Association of evaluation methods of the effective permittivity of heterogeneous media on the basis of a generalized singular approximation

Колесников, В. И.; Yakovlev, V. B.; Bardushkin, V. V.; Lavrov, I. V.; Сычев, А. П.; Yakovleva, E.N.

doi:10.1134/s1028335813090012

Cited by 12 publications

(16 citation statements)

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“…Then, considering the body as unlimited (in this case, ), the solution of problem (8) can be written in the form of the convolution [10]:…”

Section: Formulation Of Problem and Derivation Of An Operator Equationmentioning

confidence: 99%

“…After a number of transformations, we obtain the desired relation between the local and average values of intensity of the electric field in an inhomogeneous medium [10]: (10) where is the tensor integral operator acting by the formula , and is the second derivative of the Green's function. Multiplying Eq.…”

Section: Formulation Of Problem and Derivation Of An Operator Equationmentioning

confidence: 99%

“…Let and be the volume fractions of the matrix and inclusions, respectively; the parameters of the body of comparison can be taken equal to the matrix parame ters [10]. The anisotropy of such a composite can manifest itself only due to the shape and the distribu tion of the orientations of inclusions.…”

Section: Composite With Isotropic Componentsmentioning

confidence: 99%

“…Let the medium contain inclusions in the shape of parallel fibers. In this case, and , the tensor is diagonal with the compo nents [10] , ,…”

Section: Composite With Isotropic Componentsmentioning

confidence: 99%

“…More exact expressions can be obtained if we take the values of permittivity calculated by the self consis tent method as the parameters of the body of compar ison [9,10]. For multicomponent polycrystals, the averaging procedure consists in the calculation of the volume average concentration of components with …”

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confidence: 99%

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A method of analysis of distributions of local electric fields in composites

et al. 2016

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A method of prediction of distributions of local electric fields in composite media based on anal ysis of the tensor operators of the concentration of intensity and induction is proposed. Both general expres sions and the relations for calculating these operators are obtained in various approximations. The analytical expressions are presented for the operators of the concentration of electric fields in various types of inhomo geneous structures obtained in the generalized singular approximation.

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“…Then, considering the body as unlimited (in this case, ), the solution of problem (8) can be written in the form of the convolution [10]:…”

Section: Formulation Of Problem and Derivation Of An Operator Equationmentioning

confidence: 99%

Section: Formulation Of Problem and Derivation Of An Operator Equationmentioning

confidence: 99%

Section: Composite With Isotropic Componentsmentioning

confidence: 99%

“…Let the medium contain inclusions in the shape of parallel fibers. In this case, and , the tensor is diagonal with the compo nents [10] , ,…”

Section: Composite With Isotropic Componentsmentioning

confidence: 99%

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A method of analysis of distributions of local electric fields in composites

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Detecting Moisture in Bauxite Using Microwaves

PAEA,

MCGUINNESS

2023

ANZIAM J.

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Mathematical modelling of microwaves travelling through bauxite ore provides a way to compute moisture content in the free space transmission method given data on signal attenuation, phase shift and variable bauxite depth. We extend a recently developed four-layer model that uses coupled ordinary differential wave equations for the electric field together with continuity boundary conditions at interfaces between ore, air and antenna to find a solution that incorporates multiple internal reflections in ore and air. The model provides good fits to data, depending on ore permittivity and conductivity. Our extensions are to use effective medium models to obtain electromagnetic properties of the ore mixture from moisture content and to incorporate the damping effects of scattering from the ore surface. Our model leads to a formula for the received signal showing how signal strengths SS and phase shifts depend on the moisture content of the bauxite ore, through the effects of moisture on permittivity and conductivity. We show that SS may be noninvertible, indicating that attenuation data alone cannot be used to infer moisture content. Combining with phase data typically corrects the noninvertibility. Reducing the operating frequency dramatically improves the usefulness of signal strength data for inferring moisture content.

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