Tuesday, 12 October 2004 - 1:50 PM

This presentation is part of : Torquato Symposium

Stochastic Geometry: Simulation and Computation of Cluster Characteristics

John Quintanilla, University of North Texas, University of North Texas, P.O. Box 311430, Department of Mathematics, Denton, TX 76203

Stochastic geometry has often been used in the literature to model the behavior of random materials. Two specific models that have been used extensively are the Boolean model and the Gaussian random field model. In this talk, we discuss recent progess in characterizing the microstructure of these models. In recent years, percolation thresholds have been computed with increasing precision by using Monte Carlo simulation, low-density cluster densities, high-density cluster statistics, and computations on inhomogeneous systems. Chord-length functions for the Boolean model have been numerically computed by inverting Laplace transforms and by approximating the model as a digitized system. Chord-length functions for the Gaussian random field model have also been obtained.

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