Dielectric function for a material containing hyp er spherical inclusions to O(c2) I. Multipole expansions

T. C. Choy, Aris Alexopoulos, M. F. Thorpe

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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 languageEnglish (US)
Pages (from-to)1973-1992
Number of pages20
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1975
StatePublished - Jan 1 1998


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

ASJC Scopus subject areas

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

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