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Asymptotic modelling of Skin-effects in coaxial cables

Geoffrey Beck 1 Sébastien Imperiale 2 Patrick Joly 3
2 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
3 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this work we tackle the modeling of non-perfectly conducting thin coaxial cables. From the non-dimensionnalised 3D Maxwells equations, we derive, by asymptotic analysis with respect to the (small) transverse dimension of the cable, a simplified effective 1D model and an effective reconstruction procedure of the electric and magnetic fields. The derived effective model involves a fractional time derivatives that accounts for the so-called skin effects in highly conducting regions.
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https://hal.inria.fr/hal-02512156
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Submitted on : Monday, October 5, 2020 - 3:38:47 PM
Last modification on : Tuesday, October 19, 2021 - 11:05:54 PM

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  • HAL Id : hal-02512156, version 2

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Geoffrey Beck, Sébastien Imperiale, Patrick Joly. Asymptotic modelling of Skin-effects in coaxial cables. SN Partial Differential Equations and Applications, Springer, 2020. ⟨hal-02512156v2⟩

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