Journal Article10.1063/1.454440
Two‐point cluster function for continuum percolation
176
TL;DR: In this article, the authors introduced a two-point cluster function C2(r1,r2) which reflects information about clustering in general continuum-percolation models.
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Abstract: We introduce a two‐point cluster function C2(r1,r2) which reflects information about clustering in general continuum–percolation models. Specifically, for any two‐phase disordered medium, C2(r1,r2) gives the probability of finding both points r1 and r2 in the same cluster of one of the phases. For distributions of identical inclusions whose coordiantes are fully specified by center‐of‐mass positions (e.g., disks, spheres, oriented squares, cubes, ellipses, or ellipsoids, etc.), we obtain a series representation of C2 which enables one to compute the two‐point cluster function. Some general asymptotic properties of C2 for such models are discussed. The two‐point cluster function is then computed for the adhesive‐sphere model of Baxter. The two‐point cluster function for arbitrary media provides a better signature of the microstructure than does a commonly employed two‐point correlation function defined in the text.
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References
Percus-Yevick Equation for Hard Spheres with Surface Adhesion
TL;DR: In this paper, it was shown that the Percus-Yevick approximation can be solved analytically for a potential consisting of a hard core together with a rectangular attractive well, provided that a certain limit is taken in which the range of the well becomes zero and its depth infinite.
1.2K
Microstructure of two‐phase random media. I. The n‐point probability functions
Salvatore Torquato,George Stell +1 more
TL;DR: In this paper, a hierarchy of equations was derived for a bed or suspension of spheres in a uniform matrix, giving the Sn in terms of the s-body distribution functions ρs associated with a statistically inhomogeneous distribution PN in the matrix.
334
Effective electrical conductivity of two‐phase disordered composite media
TL;DR: In this article, the perturbation expansions of the effective electrical conductivity σe of any two-phase isotropic composite medium of arbitrary dimensionality d (where d = 2,3) are derived.
276
Percolation behaviour of permeable and of adhesive spheres
Y C Chiew,Eduardo D. Glandt +1 more
TL;DR: In this paper, the percolation transition is defined as a function of the interpenetrability of the particles, and is found to correspond to an average coordination number z = 4.
235
Pair connectedness and cluster size
TL;DR: In this article, a theory of pair connectedness is developed for fluid as well as lattice systems when the presence of physical clusters of particles in the system is explicitly taken into account.
206
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