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Thomson problem in one dimension: Minimal energy configurations of N charges on a curve

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  • Amore, Paolo
  • Jacobo, Martin

Abstract

We have studied the configurations of minimal energy of N charges on a curve on the plane, interacting with a repulsive potential Vij=1∕rijs, with s≥1 and i,j=1,…,N. Among the examples considered are ellipses of different eccentricity, a straight wire and a cardioid. We have found that, for some geometries, multiple minima are present, as well as points of unstable equilibrium. For the case of the cardioid, we observe that the presence of the cusp has a dramatic effect on the distribution of the charges, in the limit N≫1.

Suggested Citation

  • Amore, Paolo & Jacobo, Martin, 2019. "Thomson problem in one dimension: Minimal energy configurations of N charges on a curve," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 256-266.
    • Handle: RePEc:eee:phsmap:v:519:y:2019:i:c:p:256-266
    DOI: 10.1016/j.physa.2018.12.040
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    References listed on IDEAS

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    1. William T. M. Irvine & Vincenzo Vitelli & Paul M. Chaikin, 2010. "Pleats in crystals on curved surfaces," Nature, Nature, vol. 468(7326), pages 947-951, December.
    2. Batle, J. & Bagdasaryan, Armen & Abdel-Aty, M. & Abdalla, S., 2016. "Generalized Thomson problem in arbitrary dimensions and non-euclidean geometries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 237-250.
    3. Petre Birtea & Dan Comănescu, 2017. "Newton Algorithm on Constraint Manifolds and the 5-Electron Thomson Problem," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 563-583, May.
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