Thomson Problem
Determine the stable equilibrium positions of 
classical electrons 
constrained to move on thesurface of a Sphere and repelling each other by an inverse square law. Exact solutions for 
to 8 are known,but 
and 11 are still unknown.
In reality, Earnshaw's theorem guarantees that no system of discrete electric charges canbe held in stable equilibrium under the influence of their electrical interaction alone (Aspden 1987).
References
Altschuler, E. L.; Williams, T. J.; Ratner, E. R.; Dowla, F.; and Wooten, F. ``Method of Constrained Global Optimization.'' Phys. Rev. Let. 72, 2671-2674, 1994. Altschuler, E. L.; Williams, T. J.; Ratner, E. R.; Dowla, F.; and Wooten, F. ``Method of Constrained Global Optimization--Reply.'' Phys. Rev. Let. 74, 1483, 1995. Ashby, N. and Brittin, W. E. ``Thomson's Problem.'' Amer. J. Phys. 54, 776-777, 1986. Aspden, H. ``Earnshaw's Theorem.'' Amer. J. Phys. 55, 199-200, 1987. Berezin, A. A. ``Spontaneous Symmetry Breaking in Classical Systems.'' Amer. J. Phys. 53, 1037, 1985. Calkin, M. G.; Kiang, D.; and Tindall, D. A. ``Minimum Energy Configurations.'' Nature 319, 454, 1986. Erber, T. and Hockney, G. M. ``Comment on `Method of Constrained Global Optimization.''' Phys. Rev. Let. 74, 1482-1483, 1995. Marx, E. ``Five Charges on a Sphere.'' J. Franklin Inst. 290, 71-74, Jul. 1970. Melnyk, T. W.; Knop, O.; and Smith, W. R. ``Extremal Arrangements of Points and Unit Charges on a Sphere: Equilibrium Configurations Revisited.'' Canad. J. Chem. 55, 1745-1761, 1977. Whyte, L. L. ``Unique Arrangement of Points on a Sphere.'' Amer. Math. Monthly 59, 606-611, 1952.
- Contour Integration
- Contracted Cycloid
- Contraction
- Contraction (Graph)
- Contraction (Tensor)
- Contradiction Law
- Contravariant Tensor
- Contravariant Vector
- Control Theory
- Convective Acceleration
- Convective Derivative
- Convective Operator
- Convergence Acceleration
- Convergence Improvement
- Convergence Tests
- Convergent
- Thomsen Graph
- Thomsen's Figure
- Thomson Lamp Paradox
- Thomson Problem
- Thomson's Principle
- Thousand
- Three
- Three-Colorable
- Threefoil Knot