Packing of Softly Repulsive Particles in a Spherical Box —A Generalised Thomson Problem

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Packing of Softly Repulsive Particles in a Spherical Box —A Generalised Thomson Problem. / Mughal, Adil.

In: Forma, Vol. 29, 2014, p. 13-19.

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@article{120686864bca4f3dbc7a385835c66f7e,
title = "Packing of Softly Repulsive Particles in a Spherical Box —A Generalised Thomson Problem",
abstract = "We study the (near or close to) ground state distribution of N softly repelling particles trapped in the interior of a spherical box. The charges mutually interact via an inverse power law potential of the form 1/r γ. We study three regimes in which the charges form an single spherical shell at the edge of the box (γ = 1), a series of concentric shells of increasing density (γ = 2) and γ = 12 for which the charges form shells with a more uniform charge distribution. We conduct numerical simulations for clusters containing up to 5000 charges and compare charge density across the system with continuum limit results. The agreement between numerical (discrete) results and the continuum limit is found to improve with increasing N. These findings are accompanied by a visual gallery of some of the low energy ground states found by simulated annealing.",
keywords = "Thomson problem, low temperature plasma, packing in a spherical box",
author = "Adil Mughal",
year = "2014",
language = "English",
volume = "29",
pages = "13--19",
journal = "Forma",
issn = "2013-7761",
publisher = "Society for Science on Form, Japan",

}

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TY - JOUR

T1 - Packing of Softly Repulsive Particles in a Spherical Box —A Generalised Thomson Problem

AU - Mughal, Adil

PY - 2014

Y1 - 2014

N2 - We study the (near or close to) ground state distribution of N softly repelling particles trapped in the interior of a spherical box. The charges mutually interact via an inverse power law potential of the form 1/r γ. We study three regimes in which the charges form an single spherical shell at the edge of the box (γ = 1), a series of concentric shells of increasing density (γ = 2) and γ = 12 for which the charges form shells with a more uniform charge distribution. We conduct numerical simulations for clusters containing up to 5000 charges and compare charge density across the system with continuum limit results. The agreement between numerical (discrete) results and the continuum limit is found to improve with increasing N. These findings are accompanied by a visual gallery of some of the low energy ground states found by simulated annealing.

AB - We study the (near or close to) ground state distribution of N softly repelling particles trapped in the interior of a spherical box. The charges mutually interact via an inverse power law potential of the form 1/r γ. We study three regimes in which the charges form an single spherical shell at the edge of the box (γ = 1), a series of concentric shells of increasing density (γ = 2) and γ = 12 for which the charges form shells with a more uniform charge distribution. We conduct numerical simulations for clusters containing up to 5000 charges and compare charge density across the system with continuum limit results. The agreement between numerical (discrete) results and the continuum limit is found to improve with increasing N. These findings are accompanied by a visual gallery of some of the low energy ground states found by simulated annealing.

KW - Thomson problem

KW - low temperature plasma

KW - packing in a spherical box

UR - http://hdl.handle.net/2160/44962

M3 - Article

VL - 29

SP - 13

EP - 19

JO - Forma

JF - Forma

SN - 2013-7761

ER -

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