Global equation of state of two-dimensional hard sphere systems

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

Volumn 63, Issue 4, 2001, Pages

  Luding, Stefan ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; DENSITY OF GASES; GRAVITATIONAL EFFECTS; PHASE TRANSITIONS; PRESSURE DISTRIBUTION; SPHERES; VOLUME FRACTION;

HARD SPHERE SYSTEMS;

EQUATIONS OF STATE OF GASES;

EID: 0035304207     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.042201     Document Type: Article

References (45)

1. J. M. Ziman, Models of Disorder (Cambridge University Press, Cambridge, England, 1979).
2. S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases (Cambridge University Press, London, 1960).
3. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic Press Limited, London, 1986).
4. L. D. Landau and E. M. Lifschitz, Physikalische Kinetik (Akademie Verlag, Berlin, 1986).
5. C. Rascon, L. Mederos, and G. Navascues, Phys. Rev. Lett. 77, 2249 (1996);
6. Phys. Rev. Lett.B. Doliwa and A. Heuer, 80, 4915 (1998).
7. J. G. Kirkwood, E. K. Maun, and B. J. Alder, J. Chem. Phys. 18, 1040 (1950);
8. J. Chem. Phys.R. J. Buehler, 19, 61 (1951);
9. J. Chem. Phys.W. W. Wood, 20, 1334 (1952).
10. B. J. Alder, S. P. Frankel, and V. A. Lewinson, J. Chem. Phys. 23, 417 (1955);
11. J. Chem. Phys.B. J. Alder and T. E. Wainwright, 31, 459 (1959);
12. B. J. AlderT. E. WainwrightPhys. Rev. 127, 359 (1962).
13. S. Torquato, Phys. Rev. E 51, 3170 (1995);
14. E. Velasco and L. Mederos, Phys. Rev. B 56, 2432 (1997).
15. A. Santos, S. B. Yuste, and M. L. D. Haro, Mol. Phys. 96, 1 (1999);
16. P. Richard, L. Oger, J.-P. Troadec, and A. Gervois, Phys. Rev. E 60, 4551 (1999).
17. H. Löwen, in Statistical Physics and Spatial Statistics LNP 554, edited by K. R. Mecke and D. Stoyan (Springer, Berlin, 2000).
18. Powders and Grains 97, edited by R. P. Behringer and J. T. Jenkins (Balkema, Rotterdam, 1997).
19. Physics of Dry Granular Media, Vol. 350 of NATO Advanced Study Institute Series E: Applied Sciences, edited by H. J. Herrmann, J.-P. Hovi, and S. Luding (Kluwer Academic Publishers, Dordrecht, 1998).
20. J. T. Jenkins and M. W. Richman, Phys. Fluids 28, 3485 (1985).
21. P. Sunthar and V. Kumaran, Phys. Rev. E 60, 1951 (1999);
22. Phys. Rev. EV. Kumaran, 59, 4188 (1999).
23. T. P. C. van Noije and M. H. Ernst, Granular Matter 1, 57 (1998).
24. J. J. Brey, J. W. Dufty, C. S. Kim, and A. Santos, Phys. Rev. E 58, 4638 (1998).
25. J. M. Montanero, V. Garzo, A. Santos, and J. J. Brey, J. Fluid Mech. 389, 391 (1999).
26. N. Sela and I. Goldhirsch, J. Fluid Mech. 361, 41 (1998).
27. The instantaneous contacts of the particles imply that exclusively two particle interactions take place. Multibody interactions can be accounted for via higher-order correlations 415 or by perturbations to the rigid potential, see section 6.3. in Ref. 3.
28. D. Henderson, Mol. Phys. 30, 971 (1975);
29. Mol. Phys.D. Henderson34, 301 (1977).
30. L. Verlet and D. Levesque, Mol. Phys. 46, 969 (1982).
31. J. Tobochnik and P. M. Chapin, J. Chem. Phys. 88, 5824 (1988).
32. S. Luding and O. Strauß, in Granular Gases, LNP 564, edited by T. Pöschel and S. Luding (Springer, Berlin, 2000).
33. S. Torquato, T. M. Truskett, and P. G. Debenedetti, Phys. Rev. Lett. 84, 2064 (2000).
34. S. Luding and S. McNamara, Granular Matter 1, 113 (1998);
35. S. LudingS. McNamarae-print cond-mat/9810009 (unpublished);
36. S. Luding and H. J. Herrmann, Chaos 9, 673 (1999).
37. B. D. Lubachevsky, J. Comput. Phys. 94, 255 (1991).
38. J. G. Berryman, Phys. Rev. A 27, 1053 (1983).
39. The magnitude of the correction at (Formula presented) is only 0.5% so that one could also use (Formula presented) with reasonable accuracy so that (Formula presented)
40. W. G. Hoover and F. H. Ree, J. Chem. Phys. 49, 3609 (1968).
41. J. F. Fernandez, J. J. Alonso, and J. Stankiewicz, Phys. Rev. Lett. 75, 3477 (1995).
42. The best-fit parameters (Formula presented) and (Formula presented) lead to even better agreement but would reproduce the inflection (negative slope) of Q within about 1.5% in the transition regime (Formula presented).
43. D. Hong, in Granular Gases, edited by T. Pöschel and S. Luding (Springer Verlag, Berlin, 2000).
44. I. N. Bronstein and K. A. Semendjajew, Taschenbuch der Mathematik (Teubner, Leipzig, 1979).
45. E. Clément and J. Rajchenbach, Europhys. Lett. 16, 133 (1991).