scholarly journals Analysis of a Coaxial Waveguide with Finite-Length Impedance Loadings in the Inner and Outer Conductors

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Feray Hacıvelioğlu ◽  
Alinur Büyükaksoy
Keyword(s):  
Reflection Coefficient ◽  
Boundary Value Problem ◽  
Finite Length ◽  
Formal Solution ◽  
Coaxial Waveguide ◽  
Algebraic Equations ◽  
Coaxial Cylinders ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Band Stop Filter

A rigorous Wiener-Hopf approach is used to investigate the band stop filter characteristics of a coaxial waveguide with finite-length impedance loading. The representation of the solution to the boundary-value problem in terms of Fourier integrals leads to two simultaneous modified Wiener-Hopf equations whose formal solution is obtained by using the factorization and decomposition procedures. The solution involves 16 infinite sets of unknown coefficients satisfying 16 infinite systems of linear algebraic equations. These systems are solved numerically and some graphical results showing the influence of the spacing between the coaxial cylinders, the surface impedances, and the length of the impedance loadings on the reflection coefficient are presented.

Cosserat Spectrum of an Axisymmetric Elasticity Problem for a Finite-Length Solid Cylinder

2018 ◽  
Vol 35 (3) ◽  
pp. 343-349
Author(s):  
Yu. V. Tokovyy
Keyword(s):  
Asymptotic Behavior ◽  
Finite Length ◽  
Solution Method ◽  
Superposition Method ◽  
Algebraic Equations ◽  
Solid Cylinder ◽  
Cosserat Spectrum ◽  
Linear Algebraic Equations ◽  
Key Features ◽  
Axisymmetric Elasticity

ABSTRACTAn algorithm for the computation and analysis of the Cosserat spectrum for an axisymmetric elasticity boundary-value problem in a finite-length solid cylinder with boundary conditions in terms of stresses is proposed. By making use of the cross-wise superposition method, the spectral problem is reduced to systems of linear algebraic equations. A solution method for the mentioned systems is presented and the asymptotic behavior of the Cosserat eigenvalues is established. On this basis, the key features of the Cosserat spectrum for the mentioned problem are analyzed with special attention given to the effect of the cylinder aspect ratio.

Wiener–Hopf analysis of the parallel plate wave guide with opposing rectangular dielectric-filled grooves

2008 ◽  
Vol 86 (5) ◽  
pp. 733-745 ◽  
Author(s):  
I H Tayyar ◽  
A Büyükaksoy ◽  
A Işıkyer
Keyword(s):  
Parallel Plate ◽  
Mixed Boundary ◽  
Dielectric Materials ◽  
Wave Guide ◽  
Algebraic Equations ◽  
Plate Wave ◽  
Linear Algebraic Equations ◽  
Band Stop Filter ◽  
Analytical Properties ◽  
Different Depths

The purpose of the present work is to provide a rigorous analysis of the parallel plate wave guide with two opposing rectangular grooves of different depths and filled with different dielectric materials. This configuration may be used as a band-stop filter. The representation of the solution to the three-part mixed boundary-value problem in terms of Fourier integrals leads to a couple of simultaneous modified Wiener–Hopf equations. By using the analytical properties of the functions that occur, the simultaneous modified Wiener–Hopf equations are reduced to the solution of four infinite systems of linear algebraic equations. These systems are solved numerically, and the band-stop filter characteristics of the reflection coefficient are studied in terms of frequency, groove sizes, and the parameters of the filling dielectric material.PACS Nos.: 42.25.Bs, 42.25.Gy, 42.82.Et

scholarly journals Excitation of anisotropic impedance metasurface in the form of elliptical cylinder.

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A.I. Semenikhin ◽  
◽  
D.V. Semenikhin ◽  
Keyword(s):  
Elliptical Cylinder ◽  
Impedance Tensor ◽  
Reflection Coefficients ◽  
Algebraic Equations ◽  
Partial Reflection ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
External Sources ◽  
Surface Impedance Tensor ◽  
Special Case

The problem of arbitrary excitation of waves by a system of external sources near an anisotropic metasurface in the form of an elliptical cylinder with a surface homogenized impedance tensor of general form is solved. The solution to the problem is written as a superposition of E- and H-waves in elliptical coordinates. The partial reflection coefficients of waves were found from the boundary conditions using the orthogonality of the Mathieu angular functions. For these coefficients, four coupled infinite systems of linear algebraic equations of the second kind are obtained. The conditions under which the solution of the excitation problem by the method of eigenfunctions is obtained in an explicit form are found and analyzed. It is shown that for this, the surface impedance tensor of a uniform metasurface must belong to a class of deviators (have zero diagonal elements). In the particular case of a mutual (most easily realized) metasurface, its impedance tensor should only be reactance. In another special case, the impedance tensor of a set of deviators describes a class of anisotropic nonreciprocal metasurfaces with the so-called perfect electromagnetic conductivity (PEMC).

scholarly journals A PROBLEM WITH PARAMETER FOR THE INTEGRO-DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 26 (1) ◽  
pp. 34-54
Author(s):  
Elmira A. Bakirova ◽  
Anar T. Assanova ◽  
Zhazira M. Kadirbayeva
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Cauchy Problems ◽  
Algebraic Equations ◽  
Integro Differential Equation ◽  
Loaded Differential Equation ◽  
Linear Algebraic Equations

