Two-point cluster function for continuum percolation

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 d...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of chemical physics 1988-05, Vol.88 (10), p.6540-6547
Main Authors: TORQUATO, S, BEASLEY, J. D, CHIEW, Y. C
Format: Article
Language:English
Subjects:
Condensed matter: structure, mechanical and thermal properties
Equations of state, phase equilibria, and phase transitions
Exact sciences and technology
Other topics in equations of state, phase equilibria, and phase transitions
Physics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.454440