### 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 language | English (US) |
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Pages (from-to) | 59-80 |

Number of pages | 22 |

Journal | Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences |

Volume | 417 |

Issue number | 1852 |

State | Published - May 9 1988 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

Torquato, S., & Lado, F. (1988). BOUNDS ON THE CONDUCTIVITY OF A RANDOM ARRAY OF CYLINDERS.

*Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences*,*417*(1852), 59-80.