n-point probability functions for a lattice model of heterogeneous media

Binglin Lu, S. Torquato

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)4453-4459
Number of pages7
JournalPhysical Review B
Issue number7
StatePublished - 1990
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics


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