Necessary Conditions on Realizable Two-Point Correlation Functions of Random Media

Details Necessary Conditions on Realizable Two-Point Correlation Functions of Random Media Necessary Conditions on Realizable Two-Point Correlation Functions of Random Media

2006-06-22

arxiv.org/abs/cond-mat/0606577v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

15 pages, 6 figures. This paper will be appearing in a special volume of "Industrial and Engineering Chemistry Research" in ho

Scientific paper

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.

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