E.I. Veliev

• PhD, Prof.
• Professor (Full) at National Technical University "Kharkiv Polytechnic Institute"

EIDV) (Словацька Республіка) Університет менеджменту безпеки в Кошице (Словацька Республіка) Університет «ARTIFEX» (Румунія) Міжнародна академія прикладних наук в Ломжі (Республіка Польща) Стамбульський технічний університет (Турецька Республіка) ГО «Міжнародна фундація науковців та освітян» ГО «Федерація, аудиторів і фінансистів АПК України» ТРАНС...

Abstract. This study investigates an effective method for solving one class of integral equations. It addresses various two dimensional problems related to do diffraction theory by metal screens, which are reduced to these integral equations. A novel approach for solving this class of integral equations is proposed. The study foceses on investigati...

The present study investigates a classical problem with different solution approaches. The E-polarized electromagnetic scattering by half-plane with fractional boundary conditions via two different methods is studied and the results are compared. The outcomes reveal that Legendre exponential functions are suitable as a complete set to express the i...

This study investigates several substantial questions arising in the diffraction by circular surfaces with the fractional boundary condition, which is the generalization of Dirichlet and Neumann boundary conditions. The study analyses the electromagnetic E-polarized plane wave diffraction by a slotted circular cylinder with the fractional boundary...

In the present study, a new methodology in computational electromagnetics is developed for two-dimensional arbitrarily-shaped objects with impedance boundary conditions. The proposed approach investigates the E-polarized electromagnetic diffraction by a two-dimensional object with the Leontovich boundary condition. The scattered electric and magnet...

The study investigates the H-polarized plane wave diffraction by a slotted cylinder with different surface impedances employing an analytical-numerical approach. The solution is obtained by expressing the current distribution on the obstacle with Gegenbauer poly-nomials considering the edge conditions. To obtain the field and current distribution o...

The study investigates the electromagnetic plane wave diffraction by two concentric slotted cylinders with variably placed slits. Unlike the previous studies, the effect of rotation on the resonance characteristics and near-field distributions is analyzed in the present work, which is not studied yet. The study focuses on diffraction by both E-and...

An accurate hybrid method (numerical-analytical method) for the diffraction of H-polarized electromagnetic plane wave by perfectly electric conducting cylindrical bodies containing edges and a longitudinal slit aperture is proposed. This method is the combination of the Method of Moment and semi-inversion method. The current density function is exp...

In this study, the cylindrical wave diffraction by double strips with different lengths and boundary conditions are investigated. The scattered fields are found by the Numerical-Analytical Approach. The double-strip structure satisfies integral boundary conditions which are the generalization of Dirichlet and Neumann boundary conditions. The electr...

In this article, there is considered the electromagnetic plane wave diffraction by the half-plane with fractional boundary conditions. As a mathematical tool, the fractional calculus is used. The theoretical part is given based on which the near field, Poynting vector and energy density distribution are calculated. Interesting results are obtained...

In this article, a new solution method is proposed for plane wave diffraction by a strip. On the surface of the strip, an integral boundary condition is used. The impedance of the strip is investigated. The theoretical and numerical analyses show that there is a relation between the complex-valued fractional order of the integral boundary condition...

In this article, the plane wave diffraction by two strips is studied. Fractional boundary condition is required on strips when the fractional order for each strip is different. The goal of the paper is to investigate the resonant properties of such structures. The mathematical apparatus for the solution of the problem is given. The frequency depend...

In this article, the diffraction of the electromagnetic wave by the building with two rooms is considered. The rooms have doors and windows with lossy dielectric walls. The electromagnetic properties of the building as an opened coupled resonator system are investigated at different source locations and several frequencies including 5G band. The pr...

In this article, the diffraction of plane electromagnetic waves by double half-planes with fractional boundary conditions is considered. As particular cases, the diffractions by wedges and corners are considered for different values of fractional orders. The results are compared to the analytical ones. The interesting properties of wedge diffractio...

The electromagnetic plane wave diffraction by the half-plane with fractional boundary conditions is considered in this article. The theoretical part is given based on that the near field, pointing vector, and energy density distribution are calculated for different values of the fractional order. The results are compared with classical cases for ma...

The book is devoted to the application of the mathematical apparatus of non-integer derivatives to the solution of the diffraction problems by the planar screens.

