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 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.

Calculation of Correlation Matrices for Linear Systems Subjected to Nonwhite Excitation

1972 ◽  
Vol 39 (2) ◽  
pp. 559-562 ◽  
Author(s):  
I-Min Yang ◽  
W. D. Iwan
Keyword(s):  
Spectral Density ◽  
Linear Systems ◽  
Random Response ◽  
Algebraic Equations ◽  
Correlation Matrices ◽  
Linear Algebraic Equations ◽  
Special Case

This paper presents an approach which provides a particularly simple and direct way of determining the instantaneous correlation matrices for the stationary random response of multidegree-of-freedom linear systems subjected to excitations of nearly arbitrary spectral density. In the special case of white excitation, the instantaneous correlation matrices are determined directly from a set of linear algebraic equations. When the excitation is nonwhite, some integrals must be evaluated before solving a system of linear algebraic equations. However, the form of these integrals is considerably simpler than that encountered in other common approaches.

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

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.

Simultaneous Wiener–Hopf equations

1980 ◽  
Vol 58 (3) ◽  
pp. 420-428 ◽  
Author(s):  
A. D. Rawlins
Keyword(s):  
Integral Equation ◽  
Half Plane ◽  
Fredholm Integral Equation ◽  
Coupled System ◽  
Algebraic Equations ◽  
Branch Points ◽  
Linear Algebraic Equations ◽  
Upper Half Plane ◽  
Infinite Set ◽  
Special Case

In Noble's book The Wiener Hopf Technique, Pergamon, 1958, he considers the coupled system of Wiener–Hopf equations (§4.4, pp. 153–154)[Formula: see text]He shows that provided the functions L(α), M(α), Q(α), and R(α) have only simple pole singularities the solution can be reduced to two sets of infinite simultaneous linear algebraic equations. In this article a different approach is used which gives the solution in the form of a Fredholm integral equation of the second kind. This Fredholm integral equation can be reduced to infinite sets of simultaneous linear algebraic equations under the less restrictive conditions that either (i) L(α)/M(α) has no branch points in the lower α-half plane: Im(α) < τ+; or (ii) Q(α)/R(α) has no branch points in the upper α-half plane: Im(α) > τ−. In the special case considered by Noble if L(α)/M(α) (or Q(α)/R(α)) only have simple poles in the lower (upper) half plane then the Fredholm integral equation reduces to one infinite set of simultaneous equations. This extends the Wiener–Hopf technique to yet a larger class of boundary value problems, and simplifies the numerical computations.

scholarly journals Diffraction of sound waves by a lined cylindrical cavity

2020 ◽  
Vol 19 (1-2) ◽  
pp. 38-56
Author(s):  
Burhan Tiryakioglu
Keyword(s):  
Mode Matching ◽  
Sound Waves ◽  
Algebraic Equations ◽  
Hopf Equation ◽  
Matching Method ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
The Fourier Transform ◽  
Sound Diffraction ◽  
Selection Of

In this paper, diffraction of sound waves through a lined cavity is analyzed rigorously. The inner–outer surfaces of the cavity and the base of the cavity are coated with three different absorbing linings. By using the Fourier transform technique in conjunction with the Mode-Matching method, the related boundary value problem is formulated as a Wiener–Hopf equation. In the solution, two infinite sets of unknown coefficients are involved that satisfy two infinite systems of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem. The graphical results are also presented which show that how efficiently the sound diffraction can be reduced by selection of problem parameters.

scholarly journals Verification of Computing Grids with Special Edge Conditions by Infinite Petri Nets

2015 ◽  
Vol 19 (6) ◽  
pp. 21-33
Author(s):  
D. A. Zaitsev
Keyword(s):  
Petri Nets ◽  
Algebraic Equations ◽  
Square Grid ◽  
Parametric Solutions ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Edge Conditions ◽  
Computing Grid

A technique of the computing grid verification using invariants of infinite Petri nets was presented. Models of square grid structures in the form of parametric Petri nets for such edge conditions as connection of edges and truncated devices were constructed. Infinite systems of linear algebraic equations were composed on parametric Petri nets for calculating p-invariants; their parametric solutions were obtained. P-invariant Petri nets are structuraly conservative and bounded that together with liveness are the properties of ideal systems. Liveness investigation based on siphons and traps can be implemented by using p-invariants of modified nets.

Sign in / Sign up

Export Citation Format

Share Document