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An asymptotic formula for the voltage potential in a perturbed ε-periodic composite medium containing misplaced inclusions of size ε
Journal article   Peer reviewed

An asymptotic formula for the voltage potential in a perturbed ε-periodic composite medium containing misplaced inclusions of size ε

M. F. Ben Hassen and E. Bonnetier
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, Vol.136(4), pp.669-700
08/2006

Abstract

We consider composite media made of homogeneous inclusions with C1,α,boundaries. Our goal is to compare the potential uε in a perfectly periodic composite with the potential uε,d, of a perturbed periodic medium, where the periodicity defects consist of misplaced inclusions. We give an asymptotic expansion of the difference uε,d − uε away from the defects and show that, to first order, a misplaced inclusion manifests itself via a polarization tensor, which is characterized.

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