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… 

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References

SHOWING 1-10 OF 32 REFERENCES
Interacting topological defects on frozen topographies
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
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
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.
  • Carraro, Nelson
  • Materials Science
    Physical 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
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
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
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
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
TLDR
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
TLDR
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.
...
1
2
3
4
...