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Integral constraints in multiple-scales problems

Published online by Cambridge University Press:  13 January 2015

S. J. CHAPMAN  and
S. E. MCBURNIE
S. J. CHAPMAN
Affiliation:
Mathematical Institute, University of Oxford, ROQ, Woodstock Road, Oxford OX2 6GG, UK emails: chapman@maths.ox.ac.uk, semcburnie@googlemail.com
S. E. MCBURNIE
Affiliation:
Mathematical Institute, University of Oxford, ROQ, Woodstock Road, Oxford OX2 6GG, UK emails: chapman@maths.ox.ac.uk, semcburnie@googlemail.com
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Abstract

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Asymptotic homogenisation via the method of multiple scales is considered for problems in which the microstructure comprises inclusions of one material embedded in a matrix formed from another. In particular, problems are considered in which the interface conditions include a global balance law in the form of an integral constraint; this may be zero net charge on the inclusion, for example. It is shown that for such problems care must be taken in determining the precise location of the interface; a naive approach leads to an incorrect homogenised model. The method is applied to the problems of perfectly dielectric inclusions in an insulator, and acoustic wave propagation through a bubbly fluid in which the gas density is taken to be negligible.

Keywords

homogenisationmultiple scalesperfect dielectricrigid inclusionsbubbly fluideffective mediumaveragingcoarse graining
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Special Anniversay Issue 5: Celebrating 75 years , October 2015 , pp. 595 - 614
Copyright
Copyright © Cambridge University Press 2015 

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