Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 5, 2010, Pages

  Jin, Yuliang ^a   Charbonneau, Patrick ^b   Meyer, Sam ^a,c   Song, Chaoming ^a,d   Zamponi, Francesco ^e  

^a CITY COLLEGE OF NEW YORK   (United States)

^b DUKE UNIVERSITY   (United States)

^c UNIVERSITÉ DE LYON   (France)

^d NORTHEASTERN UNIVERSITY   (United States)

^e LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY DIMENSION; HIGH-DIMENSIONAL; HIGHER ORDER CORRELATION; JAMMED PACKINGS; LIQUID STATE; NUMERICAL RESULTS; RANDOM CLOSE PACKINGS; SADDLE POINT; SPHERE PACKINGS; SPHERICAL PARTICLE; THEORETICAL APPROACH;

JAMMING; SPHERES; STATISTICAL MECHANICS;

DENSITY FUNCTIONAL THEORY;

EID: 78651350602     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.051126     Document Type: Article

References (65)

1. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd ed., A Series of Comprehensive Mathematics Vol. 290 (Springer-Verlag, New York, 1999).
2. C. A. Rogers, Packing and Covering (Cambridge University Press, Cambridge, 1964).
3. K. Ball, Int. Math. Res. Notices (1992) 217. 10.1155/S1073792892000242
4. M. Krivelevich, S. Litsyn, and A. Vardy, Int. Math. Res. Notices (2004) 2271. 10.1155/S1073792804140464
5. G. A. Kabatiansky and V. I. Levenshtein, Probl. Inf. Transm. 14, 1 (1978).
6. S. Torquato and F. H. Stillinger, Exp. Math. 15, 307 (2006).
7. G. D. Scott and D. M. Kilgour, J. Phys. D 2, 863 (1969). 10.1088/0022-3727/2/6/311
8. C. H. Bennett, J. Appl. Phys. 43, 2727 (1972). 10.1063/1.1661585
9. P. Pusey and W. Van Megen, Nature (London) 320, 340 (1986). 10.1038/320340a0
10. S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Springer-Verlag, New York, 2002).
11. M. Schröter, D. I. Goldman, and H. L. Swinney, Phys. Rev. E 71, 030301 (R) (2005). 10.1103/PhysRevE.71.030301
12. K. E. Daniels and R. P. Behringer, J. Stat. Mech.: Theory Exp. (2006) P07018. 10.1088/1742-5468/2006/07/P07018
13. O. Dauchot, G. Marty, and G. Biroli, Phys. Rev. Lett. 95, 265701 (2005). 10.1103/PhysRevLett.95.265701
14. A. R. Abate and D. J. Durian, Phys. Rev. E 74, 031308 (2006). 10.1103/PhysRevE.74.031308
15. M. Pica Ciamarra, M. Nicodemi, and A. Coniglio, Phys. Rev. E 75, 021303 (2007). 10.1103/PhysRevE.75.021303
16. M. Jerkins, M. Schröter, H. L. Swinney, T. J. Senden, M. Saadatfar, and T. Aste, Phys. Rev. Lett. 101, 018301 (2008). 10.1103/PhysRevLett.101.018301
17. T. S. Majmudar, M. Sperl, S. Luding, and R. P. Behringer, Phys. Rev. Lett. 98, 058001 (2007). 10.1103/PhysRevLett.98.058001
18. B. D. Lubachevsky and F. H. Stillinger, J. Stat. Phys. 60, 561 (1990). 10.1007/BF01025983
19. A. Donev, S. Torquato, and F. H. Stillinger, Phys. Rev. E 71, 011105 (2005). 10.1103/PhysRevE.71.011105
20. M. Skoge, A. Donev, F. H. Stillinger, and S. Torquato, Phys. Rev. E 74, 041127 (2006). 10.1103/PhysRevE.74.041127
21. H. A. Makse, D. L. Johnson, and L. M. Schwartz, Phys. Rev. Lett. 84, 4160 (2000). 10.1103/PhysRevLett.84.4160
22. H. P. Zhang and H. A. Makse, Phys. Rev. E 72, 011301 (2005). 10.1103/PhysRevE.72.011301
23. A. S. Clarke and H. Jónsson, Phys. Rev. E 47, 3975 (1993). 10.1103/PhysRevE.47.3975
24. C. S. O'Hern, S. A. Langer, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett. 88, 075507 (2002). 10.1103/PhysRevLett.88.075507
25. C. S. O'Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. E 68, 011306 (2003). 10.1103/PhysRevE.68.011306
26. L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. E 73, 041304 (2006). 10.1103/PhysRevE.73.041304