The article proposes a numerically approximate method for solving a boundary value problem for an integro-differential equation with a parameter and considers its convergence, stability, and accuracy. The integro-differential equation with a parameter is approximated by a loaded differential equation with a parameter. A new general solution to the loaded differential equation with a parameter is introduced and its properties are described. The solvability of the boundary value problem for the loaded differential equation with a parameter is reduced to the solvability of a system of linear algebraic equations with respect to arbitrary vectors of the introduced general solution. The coefficients and the right-hand sides of the system are compiled through solutions of the Cauchy problems for ordinary differential equations. Algorithms are proposed for solving the boundary value problem for the loaded differential equation with a parameter. The relationship between the qualitative properties of the initial and approximate problems is established, and estimates of the differences between their solutions are given.

scholarly journals Quasihomogeneous Infinite Systems of Linear Algebraic Equations

2018 ◽  
Vol 1141 ◽  
pp. 012105
Author(s):  
F. M. Fedorov ◽  
N. N. Pavlov ◽  
O. F. Ivanova ◽  
S. V. Potapova
Keyword(s):  
Algebraic Equations ◽  
Infinite Systems ◽  
Linear Algebraic Equations

Electromagnetic field of the circular magnetic source in biconical section

2020 ◽  
Vol 2020 (48) ◽  
pp. 5-10
Author(s):  
O.M. Sharabura ◽  
◽  
D.B. Kuryliak ◽  
Keyword(s):  
Field Pattern ◽  
Geometrical Parameters ◽  
Algebraic Equations ◽  
Axially Symmetric ◽  
Reduction Procedure ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Regularization Techniques ◽  
Far Field Pattern ◽  
Analytical Regularization

The problem of axially-symmetric electromagnetic wave diffraction from the perfectly conducting biconical scatterer formed by the finite cone placed in the semi-infinite conical region is solved rigorously using the mode-matching and analytical regularization techniques. The problem is reduced to the infinite systems of linear algebraic equations (ISLAE) of the second kind. The obtained equations admit the reduction procedure and can be solved with a given accuracy for any geometrical parameters and frequency. The numerical examples of the solution are presented. The analysis of the source location influences on the far-field pattern for different geometrical parameters of the bicone is carried out.

scholarly journals ON A METHOD FOR SOLVING A LINEAR BOUNDARY VALUE PROBLEM FOR A SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS CONTAINING THE PARAMETER

2021 ◽  
Vol 73 (1) ◽  
pp. 23-31
Author(s):  
N.B. Iskakova ◽  
◽  
G.S. Alihanova ◽  
А.K. Duisen ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Degenerate Kernel ◽  
Algebraic Equations ◽  
Integro Differential Equation ◽  
Linear Algebraic Equations ◽  
The Given

In the present work for a limited period, we consider the system of integro-differential equations of containing the parameter. The kernel of the integral term is assumed to be degenerate, and as additional conditions for finding the values of the parameter and the solution of the given integro-differential equation, the values of the solution at the initial and final points of the given segment are given. The boundary value problem under consideration is investigated by D.S. Dzhumabaev's parametrization method. Based on the parameterization method, additional parameters are introduced. For a fixed value of the desired parameter, the solvability of the special Cauchy problem for a system of integro-differential equations with a degenerate kernel is established. Using the fundamental matrix of the differential part of the integro-differential equation and assuming the solvability of the special Cauchy problem, the original boundary value problem is reduced to a system of linear algebraic equations with respect to the introduced additional parameters. The existence of a solution to this system ensures the solvability of the problem under study. An algorithm for finding the solution of the initial problem based on the construction and solutions of a system of linear algebraic equations is proposed.

The radiation and scattering of surface waves by a vertical circular cylinder in a channel

1992 ◽  
Vol 338 (1650) ◽  
pp. 325-357 ◽  
Keyword(s):  
Circular Cylinder ◽  
Gravity Waves ◽  
The Body ◽  
Far Field ◽  
Algebraic Equations ◽  
Surface Gravity Waves ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Correct Form ◽  
Body Boundary

In this paper we consider the problems of the radiation and scattering of surface gravity waves by a vertical circular cylinder placed on the centreline of a channel of width 2 d and depth H , and either extending from the bottom through the free surface or truncated so as to fill only part of the depth. These problems are solved, for arbitrary incident wavenumber k , by constructing appropriate multipoles for cylinders placed symmetrically in channels and then using the body boundary condition to derive a set of infinite systems of linear algebraic equations. For the general problems considered here, this method is superior to the more usual approach of using a set of image cylinders to model the channel walls, in particular the occurrence of modes other than the fundamental when kd > is accurately modelled and the correct form predicted for the far-field.

Special infinite systems of linear algebraic equations

2021 ◽  
Author(s):  
Foma M. Fedorov ◽  
Oksana F. Ivanova ◽  
Nikifor N. Pavlov ◽  
Sargylana V. Potapova
Keyword(s):  
Algebraic Equations ◽  
Infinite Systems ◽  
Linear Algebraic Equations
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