The convergence of integral expressions for the effective properties of heterogeneous media

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Abstract

We present a very brief and general proof that the series expansion for the effective constant of a heterogeneous medium can be expressed in irreducible cluster integrals only. The argument does not use details of the cluster expansion. On the other hand, for any given expansion it provides a simple prescription to obtain irreducibility. For dielectric polarisation and other phenomena in which the interaction propagator falls off as R−3, this irreducibility guarantees absolute convergence of the integrals.
Original languageEnglish
Pages (from-to)377-381
JournalPhysica A: Statistical and Theoretical Physics
Volume157
Issue number1
DOIs
Publication statusPublished - 1989
Externally publishedYes

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