The Structure of Metastable States in The Thomson Problem

@inproceedings{Bondarenko2015TheSO,
  title={The Structure of Metastable States in The Thomson Problem},
  author={Anatoly N. Bondarenko and Mikhail Karchevskiy and Leonid Kozinkin},
  year={2015}
}
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 asymptotic solutions depending on the particle count. Metastable states of charged point systems on a unit sphere were considered and the probability of falling into the basin of each state was obtained. Founded upon the algorithm and dual lattice representation approach, the framework for rapid… 
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References

SHOWING 1-10 OF 16 REFERENCES
Many-particle jumps algorithm and Thomson's problem
We study Thomson's problem using a new numerical algorithm, valid for any interacting complex system based on the consideration of simultaneous many-particle transitions to reduce the characteristic
Structure and dynamics of spherical crystals characterized for the Thomson problem
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
Why charges go to the surface: A generalized Thomson problem
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
Ground State Energy of Unitary Fermion Gas with the Thomson Problem Approach
The dimensionless universal coefficient ξ defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T = 0. The classical
Equilibrium configurations of N equal charges on a sphere
The emergence of new levels of complexity that often accompanies the transition from few- to many-body systems is clearly illustrated by the progression of equilibrium states of N charges on the
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.
Genetic-algorithm energy minimization for point charges on a sphere.
We demonstrate that a recently developed approach for optimizing atomic structures is very effective for attacking the Thomson problem of finding the lowest-energy configuration of $N$ point charges
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.
Method of constrained global optimization.
TLDR
This work illustrates CGO with two problems---Thomson's problem of finding the minimum-energy configuration of unit charges on a spherical surface, and a problem of assigning offices---for which CGO finds better minima than other methods.
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