Exact relations between magnetoresistivity tensor components of conducting composites with a columnar microstructure

Yakov M. Strelniker, David J. Bergman

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

A recently discovered duality transformation for a three-dimensional columnar medium (i.e., a medium that is uniform along some fixed direction, called the columnar axis) is applied to a two-constituent composite medium. This leads to a generalization of Keller’s theorem: Exact relations are found between in-plane components (i.e., components that are perpendicular to the columnar axis) of the bulk effective resistivity or conductivity tensor of the columnar composite medium and similar quantities of a dual problem. These are used to find exact relations between in-plane bulk effective magnetoresistivity and magnetoconductivity components of a conductor/insulator mixture and those of a normal conductor/perfect conductor mixture with the same microstructure. The exact relations are applied to and tested on a number of available results on in-plane magnetoresistance in columnar composites, including an effective medium approximation, numerical computations on periodic microstructures, and closed form expressions for the asymptotic behavior at strong magnetic fields in periodic microstructures.

Original languageEnglish
Pages (from-to)6288-6297
Number of pages10
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume61
Issue number9
DOIs
StatePublished - 2000

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