## 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) |
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Pages (from-to) | 207-214 |

Number of pages | 8 |

Journal | IEEE Transactions on Geoscience and Remote Sensing |

Volume | 28 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1990 |

Externally published | Yes |

## ASJC Scopus subject areas

- Electrical and Electronic Engineering
- General Earth and Planetary Sciences