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Inverse Transport Problems for Composite Media

Published online by Cambridge University Press:  28 February 2011

Ross C. Mcphedran  and
Graeme W. Milton
Ross C. Mcphedran
Affiliation:
School of Physics, University of Sydney, Sydney N.S.W. 2006, Australia
Graeme W. Milton
Affiliation:
Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, U.S.A.
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Abstract

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.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 195: Symposium S – Physical Phenomena in Granular Materials , 1990 , 257
Copyright
Copyright © Materials Research Society 1990

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References

REFERENCES

1. Gajdardziska-Josifovska, M., McPhedran, R.C., Cockayne, D.J.H., D.R. McKenzie, and R.E. Collins, Appl. Optics, 28, 2736 (1989); 28, 2744 (1989).Google Scholar
2. Gajdardziska-Josifovska, M., Ootical Properties and Microstructure of Cermets, M.Sc. thesis, the University of Sydney, 1986 (unpublished).Google Scholar
3. Lamb, W., Wood, D.M. and Ashcroft, N.W., Phys. Rev. B21, 2248 (1980).Google Scholar
4. McPhedran, R.C., Botten, L.C., Craig, M.S., Neviere, M. and Maystre, D., Optica Acta 29, 289 (1982).Google Scholar
5. Bell, J.M.. Derrick, G.H. and McPhedran, R.C., Optica Acta 29, 1475 (1982).Google Scholar
6. Landauer, R., in Electrical Transport and Optical Properties of Inhomogeneous Media, edited by Garland, J.C. and Tanner, D.B., (Am. Inst. Phys. Conf. Proc. 40, 1977) p2.Google Scholar
7. Milton, G.W., Commun. Math. Phys. 99, 463 (1985).Google Scholar
8. Norris, A., Mech. Mater. 4, 1 (1985).Google Scholar
9. Avellaneda, M., Commin. Pure Appl. Math. 40, 527 (1987).Google Scholar
10. Hashin, Z. and Shtrikman, S., J. Appl. Phys. 33, 3125 (1962).Google Scholar
11. Sheng, P., Phys. Rev. Lett., 45, 60 (1980).Google Scholar
12. Bergman, D.J., Ann. Phys. 138, 78 (1982).Google Scholar
13. Milton, G.W., J. Appl. Phys. 52, 5286 (1981); 52, 5294 (1981).Google Scholar
14. McPhedran, R.C. and Milton, G.W., Appl. Phys. A26, 207 (1981).Google Scholar
15. Keller, J.B., J. Math. Phys. 5, 548 (1964).Google Scholar
16. McPhedran, R.C., McKenzie, D.R. and Milton, G.W., Appl. Phys. A29, 19 (1982).Google Scholar
17. Gadenne, P., Beghdadi, A., and Lafait, J., Opt. Commun. 65, 17 (1988).Google Scholar