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

M.A.J. Michels

doi:10.1016/0378-4371(89)90330-0

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

M.A.J. Michels

Research output: Contribution to journal › Article › Academic › peer-review

3 Citations (Scopus)

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 language	English
Pages (from-to)	377-381
Journal	Physica A: Statistical and Theoretical Physics
Volume	157
Issue number	1
DOIs	https://doi.org/10.1016/0378-4371(89)90330-0
Publication status	Published - 1989
Externally published	Yes

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title = "The convergence of integral expressions for the effective properties of heterogeneous media",

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.",

author = "M.A.J. Michels",

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T1 - The convergence of integral expressions for the effective properties of heterogeneous media

AU - Michels, M.A.J.

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

U2 - 10.1016/0378-4371(89)90330-0

DO - 10.1016/0378-4371(89)90330-0

M3 - Article

SN - 0378-4371

VL - 157

SP - 377

EP - 381

JO - Physica A: Statistical and Theoretical Physics

JF - Physica A: Statistical and Theoretical Physics

IS - 1

ER -

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

Abstract

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