Battye, Richard A. and Gibbons, Gary W. and Sutcliffe, Paul M.
(2002)
*
Central configurations in three dimensions.
*
Proceedings of the Royal Society A- Mathematical Physical and Engineering Sciences,
459
(2032).
pp. 911-943.
ISSN 1364-5021 .
(doi:10.1098/rspa.2002.1061)
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Official URL http://rspa.royalsocietypublishing.org/content/459... |

## Abstract

We consider the equilibria of point particles under the action of two-body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in particular, as homothetic time-dependent solutions to Newton's equations of motion and as stationary states in the one-component-plasma model. Concentrating mainly on the case of an inverse square law balanced by a linear force, we compute numerically equilibria and their statistical properties. When all the masses (or charges) of the particles are equal, for small numbers of points, they are regular convex deltahedra, which, on increasing the number of points, give way to a multi-shell structure. In the limit of a large number of points, we argue, using an analytic model, that they form a homogeneous spherical distribution of points, whose spatial distribution appears, from our preliminary investigation, to be similar to that of a Bernal hard-sphere liquid.

Item Type: | Article |
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Additional information: | Full-text freely available via Official Url Link |

Uncontrolled keywords: | central configurations; point particles; sphere packing |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics |

Depositing User: | Judith Broom |

Date Deposited: | 14 Sep 2008 14:21 |

Last Modified: | 17 Jun 2014 10:34 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/7972 (The current URI for this page, for reference purposes) |

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