Thin-wire radiating structures with double symmetry

The problems of electrodynamic analysis of thin-wire radiating structures with double symmetry are considered. New generalized integral representations of the electromagnetic field are obtained for the case of structures with single and double symmetries. Based on the obtained expressions, mathematical models of two - and four-way elliptical spiral antennas are constructed. It is shown that taking into account double symmetry in solving the internal electrodynamic problem leads to a set of independent Fredholm integral equations of the first kind written with respect to the distributions of normal current waves, which significantly simplifies the solution of the internal electrodynamic problem. Comparisons of current distributions along conductors, their input resistance dependences on the radius of the structure, and normalized radiation patterns for two- and four-way spiral emitters are presented.

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Solving problems of radiation and diffraction electromagnetic waves based on integral representations electromagnetic field

Physics of Wave Processes and Radio Systems ◽

10.18469/1810-3189.2020.23.4.19-35 ◽

2021 ◽

Vol 23 (4) ◽

pp. 19-35

Author(s):

Dmitry P. Tabakov ◽

Sergey V. Morozov

Keyword(s):

Mathematical Model ◽

Electromagnetic Field ◽

Electromagnetic Waves ◽

Potential Method ◽

Field Method ◽

Integral Representations ◽

Electrodynamic Problem ◽

Electrodynamic Analysis ◽

Projection Functions ◽

Further Development

Annotation Various forms of integral representations of the electromagnetic field are considered. It is shown that the use of analytically developed integral representations of the electromagnetic field instead of the vector potential method makes it possible to significantly simplify the formulation of the internal and external electrodynamic problem for specific structures. The numerical results of solving problems of radiation and diffraction of electromagnetic waves are presented. It is shown that taking into account the peculiarities of the geometry and using projection functions close to the eigenfunctions of the integral operator of the internal electrodynamic problem for basic elements make it possible to construct effective algorithms for the electrodynamic analysis of metastructures. A mathematical model of a multistage chiral frame is proposed. By the example of a tubular vibrator, the possibility of approximating the solution of an internal electrodynamic problem using eigenfunctions is demonstrated. The prospects for further development of the integral representations of the electromagnetic field method are considered.

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DOUBLE SYMMETRIES IN FIELD THEORIES

Modern Physics Letters A ◽

10.1142/s0217732300000360 ◽

2000 ◽

Vol 15 (05) ◽

pp. 379-389 ◽

Cited By ~ 11

Author(s):

L. M. SLAD

Keyword(s):

Symmetry Group ◽

High Efficiency ◽

Weak Interactions ◽

Field Theories ◽

Symmetric Field ◽

Dual Status ◽

Double Symmetry ◽

Double Symmetries ◽

Qualitative Characteristics

In this letter a concept of double symmetry is introduced, and its qualitative characteristics and rigorous definitions are given. We describe two ways of constructing the double-symmetric field theories and present an example demonstrating the high efficiency of one of them. Noting the existing double-symmetric theories we draw attention to a dual status of the group SU (2)L ⊗ SU (2)R as a secondary symmetry group, and in this connection we briefly discuss logically possible aspects of the P-violation in weak interactions.

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On the Solution of some Axisymmetric Boundary Value Problems by means of Integral Equations

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500010889 ◽

1963 ◽

Vol 13 (3) ◽

pp. 235-246 ◽

Cited By ~ 34

Author(s):

W. D. Collins

Keyword(s):

Boundary Value Problems ◽

Integral Equations ◽

Boundary Value ◽

Diffraction Theory ◽

Integral Representations ◽

Fredholm Integral Equations ◽

Fredholm Equations ◽

Abel Integral Equations ◽

Spherical Caps ◽

Method Show

This paper concludes a series of papers (1) on a group of axisymmetric boundary value problems in potential and diffraction theory by considering some potential problems for a circular annulus. The Dirichlet problem for an annulus has recently been considered by Gubenko and Mossakovskiǐ (2), who, by a somewhat complicated method, show it to be governed by either one of two Fredholm integral equations of the second kind. The purpose of the present paper is to show how the method developed in previous papers, by which certain integral representations of the potentials in problems for circular disks arid spherical caps are used to reduce such problems to the solutions of either single Abel integral equations or Abel and Fredholm equations, can be applied to both the Dirichlet and Neumann problems for the annulus to give reasonably straightforward derivations of the governing Fredholm equations.

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DOUBLE STRUCTURES AND DOUBLE SYMMETRIES FOR THE EINSTEIN–KALB–RAMOND THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x06031259 ◽

2006 ◽

Vol 21 (02) ◽

pp. 361-372 ◽

Cited By ~ 2

Author(s):

YA-JUN GAO

Keyword(s):

Function Method ◽

Equations Of Motion ◽

Complex Function ◽

Complex Method ◽

Complex Matrix ◽

Fractional Linear Transformation ◽

Double Complex ◽

Ernst Potential ◽

Double Symmetry ◽

Double Symmetries

We further study the two-dimensional reduced Einstein–Kalb–Ramond (EKR) theory in the axisymmetric case by using the so-called double-complex function method. We find a doubleness symmetry of this theory and exploit it so that some double-complex d×d matrix Ernst-like potential can be constructed, and the associated equations of motion can be extended into a double-complex matrix Ernst-like form. Then we give a double symmetry group [Formula: see text] for the EKR theory and verify that its action can be realized concisely by a double-complex matrix, form generalization of the fractional linear transformation on the Ernst potential. These results demonstrate that the theory under consideration possesses more and richer symmetry structures. Moreover, as an application, we obtain an infinite chain of double-solutions of the EKR theory showing that the double-complex method is more effective. Some of the results in this paper cannot be obtained by the usual (nondouble) scheme.

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Electrodynamic analysis of nanoantennas at millimeter and optical wavelength ranges

International Journal of Microwave and Wireless Technologies ◽

10.1017/s1759078713000196 ◽

2013 ◽

Vol 5 (4) ◽

pp. 537-550

Author(s):

Alexander M. Lerer ◽

Elena V. Golovacheva ◽

Anatoly B. Kleshchenkov ◽

Gennady A. Shurov ◽

Pavel V. Makhno ◽

...

Keyword(s):

Electromagnetic Waves ◽

Zno Nanorods ◽

Computation Time ◽

Integral Representations ◽

Integrodifferential Equations ◽

Optical Antennas ◽

Optical Wavelength ◽

Electrodynamic Analysis ◽

Dielectric Bodies ◽

Order Of Magnitude

Electrodynamics models and radiophysical properties of carbon nanotube-dipoles (isolated on the substrate lattices), metallic optical antennas and optical antennas, formed from ZnO nanorods coated with metal films were developed and investigated. The models are based on numerically analytical solution of integrodifferential equations describing the diffraction of electromagnetic waves on impedance and dielectric bodies. The use of integral representations of the kernels of integrodifferential equations allowed us to overcome the difficulties of solution, associated with the singularity of kernels and to reduce the computation time by an order of magnitude.

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