Conduction of the three-dimensional model of a composite with structural anisotropy

The electric conduction of the model of a structurally anisotropic composite that represents an isotropic matrix with disk-shaped inclusions (oblate spheroids) is analytically studied. The disks have the same orientation and their centers are randomly distributed in the composite volume. The cases of dielectric and ideally conducting inclusions are considered. The conduction of the model in a broad concentration range is described by the approximate effective medium method. Conduction in the critical region (in the vicinity of the metal–dielectric phase transition point) is studied using the similarity hypothesis.     

Conductivity of a two-dimensional model of a structurally anisotropic composite with a system of scratches

The conductivity of a two-dimensional model of a structurally anisotropic composite, an isotropic matrix with nonconducting inclusions in the form of parallel scratches, is considered. The centers of the scratches are randomly distributed over the (x, y) plane. An approximate method is applied to derive an expression for the effective conductivity tensor, which satisfactorily describes of the electric conductivity of the model over a wide range of concentrations.     

含成层杂质的复合媒质的电导性质

本文用瑞利模型研究含成层杂质的复合媒质的直流电导性质,推导了适用于此类复合媒质的广义瑞利恒等式,并定义系统的有效电导率。对于具有立方对称性的系统,给出复合媒质有效电导率的解析计算公式。 关键词：     

On the distribution of a current in hall medium with metallical inclusions

Hall (σ_xx=0, σ_xy=const, where σ_ik is the conductivity tensor) medium with metallic inclusions is considered. The current (fields) distribution in such medium is established. It is shown that the electric field vanishes in the inclusion of a metallic phase and consequently the electric current streamlines miss these inclusions. The effective characteristics of the medium are calculated.     

Effect of scratches on the conductivity of anisotropic thin films

The conductivity of a two-dimensional composite with natural anisotropy, a thin anisotropic film with a system of randomly distributed nonconducting scratches is considered. An exact expression for the conductivity in the approximation linear in the concentration of scratches is derived. The case of consider-able concentrations is examined using the generalized effective-medium theory. The conductivity near the percolation threshold is treated in the framework of similarity theory.     

Effective electrical characteristics of a two-dimensional three-component doubly-periodic system with circular inclusions

The problem of the electric conductivity of a two-dimensional three-component system containing periodically arranged conducting circular inclusions of two types has been solved. A consistent method for the calculation of the conductivity and other effective electrical characteristics of this model is proposed, which is applicable in the case of arbitrary component concentrations. A complex potential outside the inclusions is expressed in terms of the Weierstrass zeta function and its derivatives. Undetermined coefficients entering into the general expression for the potential are determined from an infinite system of algebraic equations. In the case of a small concentration of inclusions, this system yields a virial expansion for the conductivity. A numerical analysis of this system of equations provides for the principal possibility of investigating various effective characteristics of the model (including the Hall coefficient and thermo emf) within the entire range of the problem parameters.     

Conductivity of the 3D model of a composite with spheroidal inclusions

The solution to the problem of the conductivity of the 3D model of a composite with inclusion having a shape of oblate ellipsoids of revolution (spheroids) has been obtained in a wide range of concentrations. The entire range of variation of the shape of inclusions (from a sphere to an infinitely thin circular disk) has been considered. The relation between the percolation thresholds in this model and the quantities characterizing its effective conductivity in the limit of low concentrations of inclusions has been established.     

Electrical conductivity of a two-dimensional model for a composite material with structural anisotropy

The electrical conductivity of a structurally anisotropic two-dimensional model for a composite material is considered. The model represents an isotropic matrix with a system of nonconducting inclusions in the form of mutually perpendicular scratches of various lengths. The centers of the scratches are chaotically distributed in plane (x, y). The approximate effective medium method is used to derive an expression for effective conductivity tensor $\hat \sigma _e$ that satisfactorily describes the electrical conductivity of this model over a wide concentration range. The model conductivity in the critical region is considered in terms of the similarity hypothesis.     

