A Multiple Scattering Solution For the Effective Permittivity of a Sphere Mixture

Weng Cho Chew; James A. Friedrich; Robert Geiger

doi:10.1109/36.46700

A Multiple Scattering Solution For the Effective Permittivity of a Sphere Mixture

Weng Cho Chew, James A. Friedrich, Robert Geiger

Research output: Contribution to journal › Article › peer-review

Abstract

A recursive algorithm to calculate the exact solution of N random assortment of spheres is described. In this algorithm, the scattering from a single sphere is expressed in a 1-sphere T matrix. Then the scattering from two spheres is expressed in terms of 2-sphere T matrices, which are related to the 1-sphere T matrix. A recursive algorithm to deduce the (n + l)-sphere T matrix from the n-sphere T matrix is derived. With this recursive algorithm, the multiple scattering from a random assortment of N spheres can be obtained. This results in an N2 algorithm rather than the normal N3 algorithm. As an example, the algorithm is used to calculate the low-frequency effective permittivity of a random assortment of 18 dielectric spheres. The effective permittivity deviates from the Maxwell-Garnett (M-G) result for high contrast and high packing fraction. With a high packing fraction, dielectric enhancement at low frequency is possible.

Original language	English (US)
Pages (from-to)	207-214
Number of pages	8
Journal	IEEE Transactions on Geoscience and Remote Sensing
Volume	28
Issue number	2
DOIs	https://doi.org/10.1109/36.46700
State	Published - Mar 1990
Externally published	Yes

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Electrical and Electronic Engineering
Earth and Planetary Sciences(all)

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10.1109/36.46700

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title = "A Multiple Scattering Solution For the Effective Permittivity of a Sphere Mixture",

abstract = "A recursive algorithm to calculate the exact solution of N random assortment of spheres is described. In this algorithm, the scattering from a single sphere is expressed in a 1-sphere T matrix. Then the scattering from two spheres is expressed in terms of 2-sphere T matrices, which are related to the 1-sphere T matrix. A recursive algorithm to deduce the (n + l)-sphere T matrix from the n-sphere T matrix is derived. With this recursive algorithm, the multiple scattering from a random assortment of N spheres can be obtained. This results in an N2 algorithm rather than the normal N3 algorithm. As an example, the algorithm is used to calculate the low-frequency effective permittivity of a random assortment of 18 dielectric spheres. The effective permittivity deviates from the Maxwell-Garnett (M-G) result for high contrast and high packing fraction. With a high packing fraction, dielectric enhancement at low frequency is possible.",

author = "Chew, {Weng Cho} and Friedrich, {James A.} and Robert Geiger",

note = "Funding Information: Manuscript received January 12, 1989: revised June 19, 1989. This work was supported by the U.S. Army Research Office under Contract No. DAAL03-87-KO006 to the University of Illinois Advanced Construction Technology Center, by the National Science Foundation under Grant NSF ECS-85291, by the Office of Naval Research under Grant N00014-89-J-1286, and by Schlumberger-Doll Research. The authors are with the Department of Electrical and Computer Engineering, University of Illinois, 1406 West Green Street, Urbana-Champaign, IL 61801. IEEE Log Number 8933254. 'The references here are exemplary and by no means complete.",

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AU - Geiger, Robert

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A Multiple Scattering Solution For the Effective Permittivity of a Sphere Mixture

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