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arXiv · 1601.04828

Newton Algorithm on Constraint Manifolds and the 5-electron Thomson problem

Petre Birtea·Dan Comănescu
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Abstract

We give a description of numerical Newton algorithm on a constraint manifold using only the ambient coordinates (usually Euclidean coordinates) and the geometry of the constraint manifold. We apply the numerical Newton algorithm on a sphere in order to find the critical configurations of the 5-electron Thomson problem. As a result, we find a new critical configuration of a regular pentagonal type. We also make an analytical study of the critical configurations found previously and determine their nature using Morse-Bott theory. Last section contains an analytical study of critical configurations for Riesz s-energy of 5-electron on a sphere and their bifurcation behavior is pointed out.

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Petre Birtea, Dan Comănescu. 2016-01-19. Newton Algorithm on Constraint Manifolds and the 5-electron Thomson problem. https://doi.org/10.1007/s10957-016-1049-0

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