Spherical design and cubature formula

introduction

The Thomson Problem, arrangement of identical charges on the surface of a sphere, has found many applications in physics, chemistry and biology.

Dhagash Mehta, Jianxu Chen, Danny Z. Chen, Halim Kusumaatmaja, David J. Wales, Kinetic Transition Networks for the Thomson Problem and Smale's 7th Problem, arXiv:1605.08459 [cond-mat.soft], May 26 2016, http://arxiv.org/abs/1605.08459
Birtea, Petre, and Dan Comănescu. “Newton Algorithm on Constraint Manifolds and the 5-Electron Thomson Problem.” arXiv:1601.04828 [math-Ph], January 19, 2016. http://arxiv.org/abs/1601.04828.
Kounchev, O., and H. Render. “Discrete Hybrid Polyharmonic Cubature Formulas with Weight on the Disc. with Error Bounds.” arXiv:1509.00060 [math], August 31, 2015. http://arxiv.org/abs/1509.00060.
http://theo.inrne.bas.bg/~dobrev/LT-11-presentations/17-June/14-Motlochova.pdf
http://www.sciencedirect.com/science/article/pii/037704279090190B
De La Harpe, Pierre, Claude Pache, and Boris B. Venkov. “Construction of Spherical Cubature Formulas Using Lattices.” arXiv:math/0505510, May 24, 2005. http://arxiv.org/abs/math/0505510.