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.

memo

• https://en.wikipedia.org/wiki/Thomson_problem
• http://demonstrations.wolfram.com/ThomsonProblemSolutions/

articles

• 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.