### Abstract

The microstructure of two-phase disordered media can be characterised in terms of a set of n-point matrix probability functions S_{n} which give the probability of finding n points all in the matrix phase. The authors obtain, for the first time, an exact analytical expression for S_{2} for a distribution of equi-sized rigid rods in a matrix at any density and for all values of its argument. They evaluate, also for the first time, S_{2} for a distribution of equi-sized rigid discs in a matrix, for a wide range of densities. Using these results for S_{2} and rigorous upper and lower bounds on S_{3}, one may obtain bounds on S_{3} for distributions of rigid rods and discs. The one- and two-dimensional results obtained here are compared to the three-dimensional results of Torquato and Stell (1983) at certain particle volume fractions.

Original language | English (US) |
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Article number | 025 |

Pages (from-to) | 141-148 |

Number of pages | 8 |

Journal | Journal of Physics A: General Physics |

Volume | 18 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1985 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

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## Cite this

*Journal of Physics A: General Physics*,

*18*(1), 141-148. [025]. https://doi.org/10.1088/0305-4470/18/1/025