Distributing many points on a sphere

E. B. Saff; A. B. J. Kuijlaars

doi:10.1007/BF03024331

The Mathematical Intelligencer

December 1997, Volume 19, Issue 1, pp 5–11

Distributing many points on a sphere

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E. B. SaffEmail author
A. B. J. Kuijlaars

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References

1.
R. Alexander, On the sum of distances betweenN points on a sphere,Ada Math. Acad, Sci. Hungar. 23 (1972), 443–448.MATHCrossRefGoogle Scholar
2.
E. L. Altschuler, T. J. Williams, E. R. Ratner, F. Dowla, and F. Wooten, Method of constrained global optimization,Phys. Rev. Lett. 72 (1994), 2671–2674.CrossRefGoogle Scholar
3.
J. Beck, Sums of distances between points on a sphere—an application of the theory of irregularities of distribution to discrete geometry,Mathematika 31 (1984), 33–41.MATHMathSciNetCrossRefGoogle Scholar
4.
B. Bergersen, D. Boal, and P. Palffy-Muhoray, Equilibrium configurations of particles on a sphere: the case of logarithmic interactions,J. Phys. A: Math. Gen. 27 (1994), 2579–2586.MATHCrossRefGoogle Scholar
5.
F. R. K. Chung, B. Kostant, and S. Sternberg, Groups and the buckyball, inLie Theory and Geometry (J.-L. Brylinski, R. Brylinski, V. Guillemin and V. Kac, eds.),Progress in Mathematics No. 123, Boston: Birkhäuser (1994), pp. 97–126.Google Scholar
6.
J. H. Conway and N. J. A. Sloane,Sphere Packings, Lattices and Groups, 2nd ed., New York: Springer-Verlag (1993).MATHGoogle Scholar
7.
J. Cui and W. Freeden, Equidistribution on the sphere,SIAM J. Sci. Comp. (to appear).Google Scholar
8.
B. E. J. Dahlberg, On the distribution of Fekete points,Duke Math. J. 45 (1978), 537–542.MATHCrossRefMathSciNetGoogle Scholar
9.
P. Delsarte, J. M. Goethals, and J.J. Seidel, Spherical codes and designs,Geom. Dedicata 6 (1977), 363–388.MATHMathSciNetCrossRefGoogle Scholar
10.
T. Erber and G. M. Hockney, Equilibrium configurations ofN equal charges on a sphere,J. Phys. A: Math. Gen. 24 (1991), L1369-L1377.CrossRefGoogle Scholar
11.
T. Erber and G. M. Hockney, Comment on “Method of constrained global optimization,”Phys. Rev. Lett. 74 (1995), 1482.CrossRefGoogle Scholar
12.
L. Glasser and A. G. Every, Energies and spacings of point charges on a sphere,J. Phys. A: Math. Gen. 25 (1992), 2473–2482.CrossRefGoogle Scholar
13.
W. Habicht and B. L. van der Waerden, Lagerung von Punkten auf der Kugel,Math. Ann. 123 (1951), 223–234.MATHCrossRefMathSciNetGoogle Scholar
14.
R. H. Hardin and N. J. A. Sloane, McLaren’s improved snub cube and other new spherical designs in three dimensions,Discr. Comp. Geom. 15 (1996), 429–442.MATHCrossRefMathSciNetGoogle Scholar
15.
J. Korevaar, Chebyshev-type quadratures: use of complex analysis and potential theory, in:Complex Potential Theory (P. M. Gauthier and G. Sabidussi, eds.), Dordrecht: Kluwer (1994), 325–364.Google Scholar
16.
J. Korevaar and J. L. H. Meyers, Spherical Faraday cage for the case of equal point charges and Chebyshev-type quadrature on the sphere,Integral Transforms and Special Functions 1 (1993), 105–117.MATHCrossRefMathSciNetGoogle Scholar
17.
A. B. J. Kuijlaars, and E. B. Saff, Asymptotics for minimal discrete energy on the sphere,Trans. Am. Math. Soc. (to appear).Google Scholar
18.
A. Lubotzky, R. Phillips, and P. Sarnak, Hecke operators and distributing points on the sphere I,Comm. Pure Appl. Math. 39 (1986), 149–186.CrossRefMathSciNetGoogle Scholar
19.
T. W. Melnyk, O. Knop, and W. R. Smith, Extremal arrangements of points and unit charges on a sphere: equilibrium configurations revisited.Can. J. Chem. 55 (1977), 1745–1761.CrossRefMathSciNetGoogle Scholar
20.
E. A. Rakhmanov, E. B. Saff, and Y. M. Zhou, Minimal discrete energy on the sphere,Math. Res. Lett. 1 (1994), 647–662.MATHMathSciNetGoogle Scholar
21.
E. A. Rakhmanov, E. B. Saff, and Y. M. Zhou, Electrons on the sphere, inComputational Methods and Function Theory (R. M. Ali, St. Ruscheweyh, and E. B. Saff, eds.), Singapore: World Scientific (1995), pp. 111–127.Google Scholar
22.
M. Shub and S. Smale, Complexity of Bezout’s theorem III: condition number and packing,J. Complexity 9 (1993), 4–14.MATHCrossRefMathSciNetGoogle Scholar
23.
K. B. Stolarsky, Sums of distances between points on a sphere. II.Proc. Am. Math. Soc. 41 (1973), 575–582.MATHCrossRefMathSciNetGoogle Scholar
24.
G. Wagner, On the means of distances on the surface of a sphere (lower bounds),Pacific J. Math. 144 (1990), 389–398.MATHMathSciNetGoogle Scholar
25.
G. Wagner, On the means of distances on the surface of a sphere II (upper bounds),Pacific J. Math. 153 (1992), 381–396.Google Scholar
26.
Y. M. Zhou, Arrangements of points on the sphere, Thesis, University of South Florida, 1995.Google Scholar

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E. B. Saff
- 1
Email author
A. B. J. Kuijlaars
- 2

1.Institute for Constructive Mathematics Department of MathematicsUniversity of South FloridaTampaUSA
2.Departement WiskundeKatholieke UniverS’teit LeuvenLeuvenBelgium

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