BOUNDS ON THE CONDUCTIVITY OF A RANDOM ARRAY OF CYLINDERS.

S. Torquato, F. Lado

Research output: Contribution to journalArticle

56 Scopus citations

Abstract

The authors consider the problem of determining rigorous third-order and fourth-order bounds on the effective conductivity of sigma //2 randomly distributed throughout a matrix of conductivity sigma //1. Both bounds involve the microstructural parameter zeta //2 which is an integral that depends upon S//3, the three-point probability function of the composite. The key multidimensional integral zeta //2 is greatly simplified by expanding the orientation-dependent terms of its integrand in Chebyshev polynomials and using the orthogonality properties of this basis set.

Original languageEnglish (US)
Pages (from-to)59-80
Number of pages22
JournalProceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences
Volume417
Issue number1852
StatePublished - May 9 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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