Comptes Rendus
Asymptotic modelling of weakly twisted electrostatic problems
Comptes Rendus. Mécanique, Volume 334 (2006) no. 2, pp. 91-97.

We present an analysis of an electrostatic field within a helicoidal structure with a twist, which is small compared to the characteristic size of the cross-section. The asymptotic results are checked against exact computations thanks to helicoidal coordinates, which preserve the intrinsically two-dimensional nature of the problem. The numerical studies are performed using the finite elements.

Nous proposons une analyse du champ électrostatique dans une structure torsadée par une approche de type perturbative, à la limite des faibles torsions. La méthode asymptotique décrite est validée à l'aide d'une modélisation exacte de la torsion qui préserve le caractère essentiellement bi-dimensionnel du problème (coordonnées hélicoïdales). Les études numériques sont menées en utilisant les éléments finis.

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Published online:
DOI: 10.1016/j.crme.2005.12.001
Keywords: Acoustics, Waves, Vibrations, Helicoidal coordinates, Finite elements, Asymptotic methods, Twisted fibres, Accuracy
Mot clés : Acoustique, Ondes, Vibrations, Coordonnées hélicoïdales, Éléments finis, Méthodes asymptotiques, Fibres torsadées, Précision

André Nicolet 1; Alexander B. Movchan 2; Sébastien Guenneau 2; Frédéric Zolla 3

1 Institut Fresnel, UMR 6133, université Aix-Marseille III, case 162, 13397 Marseille cedex 20, France
2 Department of Mathematical Sciences, Liverpool University, Liverpool L69 3BX, UK
3 Institut Fresnel, UMR 6133, université Aix-Marseille I, case 162, 13397 Marseille cedex 20, France
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     title = {Asymptotic modelling of weakly twisted electrostatic problems},
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André Nicolet; Alexander B. Movchan; Sébastien Guenneau; Frédéric Zolla. Asymptotic modelling of weakly twisted electrostatic problems. Comptes Rendus. Mécanique, Volume 334 (2006) no. 2, pp. 91-97. doi : 10.1016/j.crme.2005.12.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.12.001/

[1] F. Zolla; G. Renversez; A. Nicolet; B. Kuhlmey; S. Guenneau; D. Felbacq Foundations of Photonic Crystal Fibres, Imperial College Press, London, 2005

[2] A. Nicolet; F. Zolla; S. Guenneau Modelling of twisted optical waveguides with edge elements, Eur. Phys. J. Appl. Phys., Volume 28 (2004), pp. 153-157 | DOI

[3] A.B. Movchan; N.V. Movchan Mathematical Modelling of Solids with Non-Regular Boundaries, CRC Press, Boca Raton, FL, 1995

[4] P. Dular; C. Geuzaine; F. Henrotte; W. Legros A general environment for the treatment of discrete problems and its application to the finite element method, IEEE Trans. Magnetics, Volume 34 (1998) no. 5, pp. 3395-3398 http://www.geuz.org (and see also the Internet address)

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