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The effective conductivity of a randomly inhomogeneous medium

โœ Scribed by E.V. Teodorovich

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
516 KB
Volume
64
Category
Article
ISSN
0021-8928

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โœฆ Synopsis

Using a representation of the solution to the diffusion equation in a randomly inhomogeneous medium in the form of a Feynman path integral an explicit expression is obtained for the effective conductivity in a space of arbitrary dimension. A calculation of the path integral only turns out to be possible in the case of a large-scale limit. In particular, it is shown that in the three-dimensional case the expression for the effective conductivity does not admit of an expansion in terms of the conductivity variance. This indicates that the use of standard perturbation theory in the form of an expansion in terms of the conductivity fluctuations is incorrect.

๐Ÿ“œ SIMILAR VOLUMES

Effective medium models for conductivity
Effective medium models for conductivity of randomly cracked locally non-homogeneous materials
โœ D.C Pham ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 55 KB

A refined effective medium scheme is developed to estimate the conductivity (thermal and electrical) of randomly cracked materials (the cracks are assumed to be insulating), accounting for possible locally non-homogeneous distribution of the cracks. Certain spaces within the materials are modelled a