Spherical codes, maximal local packing density, and the golden ratio

Journal of Mathematical Physics

Volumn 51, Issue 4, 2010, Pages

  Hopkins, Adam B ^a   Stillinger, Frank H ^a   Torquato, Salvatore ^a,b  

^a PRINCETON UNIVERSITY   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953274752     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3372627     Document Type: Article

References (23)

1. Conway J.H. Sloane N.J. A. Sphere Packings, Lattices and Groups 1998, (Springer, New York).
2. Ericson T. Zinoviev V. Codes on Euclidean Spheres 2001, and, (North-Holland, Amsterdam, ).
3. Cohn H. Kumar A. N.Y. J. Math. 2007, 13:147., 1076-9803.
4. Lenard A. Arch. Ration. Mech. Anal. 1975, 59:219. AVRMAW, 0003-9527.
5. Torquato S. Stillinger F. J. Phys. Chem. B 2002, 106:8354. JPCBFK, 1089-5647, 10.1021/jp0208687.
6. Kuna T. Lebowitz J.L. Speer E.R. J. Stat. Phys. 2007, 129:417. JSTPBS, 0022-4715, 10.1007/s10955-007-9393-y.
7. Torquato S. Stillinger F.H. Exp. Math. 2006, 15:307. 1058-6458.
8. Hopkins A.B. Stillinger F.H. Torquato S. Phys. Rev. E 2009, 79:031123. PLEEE8, 1063-651X, 10.1103/PhysRevE.79.031123.
9. Cohn H. Elkies N. Ann. Math. 2003, 157:689. ANMAAH, 0003-486X, 10.4007/annals.2003.157.689.
10. Cohn H. Kumar A. and (unpublished).
11. Cohn H. Kumar A. Torquato S. and (unpublished).
12. 3.
13. max(R) is defined locally in terms of one central sphere, whereas Z(R) in Eq. is defined globally in terms of a probability density, or in the case of a finite packing, in terms of an average over all spheres.
14. Melissen H. Geom. Dedic. 1994, 50:15. GEMDAT, 0046-5755, 10.1007/BF01263647.
15. Cohn H. Kumar A. Ann. Math. 2009, 170:1003. ANMAAH, 0003-486X.
16. Musin O.R. Ann. Math. 2008, 168:1. ANMAAH, 0003-486X, 10.4007/annals.2008.168.1.
17. Sloane N.J. A. Hardin R.H. Smith W.D. and.
18. S(120)=τ.
19. Wyner A.D. Bell Syst. Tech. J. 1965, 44:1061. BSTJAN, 0005-8580.
20. Rankin R.A. Proc. Glasgow Math. Assoc. 1955, 2:139. 10.1017/S2040618500033219.
21. Kabatiansky G.A. Levenshtein V.I. Probs. of Info. Trans. 1978, 14:1. 0032-9460.
22. Böröczky K. Acta Math. Acad. Sci. Hung. 1978, 32:243. ACMTAV, 0001-5954, 10.1007/BF01902361.
23. Boyvalenkov P. Danev D. Arch. Math. 2001, 77:360. ACVMAL, 0003-889X, 10.1007/PL00000504.