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ON OPTIMAL CLOAKING-BY-MAPPING TRANSFORMATIONS

Abstract : A central ingredient of cloaking-by-mapping is the diffeomorphisn which transforms an annulus with a small hole into an annulus with a finite size hole, while being the identity on the outer boundary of the annulus. The resulting meta-material is anisotropic, which makes it difficult to manufacture. The problem of minimizing anisotropy among radial transformations has been studied in [4]. In this work, as in [4], we formulate the problem of minimizing anisotropy as an energy minimization problem. Our main goal is to provide strong evidence for the conjecture that for cloaks with circular boundaries, non-radial transformations do not lead to lower degree of anisotropy. In the final section, we consider cloaks with non-circular boundaries and show that in this case, non-radial cloaks may be advantageous, when it comes to minimizing anisotropy.
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Preprints, Working Papers, ...
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https://hal.sorbonne-universite.fr/hal-03335152
Contributor : Yves Capdeboscq Connect in order to contact the contributor
Submitted on : Monday, September 6, 2021 - 8:31:46 AM
Last modification on : Tuesday, September 28, 2021 - 5:16:36 PM

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  • HAL Id : hal-03335152, version 1
  • ARXIV : 2109.02397

Citation

Yves Capdeboscq, Michael Vogelius. ON OPTIMAL CLOAKING-BY-MAPPING TRANSFORMATIONS. 2021. ⟨hal-03335152⟩

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