Structure and dynamics of spherical crystals characterized for the Thomson problem

@article{Wales2006StructureAD,
  title={Structure and dynamics of spherical crystals characterized for the Thomson problem},
  author={David J. Wales and Sidika Ulker},
  journal={Physical Review B},
  year={2006},
  volume={74},
  pages={212101}
}
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 previous work, with particularly large improvements for N 400. Our analysis reveals interesting topological defects, which are likely to play an important role in determining the mechanical and electrical properties of systems confined to a spherical geometry. We also find low-energy rearrangements for… 

Figures and Tables from this paper

Parameter-free shell model of spherical Coulomb crystals.
An accurate shell model of spherical Coulomb crystals is presented. Employing intrashell angular particle positions that correspond to the global energy minima of the pertinent Thomson problems, it
Properties of Coulomb crystals: rigorous results.
TLDR
The leading term in the asymptotic expression for the shell capacity that appears in the recently introduced approximate model of Coulomb crystals is obtained, providing in turn explicit large-N asymPTotics for e(N) and the mean crystal radius.
Modified Thomson problem.
  • J. Cioslowski
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
TLDR
The modified Thomson problem, which concerns an assembly of N particles mutually interacting through a Coulombic potential and subject to a Coul Lombic-harmonic confinement, is introduced and the perturbed spherical Coulomb crystal regime emerges.
Two and three electrons on a sphere: A generalized Thomson problem
Generalizing the classical Thomson problem to the quantum regime provides an ideal model to explore the underlying physics regarding electron correlations. In this work, we systematically investigate
The Structure of Metastable States in The Thomson Problem
A practical numerical method for the effective solution of the Thomson Problem is proposed. The developed iterative algorithm allows to conduct theoretical researches such as study of the number of
Topological defect motifs in two-dimensional Coulomb clusters.
TLDR
The minima hopping algorithm based on molecular dynamics is used to efficiently locate the ground- and low-energy metastable states, and their structure is analysed by means of the Delaunay triangulation.
Magic numbers for vibrational frequency of charged particles on a sphere
  • S. Ono
  • Physics
    Physical Review B
  • 2021
Finding minimum energy distribution of N charges on a sphere is known as the Thomson problem. Here, we study the vibrational properties of the N charges in the lowest energy state within the harmonic
...
...

References

SHOWING 1-10 OF 40 REFERENCES
Global minimum for Thomson's problem of charges on a sphere.
TLDR
This work explicitly finds that analogues of the tetrahedral and dihedral configurations for N larger than 306 and 542, respectively, are not global minima, thus helping to confirm the theory of Dodgson and Moore that as N grows, dislocation defects can lower the lattice strain of symmetric configurations and concomitantly the energy.
Symmetric patterns of dislocations in Thomson’s problem
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
Crystalline order on a sphere and the generalized Thomson problem.
TLDR
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.
Defect-free global minima in Thomson's problem of charges on a sphere.
TLDR
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.
Possible Global Minimum Lattice Configurations for Thomson`s Problem of Charges on a Sphere
What configuration of N point charges on a conducting sphere minimizes the Coulombic energy? J.J. Thomson posed this question in 1904. For N{le}112, numerical methods have found apparent global
Grain Boundary Scars and Spherical Crystallography
TLDR
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.
Crystalline Particle Packings on a Sphere with Long Range Power Law Potentials
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
Investigation on the ground states of a model thin-film superconductor on a sphere
We consider the problem of finding the ground state of a model type-II superconductor on the two-dimensional surface of a sphere, penetrated by N vortices. Numerical work shows the ground states to
Grain boundary scars on spherical crystals.
TLDR
The introduction of fluorescently labeled particles enables us to determine the location and orientation of grain boundary scars and it is found that the total number of scars and the number of excess dislocations per scar agree with theoretical predictions.
...
...