Why charges go to the surface: A generalized Thomson problem

@article{Levin2003WhyCG,
  title={Why charges go to the surface: A generalized Thomson problem},
  author={Yan Levin and Jeferson J. Arenzon},
  journal={EPL},
  year={2003},
  volume={63},
  pages={415-418}
}
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 expels all the charges to the surface of the sphere. However, for γ > 1 and n > nc(γ) occupation of the bulk becomes energetically favorable. It is curious to note that the Coulomb law lies exactly on the interface between these two regimes. 
View PDF on arXiv
27 Citations
Highly Influential Citations
1
Background Citations
6
Methods Citations
1

Figures from this paper

27 Citations

Citation Type

Citation Type

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…
Electromagnetic instability of the Thomson problem
The classical Thomson problem of n charged particles confined to the surface of a sphere of radius a is analyzed within the Darwin approximation of electrodynamics. For n nc(a) the Wigner lattice is…
Generalized Thomson problem in arbitrary dimensions and non-euclidean geometries
On the connected-charges Thomson problem
We investigate the modifications brought about by the linear connectivity among charges in the classical Thomson problem. Instead of packing with local hexagonal order interspersed with topological…
Probing infinity in bounded two-dimensional electrostatic systems.
TLDR
This work considers fractals to be physical entities, with charges located in their vertices or nodes, and describes how energy diverges at charge accumulation points in the fractal, that is, almost everywhere by definition.
Charge reversal at 0 K
In this contribution we shall explore the conditions under which a charged sphere in contact with a charge reservoir undergoes a charge reversal. The calculations are confined to zero temperature,…
Numerical Study of the Structure of Metastable Configurations for the Thomson Problem
A numerical method is proposed for solving the Thomson problem – finding stable positions for a system of N point charges distributed on a sphere that minimize the potential energy of the system. The…
Discrete transformations in the Thomson Problem
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…
Electrostatics in soft matter.
  • R. Messina
  • Physics, Chemistry
    Journal of physics. Condensed matter : an Institute of Physics journal
  • 2009
TLDR
Recent progress in understanding the effect of electrostatics in soft matter is presented, and theoretical and simulational aspects, including the experimental motivations, will be discussed.
...
1
2
3
...

References

SHOWING 1-10 OF 19 REFERENCES
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.
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.
I
AIV Assembly, Integration, Verification AOA Angle of Attack CAD Computer Aided Design CFD Computational Fluid Dynamics GLOW Gross Lift-Off Mass GNC Guidance Navigation and Control IR Infra-Red LEO…
Phys
  • Rev. Lett. 89, 185502
  • 2002
Phys. Rev. Lett
  • Phys. Rev. Lett
  • 2002
Rep
  • Prog. Phys. 65, 1577
  • 2002
Rep. Prog. Phys
  • Rep. Prog. Phys
  • 2002
Phys
  • Rev. E 64, 021405
  • 2001
Phys. Rev. E
  • Phys. Rev. E
  • 2001
Phys
  • Rev. E 60, 5802
  • 1999
...
1
2
...