Equilibrium configurations of N equal charges on a sphere

Erber, T.; Hockney, G.

doi:10.1088/0305-4470/24/23/008

Cited by 159 publications

(165 citation statements)

References 11 publications

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“…Nevertheless, although in general the exact ground state is not available, its energy is very well approximated by the simple expression given by Eq. (169) with Z = 0 [99,100].…”

Section: Overchargingmentioning

confidence: 99%

Introduction to statistical mechanics of charged systems

Levin¹

2004

Braz. J. Phys.

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The paper is the summary of lectures given in São Carlos, Brazil during the 2004 Summer School on Statistical Mechanics. My objective was to provide the students with some basic tools necessary to study the thermodynamics of Coulomb systems. I have restricted myself to simple models and techniques, which nevertheless, when used correctly can give a clear insight into the fundamental physics behind various complex phenomena that appear when the interactions between the system's constituents are dominated by the long ranged Coulomb force.

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“…Nevertheless, although in general the exact ground state is not available, its energy is very well approximated by the simple expression given by Eq. (169) with Z = 0 [99,100].…”

Section: Overchargingmentioning

confidence: 99%

Introduction to statistical mechanics of charged systems

Levin¹

2004

Braz. J. Phys.

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“…However, no Th configurations are produced. The dodecahedron is produced for N = 20, whilst the arrangements for N = 32, 44 (Edmundson, 1992;Weinrach et al, 1990;Erber &Hockney, 1991) and92 (Edmundson, 1991) are all global minima.…”

Section: "5 Seriesmentioning

confidence: 99%

“…The symmetry adopted by N point charges on the surface of a sphere such that the Coulombic potential is a minimum has been determined by several investigators: Ashby & Brittin (1986); Edmundson (1992); Erber & Hockney (1991) ;Frickel & Bronk (1987); Melnyk, Knop & Smith (1977); Rafac, Schiffer, Hangst, Dubin & Wales (1991) ;Weinrach, Carter, Bennett & McDowell (1990);Wille (1986). Table 1 lists the values of N when the arrangements display tetrahedral or octahedral symmetry.…”

Section: Introductionmentioning

confidence: 99%

The arrangement of point charges with tetrahedral and octahedral symmetry on the surface of a sphere with minimum Coulombic potential energy

Edmundson¹

1993

Acta Cryst Sect A

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“…Extensive computations for optimal configurations and their corresponding extremal energies have been reported in a number of articles. Most deal with the Coulomb case (t = 1) [33,34]. It has been observed that for a large N there are many local minima in the energy minimization problem.…”

Section: Uniform Sampling Based In Fekete Points In 4d (Uf4)mentioning

confidence: 99%

Uniform distribution of projection data for improved reconstruction quality of 4D EPR imaging

Ahmad¹,

Vikram²,

Clymer³

et al. 2007

Journal of Magnetic Resonance

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In continuous wave (CW) electron paramagnetic resonance imaging (EPRI), high quality of reconstruction in a limited acquisition time is a high priority. It has been shown for the case of 3D EPRI, that a uniform distribution of the projection data generally enhances reconstruction quality. In this work, we have suggested two data acquisition techniques for which the gradient orientations are more evenly distributed over the 4D acquisition space as compared to the existing methods. The first sampling technique is based on equal solid angle partitioning of 4D space, while the second technique is based on Fekete points estimation in 4D to generate a more uniform distribution of data. After acquisition, filtered backprojection (FBP) is applied to carryout the reconstruction in a single stage. The single-stage reconstruction improves the spatial resolution by eliminating the necessity of data interpolation in multi-stage reconstructions. For the proposed data distributions, the simulations and experimental results indicate a higher fidelity to the true object configuration. Using the uniform distribution, we expect about 50% reduction in the acquisition time over the traditional method of equal linear angle acquisition.

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Equilibrium configurations of N equal charges on a sphere

Cited by 159 publications

References 11 publications

Introduction to statistical mechanics of charged systems

Introduction to statistical mechanics of charged systems

The arrangement of point charges with tetrahedral and octahedral symmetry on the surface of a sphere with minimum Coulombic potential energy

Uniform distribution of projection data for improved reconstruction quality of 4D EPR imaging

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