Electric conductivity of inhomogeneous two-component media in two dimensions

The electric conductivity is calculated for regular inhomogeneous two-component isotropic medium in which droplets of one phase with conductivity σ₂ are embedded in another, with conductivity σ₁. An expression is formulated that can be used in many different situations and is of particular relevance in the case where the relative proportion of the components is temperature-dependent and varies over a wide range. Behavior of the effective conductivity depends on the spatial arrangements and the shape of the inclusions.     

Effective AC response of nonlinear spherical coated composite

An effective nonlinear response of a nonlinear composite with spherical coated inclusions randomly embedded in a host medium under the action of an external AC electric field, {{\bm E}}_a = {{\bm E}}_1 \sin (\omega t) + {{\bm E}}_3 \sin (3\omega t), is investigated using a perturbation method. The local potentials of the composite at higher harmonics are given both in the region of local inclusion particles and in the local host region under the external AC electric field. All effective nonlinear responses of the composite and the relationship between the effective nonlinear responses at the fundamental frequency and third harmonics are also studied for spherical coated inclusion in a dilute limit.     

Nanocomposite-based ultrathin polarization beamsplitter

In terms of the effective medium approximation, the optical properties of heterogeneous composite materials with disordered nanosized metal inclusions of spheroidal shape with plasmon resonances lying in the visible spectral range are studied. The conditions are analyzed under which the optical characteristics of the composite with axial symmetry of the inclusion orientation distribution with respect to a certain preferential direction significantly depends on the electric field direction in the electromagnetic wave. It is shown that, in the vicinity of the plasmon resonance of inclusions, the composite layer of subwavelength thickness may exhibit a high polarization selectivity in both reflection and transmission with moderate absorption. The effect of the orientational disorder of inclusions on the optical characteristics of a polarization splitter of this kind is discussed. The predictions based on equations of quasi-electrostatic effective-medium model agree well with the results of exact numerical solution of the Maxwell equations.     

To the theory of conduction of binary composites

The relationship between the local electric field strength in a binary composite, as an example, with its macroscopic characteristics of a nonuniform medium (effective conductivity σ _e and the derivatives of σ _e with respect to the concentrations and conductivities of the individual components) is discussed. It was demonstrated that the determination of all these parameters in a numerical experiment makes it possible to obtain a detailed information on the properties of the effective conductivity σ _e , especially near the percolation threshold, a metal-dielectric phase transition.     

Effect of macroscopic inclusions on the electrical constants of solids

The problem of streamline current flow in an anisotropic medium with an ellipsoidally shaped macroscopic inclusion having a conductivity tensor different from that of the medium is solved. The solution obtained allowed us to find an expression for the effective conductivity tensor of the anisotropic medium with anisotropic ellipsoidal inclusions in a magnetic field. The problem of the effective values of the magnetoresistance coefficients of a medium with spherical dielectric inclusions is examined as a special case of the application of the general formula. It is shown how one may analyze galvanomagnetic effects in composites with the aid of the results obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 32–37, May, 1978.The authors are deeply grateful to V. M. Lenchenko for his continuous attention to this paper and for valuable comments.     

Thermoelectric composite materials based on intermediate-valence cerium and ytterbium intermetallic compounds

An important thermoelectric characteristic-the power factor of composite thermoelectric materials—is calculated on the basis of performed measurements of the thermopower, electric conductivity, thermal conductivity, and reference data. The investigated composites consist of intermediate-valence CeNi and YbAl₃ intermetallic systems and elementary metals, nickel and chromium. On account of the specific transport properties of a heterogeneous medium, it becomes possible to increase the value of the power factor in composites at a sufficiently low concentrations of rare-earth-element-based intermetallic compounds. The dependences of the composite-thermoelectric-material power factor on the temperature and the mass fraction of valence-instable components are obtained.     