27. E. Somfai, M. van Hecke, W. G. Ellenbroek, K. Shundyak, and W. van Saarloos, Phys. Rev. E 75, 020301 (2007). 10.1103/PhysRevE.75.020301
28. S. Torquato, T. M. Truskett, and P. G. Debenedetti, Phys. Rev. Lett. 84, 2064 (2000). 10.1103/PhysRevLett.84.2064
29. R. D. Kamien and A. J. Liu, Phys. Rev. Lett. 99, 155501 (2007). 10.1103/PhysRevLett.99.155501
30. Y. Jin and H. A. Makse, Physica A 389, 5362 (2010). 10.1016/j.physa.2010. 08.010
31. C. Radin, J. Stat. Phys. 131, 567 (2008). 10.1007/s10955-008-9523-1
32. G. Parisi and F. Zamponi, Rev. Mod. Phys. 82, 789 (2010). 10.1103/RevModPhys.82.789
33. G. Parisi, J. Stat. Phys. 132, 207 (2008). 10.1007/s10955-008-9539-6
34. G. Parisi, Statistical Field Theory (Addison-Wesley, Reading, MA, 1988).
35. J. A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201 (R) (2009). 10.1103/PhysRevE.79.030201
36. J. A. van Meel, B. Charbonneau, A. Fortini, and P. Charbonneau, Phys. Rev. E 80, 061110 (2009). 10.1103/PhysRevE.80.061110
37. S. F. Edwards and R. B. S. Oakeshott, Physica A 157, 1080 (1989). 10.1016/0378-4371(89)90034-4
38. R. Blumenfeld and S. F. Edwards, Phys. Rev. Lett. 90, 114303 (2003). 10.1103/PhysRevLett.90.114303
39. Y. Srebro and D. Levine, Phys. Rev. E 68, 061301 (2003). 10.1103/PhysRevE.68.061301
40. R. Blumenfeld and S. F. Edwards, Eur. Phys. J. E 19, 23 (2006). 10.1140/epje/e2006-00014-7
41. T. Aste and T. Di Matteo, Phys. Rev. E 77, 021309 (2008). 10.1103/PhysRevE.77.021309
42. G. Frenkel, R. Blumenfeld, Z. Grof, and P. R. King, Phys. Rev. E 77, 041304 (2008). 10.1103/PhysRevE.77.041304
43. C. Song, P. Wang, and H. A. Makse, Nature (London) 453, 629 (2008). 10.1038/nature06981
44. M. Danisch, Y. Jin, and H. A. Makse, Phys. Rev. E 81, 051303 (2010). 10.1103/PhysRevE.81.051303
45. S. Meyer, C. Song, Y. Jin, K. Wang, and H. A. Makse, Physica A 389, 5137 (2010). 10.1016/j.physa.2010.07.030
46. C. Song, P. Wang, Y. Jin, and H. A. Makse, Physica A 389, 4497 (2010). 10.1016/j.physa.2010.06.043
47. H. Reiss, H. L. Frisch, and J. L. Lebowitz, J. Chem. Phys. 31, 369 (1959). 10.1063/1.1730361
48. S. Torquato, B. Lu, and J. Rubinstein, Phys. Rev. A 41, 2059 (1990). 10.1103/PhysRevA.41.2059
49. J. G. Kirkwood, J. Chem. Phys. 3, 300 (1935). 10.1063/1.1749657
50. > (c).
51. M. Otsuki and H. Hayakawa, Prog. Theor. Phys. 121, 647 (2009). 10.1143/PTP.121.647
52. J. D. Bernal and J. Mason, Nature (London) 188, 910 (1960). 10.1038/188910a0
53. J. G. Berryman, Phys. Rev. A 27, 1053 (1983). 10.1103/PhysRevA.27.1053
54. C (c) as suggested in.
55. S. Torquato and F. H. Stillinger, Phys. Rev. E 73, 031106 (2006). 10.1103/PhysRevE.73.031106
56. J. Talbot, G. Tarjus, P. R. V. Tassel, and P. Viot, Colloids Surf., A 165, 287 (2000). 10.1016/S0927-7757(99)00409-4
57. S. Torquato, O. U. Uche, and F. H. Stillinger, Phys. Rev. E 74, 061308 (2006). 10.1103/PhysRevE.74.061308
58. T. R. Kirkpatrick and P. G. Wolynes, Phys. Rev. A 35, 3072 (1987). 10.1103/PhysRevA.35.3072
59. H. L. Frisch and J. K. Percus, Phys. Rev. E 60, 2942 (1999). 10.1103/PhysRevE.60.2942
60. G. Parisi and F. Slanina, Phys. Rev. E 62, 6554 (2000). 10.1103/PhysRevE.62.6554
61. P. Chaudhuri, L. Berthier, and S. Sastry, Phys. Rev. Lett. 104, 165701 (2010). 10.1103/PhysRevLett.104.165701
62. A. Ikeda and K. Miyazaki, Phys. Rev. Lett. 104, 255704 (2010). 10.1103/PhysRevLett.104.255704
63. B. Schmid and R. Schilling, Phys. Rev. E 81, 041502 (2010). 10.1103/PhysRevE.81.041502
64. A. Scardicchio, F. H. Stillinger, and S. Torquato, J. Math. Phys. 49, 043301 (2008). 10.1063/1.2897027
65. N. J. A. Sloane, http://www.research.att.com/njas/