Macroscopic Behavior and Morphology of Random Media.

Details Macroscopic Behavior and Morphology of Random Media. Macroscopic Behavior and Morphology of Random Media.

Feb 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phdt........60k&link_type=abstract

Thesis (PH.D.)--NORTH CAROLINA STATE UNIVERSITY, 1991.Source: Dissertation Abstracts International, Volume: 52-03, Section: B, p

Statistics

Computation

Scientific paper

The purpose of the research is to develop efficient analytical and computational techniques to relate the various effective macroscopic properties of random media to their constituent phase properties and their microstructures. The microstructure plays a key role in the determination of the effective properties. Two general problems are considered: (i) statistical characterization of microstructures of random media; and (ii) calculation of effective properties of such materials. The pair-connectedness function P(r) , the mean cluster size S and the percolation threshold phic of a continuum percolation model of bidispersed overlapping spheres is determined via Monte Carlo simulation. The mean number of clusters < nc > and related quantities such as the mean numbers of monomers, dimers, trimers etc. of a continuum percolation model of overlapping spheres are then estimated analytically and computationally. Various rigorous bounds are computed and comparison with simulation results is given. A Brownian motion simulation algorithm is developed to efficiently compute effective diffusion parameters. The technique is used to compute the effective conductivity sigmae for two - and three-dimensional distributions of spheres. The Brownian motion simulation algorithm is also applied to compute the diffusion-controlled trapping rate k for a statistically anisotropic distribution of the oriented, hard spheroidal traps, and using a new relation linking k to the fluid permeability tensor K, information about K for this anisotropic porous medium is inferred. Finally, the problem of the passive advection of a scalar in a prescribed random velocity field with molecular diffusion is considered. New advection -diffusion algorithm is developed and applied to simple models of layered flow fields where the exact evaluations on the effective diffusivity D^* and the anomalous behavior of a random walk are available. The effective diffusivity D^* and the Lagrangian velocity autocorrelation function {cal R}(t) of a random velocity field are computed by using the advection-diffusion algorithm.

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