## Abstract

A new Brownian motion simulation technique developed by Torquato and Kim [Appl. Phys. Lett. 55, 1847 (1989)] is applied and further developed to compute "exactly" the effective conductivity σ_{e} of n-phase heterogeneous media having phase conductivities σ_{1}, σ_{2},..., σ_{n} and volume fractions φ_{1}, φ_{2},., φ_{n}. The appropriate first passage time equations are derived for the first time to treat d-dimensional media (d=1, 2, or 3) having arbitrary microgeometries. For purposes of illustration, the simulation procedure is employed to compute the transverse effective conductivity σ_{e} of a two-phase composite composed of a random distribution of infinitely long, oriented, hard cylinders of conductivity σ_{2} in a matrix of conductivity σ_{1} for virtually all volume fractions and for several values of the conductivity ratio α=σ_{2}/σ_{1}, including perfectly conducting cylinders (α=∞). The method is shown to yield σ_{e} accurately with a comparatively fast execution time.

Original language | English (US) |
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Pages (from-to) | 3892-3903 |

Number of pages | 12 |

Journal | Journal of Applied Physics |

Volume | 68 |

Issue number | 8 |

DOIs | |

State | Published - 1990 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)