Haigang Li, Fang Wang, Longjuan Xu
Published 2018-08-10Version 1
In composite materials, the inclusions are frequently spaced very closely. The electric field concentrated in the narrow regions between two adjacent perfectly conducting inclusions will always become arbitrarily large. In this paper, we establish an asymptotic formula of the electric field in the zone between two spherical inclusions with different radii in three dimensions. An explicit blowup factor relying on radii is obtained, which also involves the digamma function and Euler-Mascheroni constant, and so the role of inclusions' radii played in such blowup analysis is identified.
Comments: 36 pages. arXiv admin note: text overlap with arXiv:1305.0921 by other authors
Blowup Analysis for the Perfect Conductivity Problem with convex but not strictly convex inclusions
Spectral analysis of the Neumann-Poincaré operator and characterization of the gradient blow-up
Characterization of the electric field concentration between two adjacent spherical perfect conductors
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