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

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 exp...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2006-08, Vol.136 (4), p.669-700
Main Authors: Ben Hassen, M. F., Bonnetier, E.
Format: Article
Language:English
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Summary: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.
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210500004650