In this article, a solution of the plane wave diffraction problem by two axisymmetric strips with different dimensions is considered. Fractional boundary conditions are required on the surface of each strip. Several cases of strip's dimension, configurations, and fractional orders are considered, and numerical results are obtained. The near electri...

M54 Eldar I. Veliyev Methods of semi-inversion and non-integer derivation in boundaryvalue problems of diffraction theory. – Kharkov: «Kontrast», – 2019 – 272 p. ISBN 978-617-7405-28-2 The monograph includes original works of the author, in which, based on the deve loped methods for solving boundary problems, the features of wave scatte ring by var...

In this paper, we have studied the analysis of current distributions and radar cross sections of the line source scattering from an impedance strip. The problem was solved with the fractional derivative method previously. Here, the specific case of the fractional derivative method is investigated. The problem under consideration on the basis of var...

In this paper, we have studied the analysis of current distributions and radar cross sections of line source scattering from impedance strip. The problem was solved with fractional derivative method previously. Here, the specific case of fractional derivative method is investigated. The problem under consideration on the basis of various methods is...

In this paper, we have considered the problem of plane wave diffraction by two strips. This structure is an open resonator which consists of two axisymmetric strips of different widths. The application of the Fractional Derivative (FDM) method allows one to obtain a general solution, which, as a particular case, contains, for fractional order (FO)...

Abstract—In this article, a solution of the plane wave diffraction problem by two axisymmetric strips with different dimensions is considered. Fractional boundary conditions are required on the surface of each strip. Several cases of strip’s dimension, configurations, and fractional orders are considered, and numerical results are obtained. The nea...

Earlier we considered the use of the apparatus of fractional derivatives to solve the two-dimensional problem of diffraction of a plane wave on an impedance strip. We introduced the concept of a "fractional strip". A "fractional strip" is understood as a strip on the surface, which is subject to fractional boundary conditions (FBC). The problem und...

Abstract— In this paper, two dimensional problem of diffraction of a cylindrical wave on an impedance strip is studied. For fractional order equal to 0.5, the solution can be found analytically. In the paper, also numerical results for fractional order equal to 0.5, is presented. Keywords— cylindrical wave, diffraction, fractional boundary conditi...

Рассмотрены ряды Шлемильха (Schlomilch), которые применяются при решении различных задач дифракции волн, при расчете волноводов сложного сечения и т.д. Однако их вычисление весьма трудоемко. Поэтому предлагаются два новых представления рядов Шлемильха по фугкциям Бесселя, которые используют быстросходящиеся ряды по элементарным функциям. В частных...

The article offers the methods of solving integral equations (IE) arising in many boundary value problems of applied electrodynamics. These methods are based on the use of orthogonal polynomials (OP), which allow to consider features of the sought functions at the ends of the region of integration. As a rule, in real radiophysical problems these fe...

Proposed method to solve difference-integral equation of a special type, arising in problems of diffraction by boundaries is described by fractional boundary condition (FBC). The method is considered on two boundaries – a strip and a half-plane with FBC when the fractional order varies from 0 to 1. The proposed method is based on application of ort...

Problems of diffraction by plane screens described by fractional boundary conditions (FBC) are considered. FBC involves fractional derivative of tangential field components. FBC can be treated as intermediate case between well known boundary conditions for perfectly electric conductor (PEC) and perfectly magnetic conductor (PMC). A method to solve...

The possibility is analyzed for applying fractional operators in the problems of electromagnetic wave reflection from plane boundaries. The fractional derivative and fractional curl operator are considered, which are obtained as a result of fractionalization of the ordinary derivation and curl operators. The fractional curl operator can be used for...

In this paper, we analyze some applications of the fractional boundary conditions (FBC) in the two-dimensional problems of wave reflection and diffraction. FBC are used to simulate reflection from dielectric slab where the fractional order depends on the layer parameters. The diffraction of an E-polarized electromagnetic field by a strip with FBC i...

In this paper two-dimensional problem of plane-wave diffraction by a "fractional strip" is studied. "Fractional strip" is introduced as a strip with fractional boundary conditions (FBC) involving fractional derivatives of the field components. FBC describe intermediate boundary between perfect electric conductor (PEC) and perfect magnetic conductor...

New fractional boundary conditions (FBC) on plane boundaries are introduced. FBC act as intermediate case between perfect electric conductor and perfect magnetic conductor. In certain sense FBC are analogue of commonly used impedance boundary conditions with pure imaginary impedance. The relation between fractional order and impedance is shown. Pla...

