Symmetric patterns of dislocations in Thomson's problem

Abstract

Determination of the classical ground state arrangement of $N$ charges on the surface of a sphere (Thomson's problem) is a challenging numerical task. For special values of $N$ we have obtained using the ring removal method of Toomre, low energy states in Thomson's problem which have icosahedral symmetry where lines of dislocations run between the 12 disclinations which are induced by the spherical geometry into the near triangular lattice which forms on a local scale.

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References in corpus (1)

• Influence of Dislocations in Thomson's Problem

Cited by in corpus (17)

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• Experimental study of energy-minimizing point configurations on spheres
• Energetically favoured defects in dense packings of particles on spherical surfaces
• Ground state of a large number of particles on a frozen topography
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• Defect free global minima in Thomson's problem of charges on a sphere
• Interstitial Fractionalization and Spherical Crystallography
• Universality in the Screening Cloud of Dislocations Surrounding a Disclination
• Correspondences between the Classical Electrostatic Thomson Problem and Atomic Electronic Structure
• Extended topological defects as sources and outlets of dislocations in spherical hexagonal crystals
• The most uniform distribution of points on the sphere
• Discrete Transformations in the Thomson Problem
• Electromagnetic instability of the Thomson Problem
• Exotic Bilayer Crystals in a Strong Magnetic Field