# Crystalline order on a sphere and the generalized Thomson problem.

@article{Bowick2002CrystallineOO, title={Crystalline order on a sphere and the generalized Thomson problem.}, author={Mark J Bowick and Angelo Cacciuto and David R. Nelson and Alex Travesset}, journal={Physical review letters}, year={2002}, volume={89 18}, pages={ 185502 } }

We attack the generalized Thomson problem, i.e., determining the ground state energy and configuration of many particles interacting via an arbitrary repulsive pairwise potential on a sphere via a continuum mapping onto a universal long range interaction between angular disclination defects parametrized by the elastic (Young) modulus Y of the underlying lattice and the core energy E(core) of an isolated disclination. Predictions from the continuum theory for the ground state energy agree with…

## 141 Citations

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…

Two-dimensional packing of soft particles and the soft generalized Thomson problem

- Materials Science
- 2011

We perform numerical simulations of a model of purely repulsive soft colloidal particles interacting via a generalized elastic potential and constrained to a two-dimensional plane and to the surface…

Two and three electrons on a sphere: A generalized Thomson problem

- PhysicsPhysical Review B
- 2018

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…

Monte Carlo study of crystalline order and defects on weakly curved surfaces.

- Materials SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

It is shown that the character and spatial distribution of defects observed in the ground state reflect the symmetries and periodicity of the two model surfaces investigated in this study.

Why charges go to the surface: A generalized Thomson problem

- Physics
- 2003

We study a variant of the generalized Thomson problem in which n particles are confined to a neutral sphere and interacting by a 1/rγ potential. It is found that for γ ≤ 1 the electrostatic repulsion…

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

- MathematicsPhysical 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.

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…

Particles on curved surfaces: a dynamic approach by a phase-field-crystal model.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

A dynamic model to study ordering of particles on arbitrary curved surfaces and annihilation of dislocations within the ordered system and premelting along grain-boundary scars is presented.

Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

It is found that the atomic configurations consist of isolated defect structures, dubbed "grain boundary scars," that form around an irreducible density of curvature-induced disclinations in an otherwise hexagonal background.

Interstitial fractionalization and spherical crystallography.

- Materials SciencePhysical 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.

## References

SHOWING 1-10 OF 32 REFERENCES

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…

Symmetric patterns of dislocations in Thomson’s problem

- Mathematics
- 1999

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…

Vortices in a thin-film superconductor with a spherical geometry

- Physics
- 1997

We report results from Monte Carlo simulations of a thin-film superconductor in a spherical geometry within the lowest-Landau-level approximation. We observe the absence of a phase transition to a…

Grain-boundary buckling and spin-glass models of disorder in membranes.

- Materials SciencePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1993

A systematic investigation is presented of grain boundaries and grain boundary networks in two dimensional flexible membranes with crystalline order. An isolated grain boundary undergoes a buckling…

Some static and dynamical properties of a two-dimensional Wigner crystal

- Physics, Materials Science
- 1977

The static ground-state energy of a two-dimensional Wigner crystal has been obtained for each of the five two-dimensional Bravais lattices. At constant electron number density the hexagonal lattice…

C60: Buckminsterfullerene

- PhysicsNature
- 1985

During experiments aimed at understanding the mechanisms by which long-chain carbon molecules are formed in interstellar space and circumstellar shells1, graphite has been vaporized by laser…

Ions at helium interfaces

- Physics
- 1995

The boundaries between different phases of condensed helium provide an interesting testing ground for studying ions in a quantum matter matrix. Here we consider the simplest positive and negative…

The interactions of π - -mesons with complex nuclei in the energy range (100–800) MeV. III. The interaction lengths and elastic scattering of 300 MeV π - -mesons in G5 emulsion

- Physics
- 1959

Abstract A stack of pellicles has been exposed to the 300 MeV πminus;-meson beam of the 660 MeV proton synchrotron at C.E.R.N., Geneva. The interaction lengths for the production of inelastic…

MATH

- Biology
- 1992

It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.

Colloidosomes: Selectively Permeable Capsules Composed of Colloidal Particles

- Materials ScienceScience
- 2002

An approach to fabricate solid capsules with precise control of size, permeability, mechanical strength, and compatibility is presented, which are hollow, elastic shells whose permeability and elasticity can be precisely controlled.