Mystery of point charges
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
We discuss the problem of finding an upper bound for the number of equilibrium points of a potential of several fixed point charges in R^n. This question goes back to J.C.Maxwell and M.Morse. Using fewnomial theory we show that for a given number of charges there exists an upper bound independent on the dimension, and show it to be 12 for three charges. We conjecture the exact upper bound for a given configuration of nonnegative charges in terms of its Voronoi diagram, and prove it asymptotically.
Cite
@article{arxiv.math-ph/0409009,
title = {Mystery of point charges},
author = {Andrei Gabrielov and Dmitry Novikov and Boris Shapiro},
journal= {arXiv preprint arXiv:math-ph/0409009},
year = {2007}
}
Comments
Latex, 29 pages, 6 figures