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Inverse Transport Problems for Composite Media

Published online by Cambridge University Press:  28 February 2011

Ross C. Mcphedran
School of Physics, University of Sydney, Sydney N.S.W. 2006, Australia
Graeme W. Milton
Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, U.S.A.
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For two-component ceramic metal composites we address the inverse problem of estimating the volume fraction occupied by each component from measurements of the transmission and absorption coefficients at various frequencies of the applied radiation. We devise the algorithms, each based on representation formulas and bounds for the complex dielectric constant that were developed by Bergman and Milton. One inversion algorithm works remarkably well when the measurements are exact but fails completely when small errors are present. The second random throw algorithm works well when the measurement errors are large but is computationally intensive and is limited to small data sets. The third method based on single and two-point inversion, while not so accurate, is simple and efficient. The last two algorithms are implemented with experimental data and good agreement is obtained with the experimentally measured true volume fraction.

Research Article
Copyright © Materials Research Society 1990

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