Transmission spectra and the effective parameters for planar metamaterials with omega shaped metallic inclusions

Planar metamaterials with omega shaped metallic inclusions were studied experimentally and theoretically. Our results show that when the incidence is perpendicular to the plane of the omega structure, the omega medium acts effectively as an electric resonator metamaterial. The stop band of the omega medium is due to the negative part of the electric resonance of the omega structure. The transmission band of the composite metamaterial (CMM) that is based on the omega medium is due to the strong positive part of the electric resonance of the omega structure. Consequently, the transmission band of the CMM does not coincide with the stop band of the omega medium. Furthermore, the transmission band of the CMM is a band with positive refractive indices. Our experimental and numerical results are in good agreement.     

On the theory of galvanomagnetic properties of composites

The conductivity of composites in the presence of a magnetic field H is considered. The galvanomagnetic characteristics for a weakly inhomogeneous medium are determined in explicit form in an approximation quadratic in the deviations of conductivity tensor $\hat \sigma $ (r) from its mean value 〈 $\hat \sigma $ 〉. The contribution to the effective conductivity tensor $\hat \sigma _e $ linear in concentration c of inclusions for a composite with a small value of c is expressed in terms of the dipole polarizability of an individual inclusion, which is defined in the transformed system in which it is surrounded by an isotropic matrix with a scalar conductivity. Transition to this system is performed using a symmetry transformation that does not change the dc equations. An approximate approach proposed for describing the galvanomagnetic properties of composites in the wide range of parameters appearing in the problem generalizes the standard theory of an effective medium to the case of anisotropic systems with inclusions of arbitrary shape in field H ≠ 0.     

Symmetry transformation in the problem of the conductivity of anisotropic composites

A transformation of the coordinates, current density, and electric field strength has been proposed such that holds the direct-current equations. One of the components of a composite can be made isotropic by choosing the coefficients of the transformation. This allows the generalization of the standard theory of the effective medium to the case of an anisotropic composite with inclusions of an arbitrary shape.     

Increase and Decrease of the Effective Conductivity of Two Phase Composites due to Polydispersity

We present a two-dimensional mathematical model of a composite material with conducting inclusions (fibers) embedded in a matrix. Our main objective is to study how polydispersity (two different sizes of particles) affects the overall conductivity of the composite. If the conductivity of inclusions is higher than the conductivity of the matrix, then previous studies suggest an increase of the effective conductivity due to polydispersity. We show that for high volume fraction when inclusions are not well-separated and percolation effects play a significant role, polydispersity may result in either an increase or decrease of the effective conductivity. Our proof is based on the method of functional equations and it provides sufficient conditions for both the increase and the decrease of the effective conductivity.     

二元无规混合系统的有效介质理论

本文从二元无规混合物的两种不同拓扑结构出发,在Maxwell-Garnett理论的基础上,提出一种自洽的方法以改进类平均场的Bruggeman有效介质理论。导出了二元无规混合物有效电导率的普适式,研究了一些实际材料的电导率和热导率问题,理论计算结果与实验数据符合甚好。 关键词：     

Effect of the spatial and temporal distribution of molecular ions in the ionospheric E-field on the behavior of <Emphasis Type="Italic">N</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript>F2 during the geomagnetic storm of March 17–23, 2015

We consider different approaches to calculating the ion composition in the lower ionosphere and use two methods for modeling the concentration of molecular ions. The first method allows us to solve an equation with an effective recombination coefficient for the total concentration of molecular ions, and the second method calculates their concentrations separately. Numerical experiments were performed using a global self-consistent model of the thermosphere, ionosphere, and protonosphere (GSM TIP) for the conditions of March 16–20, 2015. We show that the second method, which provides a more accurate approximation, leads to significant consequences. Due to a strong change in the calculated concentration of ions in the E-region, the conductivity varies thus affecting the qualitative and quantitative behavior of the electric dynamo field at low and equatorial latitudes. Even without mesospheric tides and the electric dynamo field in the F-region, the calculation of partial concentrations of molecular ions makes it possible to qualitatively reproduce the outburst of the eastern electric field observed at the geomagnetic equator and in its low-latitude vicinity. During geomagnetic disturbances, a more accurate approximation leads to significant changes in the pattern of electron density perturbations at the heights of the ionospheric F-region in comparison with that obtained with the calculated total concentration of molecular ions.