Journal ArticleDOI
Microstructure of two-phase random media.III: The n-point matrix probability functions for fully penetrable spheres
Salvatore Torquato,George Stell +1 more
TLDR
In this paper, the two-and three-point matrix probability functions for a two-phase random and homogeneous system of impenetrable spheres were examined and an exact analytical expression for the two point matrix function S2 through second order in the number density of particles was given.Abstract:
We examine the two‐ and three‐point matrix probability functions for a two‐phase random and homogeneous system of impenetrable spheres. For such a system, we give an exact analytical expression for the two‐point matrix function S2 through second order in the number density of particles. Moreover, the two‐point matrix function is evaluated, for the first time, for a very wide range of densities. We also discuss the evaluation of the three‐point matrix function S3 for an impenetrable‐sphere system and provide new expressions that may be used to estimate it.read more
Citations
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Journal ArticleDOI
Determination of the size of the representative volume element for random composites: statistical and numerical approach
TL;DR: In this article, a quantitative definition of the representative volume element (RVE) size is proposed, which can be associated with a given precision of the estimation of the overall property and the number of realizations of a given volume V of microstructure that one is able to consider.
Journal ArticleDOI
Random Heterogeneous Media: Microstructure and Improved Bounds on Effective Properties
TL;DR: In this paper, the authors reviewed recent advances made in the determination and calculation of improved bounds on the effective properties of random heterogeneous media that depend upon the microstructure via n-point correlation functions.
Book ChapterDOI
Physical Properties of Macroscopically Inhomogeneous Media
David J. Bergman,David Stroud +1 more
TL;DR: In this article, the authors discuss several composites or granular or porous materials that display inhomogeneity on a macroscopic scale and present a discussion of the effective medium approximation, electrostatic resonances, exact bounds, and analytical properties.
Journal ArticleDOI
Medial axis analysis of void structure in three-dimensional tomographic images of porous media
TL;DR: In this article, the medial axis is constructed during an iterative erosion procedure which replaces the image of the void structure with a smaller version obtained by eroding its surface layer of voxels.
References
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Journal ArticleDOI
Scattering by an Inhomogeneous Solid. II. The Correlation Function and Its Application
TL;DR: In this paper, the angular intensity distribution of x-rays scattered by porous materials (hole structures) in the range of small angles is characterized by an exponential correlation function in the case of a distribution of holes of random shape and size in solid; a theoretical derivation of the exponential function is given for this case.
Journal ArticleDOI
Equation of State for Hard Spheres
TL;DR: In this paper, simple and exact expressions for the compressibility and pressure equations of state predicted by the Percus-Yevick equation for hard spheres were found for Wainwright and Alder.
Journal ArticleDOI
Random Sequential Addition of Hard Spheres to a Volume
TL;DR: In this article, the authors show that the configurations produced by placing spheres one at a time in a volume, subject to no overlap of the spheres but otherwise placing each at a point chosen at random, differ in a fundamental way from the configurations characteristic of a hard-sphere system of the same density which is in thermodynamic equilibrium.
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