Defect free global minima in Thomson’s problem of charges on a sphere
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URI: http://arxiv.org/abs/cond-mat/0509501URI: http://hdl.handle.net/10317/584
ISSN: 1550-2376
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Física AplicadaFecha de publicación
2006Editorial
American Physical SocietyCita bibliográfica
ATSCHULER, ERIC LEWIN, PÉREZ GARRIDO, ANTONIO. Defect free global minima in Thomson’s problem of charges on a sphere. Phisical Review E, 73 (3): 036108-1 - 036108-6, 2006. ISSN 2006Palabras clave
Problema de ThomsonEsferas
Teoría de la elasticidad
Teoría de Dodgson y Moore
Resumen
Given N unit points charges on the surface of a unit conducting sphere, what configuration of charges minimizes the Coulombic energy PN
i>j=1 1/rij? Due to an exponential rise in good local minima, finding global minima for this problem, or even approaches to do so has proven extremely difficult. For N = 10(h2 + hk + k2) + 2 recent theoretical work based on elasticity theory, and subsequent numerical work has shown, that for N > 500–1000 adding dislocation defects to a symmetric icosadeltahedral lattice lowers the energy. Here we show that in fact this approach holds
for all N, and we give a complete or near complete catalogue of defect free global minima.
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