Macroscopic conductivity of random inhomogeneous media. Calculation methods

Fokin, A. G.

doi:10.1070/pu1996v039n10abeh000173

Cited by 14 publications

(10 citation statements)

References 69 publications

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“…Still, we must stress the large volume of literature produced in a number of disciplines with the aim of finding representative parameters in the theory of conductive media. Such disciplines would include electrical conductivity (see, e.g., Fokin [1996] for a review and Kaganova [2003]), thermal conductivity [e.g., Caldimi and Mahajan , 1999; Boomsma and Poulikakos , 2001], galvanomagnetic conductivity [e.g., Kaganova and Kaganov , 2004; Bergman and Stroud , 2000], and electronic conductivity [e.g., Du et al , 2004].…”

Section: Introductionmentioning

confidence: 99%

Representative hydraulic conductivities in saturated groundwater flow

Sánchez-Vila

Guadagnini

Carrera

2006

Reviews of Geophysics

275

209

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Heterogeneity is the single most salient feature of hydrogeology. An enormous amount of work has been devoted during the last 30 years to addressing this issue. Our objective is to synthesize and to offer a critical appraisal of results related to the problem of finding representative hydraulic conductivities. By representative hydraulic conductivity we mean a parameter controlling the average behavior of groundwater flow within an aquifer at a given scale. Three related concepts are defined: effective hydraulic conductivity, which relates the ensemble averages of flux and head gradient; equivalent conductivity, which relates the spatial averages of flux and head gradient within a given volume of an aquifer; and interpreted conductivity, which is the one derived from interpretation of field data. Most theoretical results are related to effective conductivity, and their application to real world scenarios relies on ergodic assumptions. Fortunately, a number of results are available suggesting that conventional hydraulic test interpretations yield (interpreted) hydraulic conductivity values that can be closely linked to equivalent and/or effective hydraulic conductivities. Complex spatial distributions of geologic hydrofacies and flow conditions have a strong impact upon the existence and the actual values of representative parameters. Therefore it is not surprising that a large body of literature provides particular solutions for simplified boundary conditions and geological settings, which are, nevertheless, useful for many practical applications. Still, frequent observations of scale effects imply that efforts should be directed at characterizing well-connected stochastic random fields and at evaluating the corresponding representative hydraulic conductivities

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Section: Introductionmentioning

confidence: 99%

Representative hydraulic conductivities in saturated groundwater flow

Sánchez-Vila

Guadagnini

Carrera

2006

Reviews of Geophysics

275

209

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“…While our overarching goal is the treatment of fullfield data pertaining to solid mechanics, the proposed method is discussed here in the context of the scalar conductivity model which has the same mathematical structure as the elasticity model yet avoids resorting to tensorial notations. Note that a Fourier-based forward solution method corresponding to this model is discussed in [24,25]. In [26, ch.…”

Section: Introductionmentioning

confidence: 99%

A full-field image conversion method for the inverse conductivity problem with internal measurements

Bellis¹,

Moulinec²

2016

Proc. R. Soc. A.

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International audienceThis article investigates a Fourier-based algorithm for computing heterogeneous material parameter distributions from internal measurements of physical fields. Within the framework of the periodic scalar conductivity model, a pair of dual Lippmann– Schwinger integral equations is derived for the sought constitutive parameters based on full intensity or current density field measurements. A numerical method based on the fast Fourier transform and fixed-point iterations is proposed. Convergence, stability and approximation quality of the method are analysed. For materials with small contrast, a first-order Born-like approximation is also obtained. Overall, the proposed reconstruction approach enables a direct conversion of full-field measurement images, possibly noisy, into maps of material conductivity. A set of numerical results is presented to illustrate the performance of the method

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“…Indeed, if we calculate ECT up to the terms independent of the small parameter 1/H only, with respect to laboratory axes LCT is σ ik (H, r) = S( κ, r)δ i3 δ k3 . We can describe such a medium as a set of plane-parallel layers perpendicular to the direction of the magnetic field H. It is known (see, e.g., [1]) that in such a medium the value of the effective conductivity is equal to the inverse the averaged resistivity. This is just our answer for σ ef || .…”

Section: Ikmentioning

confidence: 99%

“…However, in the general case this problem has not been solved yet. In this Introduction we do not pretend to give the full list of references, but refer the readers to the review paper by A.G.Fokin [1], where the long list of references relating to different aspects of the problem is presented. We concentrate mainly on the known exact solutions for the effective conductivity tensor (ECT).…”

Section: Introductionmentioning

confidence: 99%

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On calculation of effective conductivity of inhomogeneous metals

Kaganova¹

2003

Physics Letters A

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In the framework of the perturbation theory an expression suitable for calculation of the effective conductivity of 3-D inhomogeneous metals in uniform magnetic field H is derived. For polycrystals of metals with closed Fermi surfaces in high magnetic fields the perturbation series defining the longitudinal and the hall elements of the perturbation series can be summed allowing us to obtain the exact expression for the leading terms of all these elements of the effective conductivity tensor.

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Macroscopic conductivity of random inhomogeneous media. Calculation methods

Cited by 14 publications

References 69 publications

Representative hydraulic conductivities in saturated groundwater flow

Representative hydraulic conductivities in saturated groundwater flow

A full-field image conversion method for the inverse conductivity problem with internal measurements

On calculation of effective conductivity of inhomogeneous metals

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