Necessary conditions on realizable two-point correlation functions of random media

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49 Scopus citations


A fascinating inverse problem that has been receiving considerable attention is the construction of realizations of random two-phase heterogeneous media with a target two-point correlation function. However, not every hypothetical two-point correlation function corresponds to a realizable two-phase medium. Here, we collect all of the known necessary conditions on the two-point correlation functions scattered throughout a diverse literature and derive a new, but simple, positivity condition. We apply the necessary conditions to test the realizability of certain classes of proposed correlation functions.

Original languageEnglish (US)
Pages (from-to)6923-6928
Number of pages6
JournalIndustrial and Engineering Chemistry Research
Issue number21
StatePublished - Oct 11 2006

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • General Chemical Engineering
  • Industrial and Manufacturing Engineering


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