Applications of fractional operators approach to electromagnetic waves reflection and diffraction problems are considered. Reflection properties of fractional or intermediate solutions obtained using fractional curl operator are analyzed. It is shown that this approach is a useful technique for the description of solutions to the reflection problem...

Applications of fractional operators approach to electromagnetic waves reflection problems are considered. Reflection properties of fractional or intermediate solutions are analyzed. It is shown that this approach is a useful technique for the description of solutions to the reflection problems for some known media in terms of the fractional order...

This paper is devoted to the description of new boundaries using the fractional field, which is constructed by applying the fractional curl operator. Fractional field allows to describe the solution of problem of reflection from specific boundaries of "impedance type", which generalizes canonical boundaries (perfect electric conductor (PEC), perfec...

In this paper the fractional curl operator curlalpha is applied to obtain fractional sources as a generalization of the electric and magnetic Hertz dipoles. A physical meaning of the fractional curl operator in considered problem is shown: curlalpha results in the coupling of the original electric and magnetic currents. For the values of the fracti...

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In this paper we introduce a new definition for fractional derivatives of function ψ(r~) which satisfies the homogeneous Helmholtz equation. It is shown, that we have come to such a presentation after consideration of "fractional" solutions of ordinary Helmholtz equation. Also "fractional boundary conditions" are introduced.

The fractional curl operator and its possible applications in electromagnetic problems are discussed. Specifically, we consider radiation from sheet and line current distributions. Applying fractionalized curl operator we obtain new "fractional" fields and corresponding "fractional" currents, and analyze their physical meanings. "Fractional" field...

The purpose of this paper is to investigate some applications of the fractionalized curl operator in the scattering problems. Using the technique of fractionalizing a linear operator we obtain the presentation for the fractional curl operator for the functions of two variables expressed via exponents. We use this presentation in a plane wave reflec...

In this study, the diffraction of a plane wave by an infinitely long strip, having the same impedance on both faces with a width of 2a is investigated. The diffracted field is expressed by an integral in terms of the induced electric and magnetic current densities. Applying the boundary condition to the integral representation of the scattered fiel...

Results of mathematical simulation of a spherical fractal emitter are presented. The application of a fractional calculation for the mathematical model generation is justified. The α-characteristic of the magnetic field component of a symmetric spherical emitter and current distribution on a surface is obtained. The properties of a spherical fracta...

The plane wave diffraction by a thin material strip is analyzed for both E and H-polarizations using a new analytical-numerical approach together with approximate boundary conditions. The problem is reduced to the solution of infinite systems of linear algebraic equations. The final results are valid provided that the thickness of the strip is smal...

The plane wave diffraction by a strip with two different surface impedances is rigorously analyzed for both E and H polarizations using a new analytical-numerical approach. Applying the boundary condition to an integral representation of the scattered field, the problem is formulated in terms of simultaneous integral equations satisfied by the elec...

In this paper, a new analytical method essentially different from the others is developed for obtaining a rigorous solution of a half-plane diffraction problem.

In this paper, we analyze the impedance strip diffraction problem for H-polarized plane wave incidence by means of an analytical-numerical approach. Applying the boundary condition to an integral representation of the scattered field, the problem is formulated as simultaneous integral equations satisfied by the electric and magnetic current density...

In the present paper we apply the concept of fractional calculus to one of the basic problems in electromagnetics, the problem of radiation of the fractal radiators and their corresponding potentials. The concept of a radiating contour fractal geometrical structure is the physical basis of our consideration. In this connection, we assume the occurr...

The analysis of the scattering by resistive strips is an important subject in diffraction theory. This geometry can be regarded as a suitable model of thin dielectric slabs and coating of finite length which are often used for radar cross section (RCS) reduction. In this paper, we shall analyze the plane wave diffraction by a resistive strip using...

Alternative representations as series of more elementary functions or an analytical form for the Schlömilch type series with the Bessel functions are derived. Various special cases of such representations, which arise in different diffraction problems are presented. By detailed examinations of the convergence in numerical computation, a great reduc...

Development of reliable models for microwave emission and scattering from terrain, ie, vegetation, snow, forest, is among the most important problems of microwave remote sensing. Current investigations in this field are mainly directed to the modeling of microwave scattering from plant elements and vegetation as a whole and modeling of the effectiv...

