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

Published online by Cambridge University Press:  12 July 2007

M. F. Ben Hassen
Affiliation:
Institut für Numerische und Angewandte Mathematik, University of Göttingen, Lotzestrasse 16–18, 37083 Göttingen, Germany (benhasse@math.uni-goettingen.de)
E. Bonnetier
Affiliation:
LMC-IMAG, Université Joseph Fourier Grenoble, BP 53, 38041 Grenoble Cedex 9, France (eric.bonnetier@imag.fr)

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,duε away from the defects and show that, to first order, a misplaced inclusion manifests itself via a polarization tensor, which is characterized.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2006

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