 |
Center for Nonlinear Studies |
In 1904 J.J. Thomson asked how one may arrange a fixed number of electrons on a sphere so as to minimize the electrostatic energy. It is easily shown that this problem has a solution for broad class of energies and any compact subset of Euclidian space. The energies we shall consider are the Riesz energies, which have as their kernel the Coulomb kernel raised to a positive power. While solutions for a fixed number of electrons are computationally and theoretically difficult, an analysis of the asymptotic behavior of the solutions yields information about the global or local structure of the sets and in certain cases establishes connections to physics. In addition we shall examine numerical techniques and results related to minimal energy problems on the sphere.
Host: Razvan Teodorescu, T-CNLS