TY - JOUR
T1 - n-point probability functions for a lattice model of heterogeneous media
AU - Lu, Binglin
AU - Torquato, S.
N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 1990
Y1 - 1990
N2 - The macroscopic properties of two-phase random heterogeneous media depend upon the infinite set of n-point probability functions S1,...,Sn. The quantity Sn(x1,...,xn) gives the probability of finding n points with positions x1,...,xn all in one of the phases. We derive a series representation of Sn for a finite-sized D-dimensional lattice model of heterogeneous media. By performing certain averages over the Sn, we then obtain explicit expressions for translationally invariant and rotationally invariant n-point probabilities. Computer simulations are carried out for low-order n-point probability functions. The theoretical and simulation results are found to be in excellent agreement.
AB - The macroscopic properties of two-phase random heterogeneous media depend upon the infinite set of n-point probability functions S1,...,Sn. The quantity Sn(x1,...,xn) gives the probability of finding n points with positions x1,...,xn all in one of the phases. We derive a series representation of Sn for a finite-sized D-dimensional lattice model of heterogeneous media. By performing certain averages over the Sn, we then obtain explicit expressions for translationally invariant and rotationally invariant n-point probabilities. Computer simulations are carried out for low-order n-point probability functions. The theoretical and simulation results are found to be in excellent agreement.
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U2 - 10.1103/PhysRevB.42.4453
DO - 10.1103/PhysRevB.42.4453
M3 - Article
AN - SCOPUS:0005325944
VL - 42
SP - 4453
EP - 4459
JO - Physical Review B
JF - Physical Review B
SN - 0163-1829
IS - 7
ER -