Frequency Dispersion of Dielectric Permittivity and Electric Conductivity of Rocks via Two-Scale Homogenization of the Maxwell Equations

Shelukhin, V. V.; Terent’ev, S. A.

doi:10.2528/pierb09021804

Cited by 16 publications

(12 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The dispersion effect is due to the Maxwell-Wagner mechanism: free charges concentrate on interface surfaces to provide continuity of electric currents across such surfaces, see [22,23]; this is why the resulting polarization of the mixture depends on the frequency of the current source. The dispersion effect has been verified numerically, see the recent papers [24,25]. For a mathematical justification, see [26].…”

Section: Introductionmentioning

confidence: 91%

Homogenization of time harmonic Maxwell equations: the effect of interfacial currents

Amirat

Shelukhin

2016

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

Communicated by H. AmmariWe consider the Maxwell equations for a composite material consisting of two phases and enjoying a periodical structure in the presence of a time-harmonic current source. We perform the two-scale homogenization taking into account both the interfacial layer thickness and the complex conductivity of the interfacial layer. We introduce a variational formulation of the differential system equipped with boundary and interfacial conditions. We show the unique solvability of the variational problem. Then, we analyze the low frequency case, high and very high frequency cases, with different strength of the interfacial currents. We find the macroscopic equations and determine the effective constant matrices such as the magnetic permeability, dielectric permittivity, and electric conductivity. The effective matrices depend strongly on the frequency of the current source; the dielectric permittivity and electric conductivity also depend on the strength of the interfacial currents. the variables with the hat symbol .O/ denote reference values and the variables with the prime superscript denote dimensionless values, respectively. Let O " and O be the reference values of " and : " D O "" 0 , D O 0 . Remind that both " and are dimensionless parameters in the Gaussian system of units. We choose O J D O O E then, in the dimensionless variables, equation (1) becomes curl 0

show abstract

Section: Introductionmentioning

confidence: 91%

Homogenization of time harmonic Maxwell equations: the effect of interfacial currents

Amirat

Shelukhin

2016

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…ε a − δ cos 2φ (27) where φ is the misalignment angle with the principal axes. (25)) of the 'optimal' design is relatively large.…”

Section: Design Of Anisotropic Dielectric Materials Tensor With Non-zementioning

confidence: 99%

“…Their numerical evaluation was demonstrated at a fixed low frequency. Similarly, another study performed numerical evaluation of the parameters within the framework of the two-scale homogenization theory taking into account frequency dispersion [27]. In this paper, we further develop this research by applying the Finite Element Method to solve numerically the homogenization problem applying two-scale homogenization method formulated in [26,45] to Maxwell equations and extract the effective parameters of periodic dielectric and magnetic materials, that can be in their most generalized form lossy and are made of inclusions with arbitrary shapes and multi-phase material constituents.…”

Section: Homogenization Theorymentioning

confidence: 99%

“…Homogenization refers to replacing the inhomogeneous, periodic material in the microscopic scale with its homogeneous effective equivalent that has the same macroscopic effect as the original inhomogeneous structure [25][26][27][28][29][30][31][32][33][34][35]. The ability of computing the homogenized material property of such repetitive composites allows replacing them with their equivalent homogenized constitutive material property such as the dielectric permittivity and magnetic permeability tensors, ε and µ.…”

Section: Homogenization Theorymentioning

confidence: 99%

See 1 more Smart Citation

Inverse Synthesis of Electromagnetic Materials Using Homogenization Based Topology Optimization

El-Kahlout¹,

Kızıltaş²

2011

PIER

View full text Add to dashboard Cite

Abstract-Recent studies on artificial materials demonstrate that substantial improvements in electromagnetic response can be attained by combining different materials subject to desired metrics. However, the perfect material combination is unique and extremely difficult to determine without automated synthesis schemes. In this paper, we develop a versatile approach to design the microstructure of periodic materials with prescribed dielectric and magnetic material tensors. The proposed framework is based on a robust material model and generalized inverse synthesis tool relying on topology optimization. The former is derived using homogenization theory and asymptotic expansion applied to Maxwell equations and can characterize the effects of anisotropy and loss of materials with periodic unit cells of arbitrary geometries and multi-phases much smaller than the wavelength. Resulting Partial Differential Equation (PDE) is solved numerically using Finite Element Analysis (FEA) and is validated with results in literature. The material model proves to be fast and numerically stable even with complex inclusions. The topology optimization problem is applied for the first time towards designing the unit cell topology of periodic electromagnetic materials from scratch with desired dielectric and magnetic tensors using offthe-shelf materials, i.e., readily available constituents obtained from El-Kahlout and Kiziltas isotropic ceramic powders. The proposed framework's capability is demonstrated with five design examples. Design with anisotropic permittivity is also fabricated. Results show that the framework is capable of designing, in an automated fashion, non-intuitive material compositions from scratch with desired electromagnetic properties.

show abstract

“…In [29,30], a mathematical model (jointly with a computer code) is developed for calculation of the electric conductivity r  of a saturated rock. The model allows one to find an optimal Archie-like law…”

Section: Electrokinetic Coupling Coefficientsmentioning

confidence: 99%

The Electrokinetic Cross-Coupling Coefficient: Two-Scale Homogenization Approach

Shelukhin¹,

Yeltsov²,

Paranichev³

2011

WJM

View full text Add to dashboard Cite

By the two-scale homogenization approach we justify a two-scale model of ion transport through a layered membrane, with flows being driven by a pressure gradient and an external electrical field. By up-scaling, the electroosmotic flow equations in horizontal thin slits separated by thin solid layers are approximated by a homogenized system of macroscale equations in the form of the Poisson equation for induced vertical electrical field and Onsager's reciprocity relations between global fluxes (hydrodynamic and electric) and forces (horizontal pressure gradient and external electrical field). In addition, the two-scale approach provides macroscopic mobility coefficients in the Onsager relations. On this way, the cross-coupling kinetic coefficient is obtained in a form which does involves the  -potential among the data provided the surface current is negligible.

show abstract

Frequency Dispersion of Dielectric Permittivity and Electric Conductivity of Rocks via Two-Scale Homogenization of the Maxwell Equations

Cited by 16 publications

References 29 publications

Homogenization of time harmonic Maxwell equations: the effect of interfacial currents

Homogenization of time harmonic Maxwell equations: the effect of interfacial currents

Inverse Synthesis of Electromagnetic Materials Using Homogenization Based Topology Optimization

The Electrokinetic Cross-Coupling Coefficient: Two-Scale Homogenization Approach

Contact Info

Product

Resources

About