An accurate numerical-analytical method of solution of the problem of wave diffraction by a perfectly conductive cylindrical body with a cross-section formed by crossing of the “key” elements (such as flat strips and cylindrical screens) is proposed. It is based on the ideas of the moment method and the partial inversion technique of the initial pr...

Electromagnetic Wve Diffraction

An efficient method of solution for problem of wave diffraction by a set of perfectly conducting flat strips is presented, where both E- and H-polarizations are treated. By using a spectral approach, the problem is reduced to a system of linear algebraic equations for the unknown Fourier coefficients of the current density function. A truncation of...

E-polarized wave scattering by a two-dimensional unclosed cylindrical screen is considered. There has been considerable interest in utilizing such structures as reflectors of various geometries in modern communication and deep-space satellites and ground antenna systems. The authors develop a simple effective method for solution to this problem and...

The effect of the anomalously weak scattering of the electromagnetic field of an open resonator by a perfectly conducting rectangular cylinder located inside the resonator has been demonstrated theoretically and experimentally. It is shown that this effect results from the antiphase addition of fields reflected from the different faces of a beam wh...

A rigorous method is proposed for solving problems of wave diffraction by an ideally conducting rectangular cylinder, considered as a composite body formed by the 'gluing' of plane ribbons. The approach is based on partial operator inversion and the method of moments. The problem involves the solution of infinite systems of linear algebraic equatio...

Wave diffraction by a plane ribbon of finite thickness is investigated in the infinite-thin-screen approximation with reference to the use of conducting screens in radio physics and electronics. Calculations of current distribution on the ribbon surface indicate that the infinite-thin-screen model can lead to significant errors in the determination...

A general method is developed for solving dual integral equtions with a kernel in the form of trigonometric functions. The proposed approach is applied to the study of the diffraction of a plane H-polarized wave by an infinitely thin and ideally conducting plane ribbon.

The effect of a finite number of two-dimensional resonant scatterers (cylinders with a longitudinal slot) on the formation of the far field of a concentrated source (a magnetic-current filament) is investigated. The quasi-optimal position and orientation of the open cylinders are determined with the aim of obtaining the maximum directive gain. It i...

The electromagnetic-field distribution in the cross section of an open resonator (OR) for the lowest oscillation mode was studied experimentally. The experiment involved the excitation of the OR by an amplitude-modulated microwave signal from a diffraction-radiation generator through one of the coupling elements on a spherical mirror at a frequency...

The focusing effect of an inhomogeneity in the form of a plane parallel layer inside an open resonator is investigated, and it is shown that such an inhomogeneity leads to changes in the resonance beam parameters. Depending on its parameters and its position within the resonator, such an inhomogeneity can behave like a focusing or a defocusing lens...

The authors investigate the spectral and energy characteristics of an open resonator with an inhomogeneity in the form of a twolayer strip grating with an arbitrary interlayer spacing for the fundamental mode. A solution of the problem is given, along with its numerical implementation for an open resonator with a single-layer grating. It is shown t...

An efficient rigorous numerical method is proposed for solving the problem of wave diffraction by a perfectly conducting polygonal cylinder. In accordance with this method, the problem of finding the scattering field of each face of the polygonal cylinder is reduced to that of solving a system of coupled paired integral equations for the Fourier tr...

The spectral and energy characteristics of an open resonator (OR) with an inhomogeneity in the form of a two-layer ribbon diffraction grating with an arbitrary distance between the gratings are studied for the main oscillation frequency of the OR. The solution and its numerical implementation are given for an OR with a one-layer grating. Two mechan...

A rigorous solution is obtained for the problem concerning the diffraction of a plane H-polarized electromagnetic wave by a grating consisting of partially shielded dielectric bars of circular cross section. By using the method of semiinversion, the problem is reduced to that of solving a system of linear algebraic equations of the second kind whic...

An efficient rigorous numerical approach is proposed for solving problems of wave diffraction by cylindrical bodies formed by parts of intersecting circular cylinders. In accordance with the method proposed here, the diffraction field of each side of the cylinder is determined by solving a system of coupled pairs of summator equations for the Fouri...

A rigorous solution of the diffraction problem is used to study the electrodynamic properties of a structure consisting of a finite number of identical open screens situated in a single plane. Emphasis is placed on the effect of such structures on the radiation field of a concentrated source in the form of a magnetic-current thread.