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The Effective Dielectric Coefficient of a Composite Medium: Rigorous Bounds from Analytic Properties

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Book cover Homogenization and Effective Moduli of Materials and Media

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 1))

Abstract

The analytic properties of the bulk effective dielectric coefficient εe of a composite medium, viewed as a function of the component coefficients ε1,ε2,…, are reviewed in Section I, and are then used to discuss rigorous bounds for (real and complex) εe when various types of partial information are available about the medium. General methods are described in Section II for constructing optimal and rigorous bounds for both real and complex εe in two-component composites. A method for constructing rigorous bounds for εe in composites made of more than two components is described in Section III. Optimum bounds are found for real εe. For complex εe the optimization problem has not been fully resolved. Nevertheless, bounds for complex εe are obtained that are better than some other bounds that have recently been derived in Refs. 6 and 7.

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Author information

Authors and Affiliations

  1. School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv, 69978, Israel

    David J. Bergman

  2. Corporate Research Science Laboratories, Exxon Research and Engineering Co., Route 22 East, Annandale, NJ, 08801, USA

    David J. Bergman

Authors
  1. David J. Bergman
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Editor information

Editors and Affiliations

  1. School of Mathematics and Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, 55455, USA

    J. L. Ericksen

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    David Kinderlehrer

  3. Courant Institute, New York University, New York, NY, 10010, USA

    Robert Kohn

  4. Centre National d’Etudes Spatiales, College de France, Paris 5, France

    J.-L. Lions

  5. Institute for Mathematics and Its Applications, University of Minnesota, 514 Vincent Hall, 206 Church Street S.E., Minneapolis, MN, 55455, USA

    J.-L. Lions

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© 1986 Springer-Verlag New York Inc.

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Bergman, D.J. (1986). The Effective Dielectric Coefficient of a Composite Medium: Rigorous Bounds from Analytic Properties. In: Ericksen, J.L., Kinderlehrer, D., Kohn, R., Lions, JL. (eds) Homogenization and Effective Moduli of Materials and Media. The IMA Volumes in Mathematics and its Applications, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8646-9_2

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  • DOI: https://doi.org/10.1007/978-1-4613-8646-9_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8648-3

  • Online ISBN: 978-1-4613-8646-9

  • eBook Packages: Springer Book Archive

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