Alexander S. Starkov

The paper examines the problem of finding normal modes in a system of two co-directional dielectric cylinders (waveguides). If the distance between the cylinders is large, their wavefields do not overlap and they can be considered independently. On the other hand, if the distance between the cylinders is small, the mode interaction becomes noticeable. This leads to a shift in the natural frequencies of the system compared to the frequencies of the non-interacting cylinders. This shift can be successfully determined using perturbation theory. Since the natural frequencies for a single cylinder are doubly degenerate due to axial symmetry, each natural frequency splits into two. Explicit expressions for the shift in natural frequency caused by the presence of the second cylinder are given, containing integrals of known functions. The dependence of the natural frequency shift on the geometrical and physical parameters of the second waveguide is calculated using the proposed approach. According to the theoretical estimates confirmed by numerical calculations, the frequency splitting is much smaller than its shift. The law of decrease of frequency change with change of distance between cylinders is analysed and analytical expressions for the distance corresponding to the maximum splitting of frequencies are derived. The results can be readily applied for modelling and optimization of various devices based on electromagnetic principles, such as antennas, waveguides, microdisk laser systems, transmission lines, and others.

The effective thermal characteristics of composite materials used in the theory of solidstate cooling are studied. Two classes of composites are considered: layered structures consisting of a large number of nano-sized layers and two-phase granular composites. It is assumed that the interfaces between media are imperfect. The Kapitza temperature jump occurs at the interfaces. The effective characteristics of layered structures are obtained using the matrix homogenization method. The homogenization of the characteristics of granular composites is based on the Bruggeman approach. Formulas taking into account the influence of the interlayer Kapitza resistance on the homogenized thermal characteristics of the structure are obtained. Expressions for average values of heat sources are derived.

Introduction. Ferroelectric films are widely used for radiotechnical, microwave microelectronic, sensoric, and energy conversion purposes. Such a diverse application range demands film materials with specific electrophysical properties. For instance, while energy storage applications require materials with a high dielectric constant, energy conversion devices largely use those with a low dielectric constant. The necessary physical properties can be achieved using multicomponent ferroelectric structures, such as solid solutions, composites, and multilayer film structures. Mechanical stresses between the substrate and ferroelectric layers play an extremely important role in dielectric properties of multilayer structures.Aim. Development of a mathematical model quantifying the ferroelectric polarization, static dielectric constant, as well as pyroelectric and electrocaloric properties of multilayered ferroelectric film structures.Materials and methods. The presented model is based on the Landau–Ginzburg–Devonshire model (LGD) considering elasticity equations and using electric induction as the order parameter.Results. The developed mathematical model based on LGD provides for a quantifiable description of dielectric, pyroelectric, and electrocaloric properties of layered ferroelectric structures. This model displays the effect of the thickness ratio of polycrystalline layers and grain size distribution on the dielectric properties of films.Conclusion. The developed quantitative model demonstrates the dependence of the thickness, grain size, and stacking order of ferroelectric layers on the dielectric constant and pyroelectric coefficient of multilayered polycrystalline film structures. The presented model can be applied when optimizing the parameters of multilayer structures with respect to their application area.

We consider the problem of determining the permittivity and the electrocaloric effect in the model of a ferroelectric ceramics grain. We assume that a grain consists of a spherical ferroelectric core coated with a dielectric shell and placed into a dielectric matrix. The transition layer thickness is assumed small as compared to the grain size. The dependence of the polarization on the electric field in the core is given by the nonlinear Ginzburg–Landau equation. The polarization reversal is induced by a change in the electric field that is considered uniform at large distance from the grain. The electrostriction effect in the core–shell–matrix three-phase system produces an elastic field described by linear equations. To take into account the effect of domain walls on the physical characteristics of the ceramics in the given model, we propose that the Kittel–Mitsui–Furuichi approach be used. The proposed computational algorithm makes it possible to refine the dependence of the number of domains on the spherical grain size. The electrocaloric effect in the grain is represented by the combination of the primary and secondary effects that appear due to ordering of dipole moments of the ferroelectric with the perovskite structure; by way of example, we consider the barium titanate ceramics. For this material, we report on the results of calculations of the dependences of the permittivity and individual electrocaloric effect components on the grain size.

The paper presents a stochastic analysis of the growth rate of viscous fingers in miscible displacement in a heterogeneous porous medium. The statistical parameters characterizing the permeability distribution of a reservoir vary over a wide range. The formation of fingers is provided by the mixing of different-viscosity fluids -- water and polymer solution. The distribution functions of the growth rate of viscous fingers are numerically determined and visualized. Careful data processing reveals the non-monotonic nature of the dependence of the front end of the mixing zone on the correlation length of the permeability (describing the medium graininess) of the reservoir formation. It is demonstrated that an increase in graininess up to a certain value causes an expansion of the distribution shape and a shift of the distribution maximum to the region of higher velocities. In addition, an increase in the standard deviation of permeability leads to a slight change in the shape and characteristics of the density distribution of the growth rates of viscous fingers. The theoretical predictions within the framework of the transverse flow equilibrium approximation and the Koval model are contrasted with the numerically computed velocity distributions.

This paper presents a theoretical model for describing the thermodynamic properties of doped ferroelectric crystals based on a modified Weiss mean-field approach. Accounting for quadrupole and octupole terms in the expression for the effective field within the Weiss model makes it possible to move from the Langevin equation to the Landau–Ginzburg equation. Furthermore, the coefficients of the Landau–Ginzburg equation can be expressed in terms of the physical parameters of the crystal lattice. For these parameters, analytical expressions are proposed that describe their change when adding dopants in ceramic matrix composites. Perovskite barium titanate ceramics with a variety of inclusions is considered as an application example of the developed method. The obtained agreement between the analytical and experimental results for barium titanate ceramics with lanthanum/magnesium/zirconium dopants gives us hope of the applicability of the present theory to the calculation of other doped ferroelectrics as well.

The paper presents a calculation of doping concentration profile in a two-layer barium titanate film, one of the layers of which contains lanthanum impurity. The theoretically predicted distributions were experimentally verified. Influence of the doping profile on the magnitude of the electrocaloric (EC) response of ferroelectric films is assessed by numerical simulation. It is demonstrated that at the same La concentration, the magnitude of the EC effect can change by 40% due to the distribution of the lanthanum concentration in the structure. The results obtained allow optimizing the technological process to ensure the required characteristics of ferroelectric thin films.