## Abstract

By averaging over pairs of hyperspheres, we have obtained the dielectric function for a binary mixture containing hyperspherical inclusions up to order c2, where c is the volume fraction of inclusions. The method used is based on multipole expansions for the potential of two spheres in a uniform field and is a generalization of the method of Jeffrey to d-dimensional space. Numerical results are presented for the second-order coefficient K in the low-c expansion of the dielectric constant for arbitrary d; these verify earlier known results, as well as showing the dependence of K on dimensionality, which is particularly simple as d -»1 and as d -> oo.

Original language | English (US) |
---|---|

Pages (from-to) | 1973-1992 |

Number of pages | 20 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 454 |

Issue number | 1975 |

DOIs | |

State | Published - Jan 1 1998 |

## Keywords

- Concentration of inclusions
- Dielectric inclusions
- Hyperspheres
- Images
- Multipole expansions
- Two inclusions

## ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)