Dielectric function for a material containing hyp er spherical inclusions to O(c2) II. Method of images

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

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We have developed the method of images for the solution of two hyperspheres in d dimensions in a uniform field in order to study the O(c2) coefficient K in the dielectric constant of the medium. The method employs extensions of image theory for classical charges and dipoles for dielectric spheres, which produce novel line charge and line dipole densities. Numerical results for K with arbitrary integer d are consistent with our previous paper I (this issue), and demonstrate that the image method shows superior convergence properties. Although computationally less convenient, the procedure is, in principle, calculable term-by-term and leads to useful analytic results in the weak scattering limit. This work also produces a simple algebraic approximation that is useful everywhere.

Original languageEnglish (US)
Pages (from-to)1993-2013
Number of pages21
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1975
StatePublished - 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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