Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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By P.-H. Zhou, L.-J. Deng, B.-I. Wu, and J. A. Kong

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To apply the power-law to random mixing composites, the power parameter α is defined as the mean depolarization factor along the external field. The formula of α is derived from the effective medium theory and beta function distribution assumption to study the geometrical influence of scatterers. According to the simulation, we prove that α = 1/3 is fit to the composites of randomly distributed spherical dielectric scatterers, whereas α = 1/2 to the flake-like or cylindrical shaped scatterers. This law can be applied to both dilute and dense condition describing the effective permittivity of random mixing composites and extended to aligned cases, which are meaningful to practical applications.

P.-H. Zhou, L.-J. Deng, B.-I. Wu, and J. A. Kong, "Influence of scatterer's geometry on power-law formula in random mixing composites," Progress In Electromagnetics Research, Vol. 85, 69-82, 2008.

1. Jackson, J. D., Classical Electrodynamics, John Wiley & Sons Inc., New York, 1974.

2. Kanaun, S. K. and D. Jeulin, "The influence of spatial distributions of inhomogeneities on effective dielectric properties of composite materials (effective field approach) ," Progress In Electromagnetics Research, Vol. 22, 51-84, 1999.

3. Koledintseva, M. Y., R. E. DuBroff, and R. W. Schwartz, "A Maxwell Garnett model for dielectric mixtures containing conducting particles at optical frequencies," Progress In Electromagnetics Research, Vol. 63, 223-242, 2006.

4. Koledintseva, M. Y., S. K. R. Chandra, R. E. DuBroff, and R. W. Schwartz, "Modeling of dielectric mixtures containing conducting inclusions with statistically distributed aspect ratio," Progress In Electromagnetics Research, Vol. 66, 213-228, 2006.

5. Sihvola, A., "Metamaterials and depolarization factors," Progress In Electromagnetics Research, Vol. 51, 65-82, 2005.

6. Mclachlan, D. S., A. Priou, I. Chenerie, E. Issac, and F. Henry, "Modeling the permittivity of composite materials with a general effective medium equation," Journal of Electromagnetic Waves and Applications, Vol. 6, No. 9, 1099-1131, 1992.

7. Zhuck, N. P., K. Schuemann, and S. N. Shulga, "Effective permittivity of a statistically inhomogeneous medium with strong permittivity fluctuations," Progress In Electromagnetics Research, Vol. 44, 169-195, 2004.

8. Sihvola, A., "Mixing rules with complex dielectric coefficients," Subsurface Sensing Technologies and Applications, Vol. 1, 393-415, 2000.

9. Lichtenecker, K., "Mischkorpertheori alsWahrscheinlichkeitsproblem," Physik. Zeitschr., Vol. 30, 805-809, 1929.

10. Birchak, J. R., C. G. Gardner, J. E. Hipp, and J. M. Victor, "High dielectric constant microwave probes for sensing soil moisture," Proc. IEEE, Vol. 62, 93-98, 1974.

11. Lichtenecker, K. and K. Rother, "Die Herleitung des logarithmischen Mischungs-gesetzes aus allegemeinen Prinzipien der stationaren Stromung," Physik. Zeitschr., Vol. 32, 255-260, 1931.

12. Jacobsen, O. H. and P. Schjonning, "Comparison of TDR calibration functions for soil water determination," Proc. Symp. Time-domain Reflectometry Applications in Soil Science, 25-33, Tjele, Denmark, September 1994.

13. Zakri, T., J. P. Laurent, and M. Vauclin, "Theoretical evidence for ‘Lichtenecker’s mixture formulae’ based on the effective medium theory," J. Phys. D: Appl. Phys., Vol. 31, 1589-1594, 1998.

14. Mourzenko, V. V., J.-F. Thovert, and P. M. Adler, "Percolation of three-dimensional fracture networks with power-law size distribution," Phys. Rev. E, Vol. 72, 036103, 2005.

15. Bogdanov, I. I., V. V. Mourzenko, J.-F. Thovert, and P. M. Adler, "Effective permeability of fractured porous media with power-law distribution of fracture size," Phys. Rev. E, Vol. 76, 036309, 2007.

16. Sihvola, A., Electromagnetic Mixing Formulas and Applications, Institution of Electrical Engineers, London, 1999.

17. Stratton, J. A., Electromagnetic Theory, McGraw-Hill, New York, 1941.

18. Landau, L. D. and E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon, Pergamon, Oxford, 1960.

19. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1972.

20. Bruggeman, D. A. G., "Berechnung verschiedener physikalischer konstanten von heterogenen substanzen: 1. Dielektrizitatskonstanten und leitfahigkeiten der mischkorper aus isotropen substanzen," Ann. Phy., Vol. 24, 636-679, 1935.

21. Jia, B., W. Lin, and S. Liu, "The study of effective medium parameters for granular media," Progress In Electromagnetics Research, Vol. 8, 89-108, 1994.

22. Chen, X. D., T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E, Vol. 70, 016608, 2004.

23. Jylha, L. and A. H. Sihvola, "Tunability of granular ferroelectric dielectric composites," Progress In Electromagnetics Research, Vol. 78, 189-207, 2008.

24. Engstrom, C. and D. Sjoberg, "On two numerical methods for homogenization of Maxwell’s equations ," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1845-1856, 2007.

25. Habashy, T. M. and A. Abubakar, "A generalized material averaging formulation for modeling of the electromagnetic fields," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 9, 1145-1159, 2007.

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