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

Weng Cho Chew, James A. Friedrich, Robert Geiger

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)207-214
Number of pages8
JournalIEEE Transactions on Geoscience and Remote Sensing
Issue number2
StatePublished - Mar 1990
Externally publishedYes

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • General Earth and Planetary Sciences


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