Chord-distribution functions of three-dimensional random media: Approximate first-passage times of Gaussian processes

The main result of this paper is a semianalytic approximation for the chord -distribution functions of three dimensional models of microstructure deriv ed from Gaussian random fields. In the simplest case the chord functions ar e equivalent to a standard first-passage time problem, i.e., the probabilit y density governing the time taken by a Gaussian random process to first ex ceed a threshold. We obtain an approximation based on the assumption that s uccessive chords are independent. The result is a generalization of the ind ependent interval approximation recently used to determine the exponent of persistence time decay in coarsening. The approximation is easily extended to more general models based on the intersection and union sets of models g enerated from the isosurfaces of random fields. The chord-distribution func tions play an important role in the characterization of random composite an d porous materials. Our results are compared with experimental data obtaine d from a three-dimensional image of a porous Fontainebleau sandstone and a two-dimensional image of a tungsten-silver composite alloy. [S1063-651X(99) 06005-5].