (Paris) II 3, 27 (1993); Y-h. Taguchi, Phys. Rev. Lett. 69, 1367 (1992); J. Phys. (France) II 2, 2103 (1992); Int. J. Mod. Phys. B 7, 1839 (1993); J.A.C. Gallas et al., J. Stat. Phys. 82, 443 (1996).
3. See, for example, J.A.C. Gallas, H.J. Herrmann, and S. Sokolowski, Phys. Rev. Lett. 69, 1371 (1992); Physica A 189, 437 (1992); T. Pöschel, J. Phys. (Paris) II 3, 27 (1993); Y-h. Taguchi, Phys. Rev. Lett. 69, 1367 (1992); J. Phys. (France) II 2, 2103 (1992); Int. J. Mod. Phys. B 7, 1839 (1993); J.A.C. Gallas et al., J. Stat. Phys. 82, 443 (1996).
4. See, for example, J.A.C. Gallas, H.J. Herrmann, and S. Sokolowski, Phys. Rev. Lett. 69, 1371 (1992); Physica A 189, 437 (1992); T. Pöschel, J. Phys. (Paris) II 3, 27 (1993); Y-h. Taguchi, Phys. Rev. Lett. 69, 1367 (1992); J. Phys. (France) II 2, 2103 (1992); Int. J. Mod. Phys. B 7, 1839 (1993); J.A.C. Gallas et al., J. Stat. Phys. 82, 443 (1996).
5. See, for example, J.A.C. Gallas, H.J. Herrmann, and S. Sokolowski, Phys. Rev. Lett. 69, 1371 (1992); Physica A 189, 437 (1992); T. Pöschel, J. Phys. (Paris) II 3, 27 (1993); Y-h. Taguchi, Phys. Rev. Lett. 69, 1367 (1992); J. Phys. (France) II 2, 2103 (1992); Int. J. Mod. Phys. B 7, 1839 (1993); J.A.C. Gallas et al., J. Stat. Phys. 82, 443 (1996).
6. See, for example, J.A.C. Gallas, H.J. Herrmann, and S. Sokolowski, Phys. Rev. Lett. 69, 1371 (1992); Physica A 189, 437 (1992); T. Pöschel, J. Phys. (Paris) II 3, 27 (1993); Y-h. Taguchi, Phys. Rev. Lett. 69, 1367 (1992); J. Phys. (France) II 2, 2103 (1992); Int. J. Mod. Phys. B 7, 1839 (1993); J.A.C. Gallas et al., J. Stat. Phys. 82, 443 (1996).
7. See, for example, J.A.C. Gallas, H.J. Herrmann, and S. Sokolowski, Phys. Rev. Lett. 69, 1371 (1992); Physica A 189, 437 (1992); T. Pöschel, J. Phys. (Paris) II 3, 27 (1993); Y-h. Taguchi, Phys. Rev. Lett. 69, 1367 (1992); J. Phys. (France) II 2, 2103 (1992); Int. J. Mod. Phys. B 7, 1839 (1993); J.A.C. Gallas et al., J. Stat. Phys. 82, 443 (1996).
8. S. Luding et al., Phys. Rev. E 50, R1762 (1994); ibid. 50, 4113 (1994).
9. S. Luding et al., Phys. Rev. E 50, R1762 (1994); ibid. 50, 4113 (1994).
10. B. Bernu and R. Mazighi, J. Phys. A 23, 5745 (1990); B. Bernu, F. Delyon, and R. Mazighi, Phys. Rev. E 50, 4551 (1994).
11. B. Bernu and R. Mazighi, J. Phys. A 23, 5745 (1990); B. Bernu, F. Delyon, and R. Mazighi, Phys. Rev. E 50, 4551 (1994).
12. S. McNamara and W.R. Young, Phys. Fluids A 4, 496 (1992); ibid. 5, 34 (1993).
13. S. McNamara and W.R. Young, Phys. Fluids A 4, 496 (1992); ibid. 5, 34 (1993).
14. S. Luding et al., Int. J. Mod. Phys. B 7, 1807 (1993); Phys. Rev. E 49, 1634 (1994).
15. S. Luding et al., Int. J. Mod. Phys. B 7, 1807 (1993); Phys. Rev. E 49, 1634 (1994).
16. I. Goldhirsch and G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993); N. Sela and I. Goldhirsch, Phys. Fluids 7, 507 (1995).
17. I. Goldhirsch and G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993); N. Sela and I. Goldhirsch, Phys. Fluids 7, 507 (1995).
18. Y. Du, H. Li, and L.P. Kadanoff, Phys. Rev. Lett. 74, 1268 (1995).
19. G. Giese, in Traffic and Granular Flow, edited by D.E. Wolf, M. Schreckenberg, and A. Bachem (World Scientific, Singapore, 1996), p. 335.
