# Symmetric patterns of dislocations in Thomson’s problem

@article{PrezGarrido1999SymmetricPO, title={Symmetric patterns of dislocations in Thomson’s problem}, author={A. P{\'e}rez-Garrido and M. .. Moore}, journal={Physical Review B}, year={1999}, volume={60}, pages={15628-15631} }

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.

#### 27 Citations

Defect-free global minima in Thomson's problem of charges on a sphere.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2006

This work shows that for N approximately same or greater than 500-1000, adding dislocation defects to a symmetric icosadeltahedral lattice lowers the energy, and gives a complete or near complete catalogue of defect free global minima. Expand

Structure and dynamics of spherical crystals characterized for the Thomson problem

- Physics
- 2006

Candidates for global minima of the Thomson problem for N charges on a sphere are located for N 400 and selected sizes up to N=972. These results supersede many of the lowest minima located in… Expand

Crystalline order on a sphere and the generalized Thomson problem.

- Physics, Medicine
- Physical review letters
- 2002

Predictions from the continuum theory for the ground state energy agree with numerical simulations of long range power law interactions of the form 1/r(gamma) (0<gamma<2) to four significant figures. Expand

Universality in the screening cloud of dislocations surrounding a disclination

- Physics
- 2003

A detailed analytical and numerical analysis for the dislocation cloud surrounding a disclination is presented. The analytical results show that the combined system behaves as a single disclination… Expand

Extended topological defects as sources and outlets of dislocations in spherical hexagonal crystals

- Physics
- 2014

Abstract Extended topological defects (ETDs) arising in spherical hexagonal crystals due to their curvature are considered. These prevalent defects carry a unit total topological charge and are… Expand

Crystalline Particle Packings on a Sphere with Long Range Power Law Potentials

- Physics
- 2006

The original Thomson problem of “spherical crystallography” seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of… Expand

Grain Boundary Scars and Spherical Crystallography

- Materials Science, Physics
- Science
- 2003

Experimental investigations of the structure of two-dimensional spherical crystals find that crystals develop distinctive high-angle grain boundaries, or scars, not found in planar crystals above a critical system size. Expand

Interstitial fractionalization and spherical crystallography.

- Physics, Medicine
- Physical chemistry chemical physics : PCCP
- 2007

A powerful, freely-available computer program is used to explore interstitial fractionalization in some detail, for a variety of power-law pair potentials, and investigates the dependence on initial conditions and the final state energies, and compares the position dependence of interstitial energies with the predictions of continuum elastic theory on the sphere. Expand

Correspondences between the Classical Electrostatic Thomson Problem and Atomic Electronic Structure

- Physics
- 2013

Abstract Correspondences between the Thomson problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change… Expand

Interacting topological defects on frozen topographies

- Physics
- 2000

We propose and analyze an effective free energy describing the physics of disclination defects in particle arrays constrained to move on an arbitrary two-dimensional surface. At finite temperature… Expand