Composites with invisible inclusions: eigenvalues of R-linear problem

2015/08/12 by Vladimir Mityushev, Mityushev, Vladimir
Mathematics · Physics and Astronomy · #30E25 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:30E25

paper · pdf · doi:10.48550/arxiv.1508.02910

10 pages, 1 figure

arxiv created 2015/08/12 · arxiv updated 2015/08/13

Abstract

An new eigenvalue \mathbb R-linear problem arisen in the theory of metamaterials is stated and constructively investigated for circular non-overlapping inclusions. An asymptotic formula for eigenvalues is deduced when the radii of inclusions tend to zero. The nodal domains conjecture related to univalent eigenfunctions is posed. Demonstration of the conjecture allows to justify that a set of inclusions can be made neutral by surrounding it with an appropriate coating.

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