20. S.B. Savage, Adv. Appl. Mech. 24, 289 (1982).
21. M. Toda, J. Phys. Soc. Jpn. 13, 1266 (1958); ibid. 14, 722 (1959); P. Mazur and E. Montroll, J. Math. Phys. 1, 70 (1960); R.J. Rubin, ibid. 1, 309 (1960); R.E. Turner, Physica 26, 274 (1960); K. Lindenberg and V. Seshahdri, Physica A 109, 483 (1981); E. Cortes, B.J. West, and K. Lindenberg, J. Chem. Phys. 82, 2708 (1985).
22. M. Toda, J. Phys. Soc. Jpn. 13, 1266 (1958); ibid. 14, 722 (1959); P. Mazur and E. Montroll, J. Math. Phys. 1, 70 (1960); R.J. Rubin, ibid. 1, 309 (1960); R.E. Turner, Physica 26, 274 (1960); K. Lindenberg and V. Seshahdri, Physica A 109, 483 (1981); E. Cortes, B.J. West, and K. Lindenberg, J. Chem. Phys. 82, 2708 (1985).
23. M. Toda, J. Phys. Soc. Jpn. 13, 1266 (1958); ibid. 14, 722 (1959); P. Mazur and E. Montroll, J. Math. Phys. 1, 70 (1960); R.J. Rubin, ibid. 1, 309 (1960); R.E. Turner, Physica 26, 274 (1960); K. Lindenberg and V. Seshahdri, Physica A 109, 483 (1981); E. Cortes, B.J. West, and K. Lindenberg, J. Chem. Phys. 82, 2708 (1985).
24. M. Toda, J. Phys. Soc. Jpn. 13, 1266 (1958); ibid. 14, 722 (1959); P. Mazur and E. Montroll, J. Math. Phys. 1, 70 (1960); R.J. Rubin, ibid. 1, 309 (1960); R.E. Turner, Physica 26, 274 (1960); K. Lindenberg and V. Seshahdri, Physica A 109, 483 (1981); E. Cortes, B.J. West, and K. Lindenberg, J. Chem. Phys. 82, 2708 (1985).
25. M. Toda, J. Phys. Soc. Jpn. 13, 1266 (1958); ibid. 14, 722 (1959); P. Mazur and E. Montroll, J. Math. Phys. 1, 70 (1960); R.J. Rubin, ibid. 1, 309 (1960); R.E. Turner, Physica 26, 274 (1960); K. Lindenberg and V. Seshahdri, Physica A 109, 483 (1981); E. Cortes, B.J. West, and K. Lindenberg, J. Chem. Phys. 82, 2708 (1985).
26. M. Toda, J. Phys. Soc. Jpn. 13, 1266 (1958); ibid. 14, 722 (1959); P. Mazur and E. Montroll, J. Math. Phys. 1, 70 (1960); R.J. Rubin, ibid. 1, 309 (1960); R.E. Turner, Physica 26, 274 (1960); K. Lindenberg and V. Seshahdri, Physica A 109, 483 (1981); E. Cortes, B.J. West, and K. Lindenberg, J. Chem. Phys. 82, 2708 (1985).
27. M. Toda, J. Phys. Soc. Jpn. 13, 1266 (1958); ibid. 14, 722 (1959); P. Mazur and E. Montroll, J. Math. Phys. 1, 70 (1960); R.J. Rubin, ibid. 1, 309 (1960); R.E. Turner, Physica 26, 274 (1960); K. Lindenberg and V. Seshahdri, Physica A 109, 483 (1981); E. Cortes, B.J. West, and K. Lindenberg, J. Chem. Phys. 82, 2708 (1985).
28. G.W. Ford, M. Kac, and P. Mazur, J. Math. Phys. 6, 504 (1965).
29. P. Ullersma, Physica 32, 27 (1966).
30. W.H. Press et al., Numerical Recipes in C (Cambridge University Press, Cambridge, 1988), p. 582.
31. intap;0
32. A. Khinchin, Mathematical Foundations of Information Theory (Dover, New York, 1957).
33. R. Livi et al., Phys. Rev. A 31, 1039 (1985).
34. C.G. Goedde, A.J. Lichtenberg, and M.A. Liebermann, Physica D 59, 200 (1992).
35. G. Giese, Dissertation, Goettingen, 1996 (unpublished).
36. See any text book on impact dynamics, e.g., W. Goldsmith, Impact (Arnold, London, 1960), p. 38.
37. T. Aspelmeier (private communication).
38. R.J. Glauber, J. Math. Phys. 4, 294 (1963).