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Shestopalov, Yury
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Publications (10 of 80) Show all publications
Angermann, L., Shestopalov, Y. V., Smirnov, Y. G. & Yatsyk, V. V. (2018). A nonlinear multiparameter EV problem. In: Beilina L., Smirnov Y. (Ed.), Progress In Electromagnetics Research Symposium: PIERS 2017, PIERS 2017: Nonlinear and Inverse Problems in Electromagnetics. Paper presented at PIERS 2017 (pp. 55-70). Springer New York LLC
Open this publication in new window or tab >>A nonlinear multiparameter EV problem
2018 (English)In: Progress In Electromagnetics Research Symposium: PIERS 2017, PIERS 2017: Nonlinear and Inverse Problems in Electromagnetics / [ed] Beilina L., Smirnov Y., Springer New York LLC , 2018, p. 55-70Conference paper, Published paper (Refereed)
Abstract [en]

We investigate a generalization of one-parameter eigenvalue problems arising in the theory of wave propagation in waveguides filled with nonlinear media to more general nonlinear multi-parameter eigenvalue problems for a nonlinear operator. Using an integral equation approach, we derive functional dispersion equations (DEs) whose roots yield the desired eigenvalues. The existence of the roots of DEs is proved and their distribution is described.

Place, publisher, year, edition, pages
Springer New York LLC, 2018
Series
Springer Proceedings in Mathematics & Statistics (PROMS) ; 243
Keywords
Dispersion equations, Multi-parameter eigenvalue problems, Nonlinear spectral theory, Dispersion (waves), Integral equations, Inverse problems, Mathematical operators, Nonlinear equations, Wave propagation, Eigenvalue problem, Eigenvalues, Integral equation approaches, Multiparameters, Non-linear media, Nonlinear operator, Spectral theory, Eigenvalues and eigenfunctions
National Category
Mathematics
Identifiers
urn:nbn:se:hig:diva-27866 (URN)10.1007/978-3-319-94060-1_5 (DOI)2-s2.0-85051146418 (Scopus ID)9783319940595 (ISBN)978-3-319-94060-1 (ISBN)
Conference
PIERS 2017
Available from: 2018-09-06 Created: 2018-09-06 Last updated: 2018-09-06Bibliographically approved
Shestopalov, Y. (2018). Complex waves in a dielectric waveguide. Wave motion, 82, 16-19
Open this publication in new window or tab >>Complex waves in a dielectric waveguide
2018 (English)In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 82, p. 16-19Article in journal (Refereed) Published
Abstract [en]

Existence of two families of symmetric complex waves in a dielectric waveguide of circular cross section is proved. Eigenvalues of the associated Sturm–Liouville problem on the half-line are determined. 

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Complex wave, Dielectric waveguide, Dispersion equation, Surface wave, Eigenvalues and eigenfunctions, Surface waves, Circular cross-sections, Complex waves, Dispersion equations, Eigenvalues, Half-line, Liouville problem, Symmetric complexes, Dielectric waveguides, complexity, dielectric property, eigenvalue, symmetry, wave dispersion
National Category
Mathematics
Identifiers
urn:nbn:se:hig:diva-27648 (URN)10.1016/j.wavemoti.2018.07.005 (DOI)2-s2.0-85050078848 (Scopus ID)
Available from: 2018-08-15 Created: 2018-08-15 Last updated: 2018-08-15Bibliographically approved
Samokhin, A., Samokhina, A. & Shestopalov, Y. (2018). Discretization Methods for Three-Dimensional Singular Integral Equations of Electromagnetism. Differential equations, 54(9)
Open this publication in new window or tab >>Discretization Methods for Three-Dimensional Singular Integral Equations of Electromagnetism
2018 (English)In: Differential equations, ISSN 0012-2661, E-ISSN 1608-3083, Vol. 54, no 9Article in journal (Refereed) In press
Abstract [en]

  Theorems providing the convergence of approximate solutions of linear operator equations to the solution of the original equation are proved. The obtained theorems are used to rigorously mathematically justify the possibility of numerical solution of the 3D singular integral equations of electromagnetism by the Galerkin method and the collocation method.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2018
Keywords
Linear operator equations, volume singular integral equations, iterations, dielectric bodies
National Category
Computational Mathematics
Identifiers
urn:nbn:se:hig:diva-27910 (URN)10.1134/S0012266118090100 (DOI)
Available from: 2018-09-17 Created: 2018-09-17 Last updated: 2018-09-24
Smirnov, Y., Smolkin, E. & Shestopalov, Y. (2018). On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular metal-dielectric waveguide filled with nonlinear radially inhomogeneous medium. Journal Electromagnetic Waves and Applications, 32(11), 1389-1408
Open this publication in new window or tab >>On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular metal-dielectric waveguide filled with nonlinear radially inhomogeneous medium
2018 (English)In: Journal Electromagnetic Waves and Applications, ISSN 0920-5071, E-ISSN 1569-3937, Vol. 32, no 11, p. 1389-1408Article in journal (Refereed) Published
Abstract [en]

Propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear inhomogeneous metal–dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations where spectral parameters are the wave propagation constants. The setting under study is reduced to a new type of nonlinear eigenvalue problem. An analytical method for solving this problem is elaborated. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

Place, publisher, year, edition, pages
Taylor & Francis, 2018
Keywords
Goubau line, Kerr nonlinearity, Maxwell’s equations, non-polarized azimuthal-symmetric electromagnetic waves, nonlinear inhomogeneous waveguide, numerical method, two-parameter eigenvalue problem, Circular waveguides, Control nonlinearities, Dielectric waveguides, Differential equations, Electromagnetic wave polarization, Electromagnetic waves, Maxwell equations, Nonlinear equations, Numerical methods, Ordinary differential equations, Problem solving, Wave propagation, Waveguides, Metal-dielectric waveguide, Nonlinear eigenvalue problem, Nonlinear inhomogeneous, Radially inhomogeneous medium, System of ordinary differential equations, Eigenvalues and eigenfunctions
National Category
Other Mathematics
Identifiers
urn:nbn:se:hig:diva-26209 (URN)10.1080/09205071.2018.1438929 (DOI)000433979500006 ()2-s2.0-85041931654 (Scopus ID)
Available from: 2018-03-06 Created: 2018-03-06 Last updated: 2018-06-25Bibliographically approved
Shestopalov, Y. (2018). Singularities of the transmission coefficient and anomalous scattering by a dielectric slab. Journal of Mathematical Physics, 59(3), Article ID 033507.
Open this publication in new window or tab >>Singularities of the transmission coefficient and anomalous scattering by a dielectric slab
2018 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, no 3, article id 033507Article in journal (Refereed) Published
Abstract [en]

We prove the existence and describe the distribution on the complex plane of the singularities, resonant states (RSs), of the transmission coefficient in the problem of the plane wave scattering by a parallel-plate dielectric slab in free space. It is shown that the transmission coefficient has isolated poles all with nonzero imaginary parts that form countable sets in the complex plane of the refraction index or permittivity of the slab with the only accumulation point at infinity. The transmission coefficient never vanishes and anomalous scattering, when its modulus exceeds unity, occurs at arbitrarily small loss of the dielectric filling the layer. These results are extended to the cases of scattering by arbitrary multi-layer parallel-plane media. Connections are established between RSs, spectral singularities, eigenvalues of the associated Sturm-Liouville problems on the line, and zeros of the corresponding Jost function.

Place, publisher, year, edition, pages
American Institute of Physics Inc., 2018
National Category
Mathematics
Identifiers
urn:nbn:se:hig:diva-26671 (URN)10.1063/1.5027195 (DOI)000428902300037 ()2-s2.0-85044305243 (Scopus ID)
Available from: 2018-05-31 Created: 2018-05-31 Last updated: 2018-05-31Bibliographically approved
Kuzmina, E. & Shestopalov, Y. (2018). Symmetric surface complex waves in Goubau Line. Cogent Engineering, 5(1)
Open this publication in new window or tab >>Symmetric surface complex waves in Goubau Line
2018 (English)In: Cogent Engineering, ISSN 2331-1916, Vol. 5, no 1Article in journal (Refereed) Published
Abstract [en]

Existence of symmetric surface complex waves in a Goubau line—a perfectly conducting cylinder of circular cross-section covered by a concentric dielectric layer—is proved by constructing perturbation of the spectrum of symmetric real waves with respect to the imaginary part of the permittivity of the dielectric cover. Closed-form iteration procedures for calculating the roots of the dispersion equation (DE) in the complex domain supplied with efficient choice of initial approximation are developed. Numerical modeling is performed with the help of a parameter-differentiation method applied to the analytical and numerical solution of DEs.

Place, publisher, year, edition, pages
Taylor & Francis, 2018
Keywords
Goubau line; losses; complex surface wave; dispersion equation; attenuation
National Category
Other Mathematics
Identifiers
urn:nbn:se:hig:diva-27907 (URN)10.1080/23311916.2018.1507083 (DOI)000444436700001 ()2-s2.0-85053273140 (Scopus ID)
Available from: 2018-09-17 Created: 2018-09-17 Last updated: 2018-09-24Bibliographically approved
Shestopalov, Y. & Kuzmina, E. (2018). Symmetric surface waves along a metamaterial dielectric waveguide and a perfectly conducting cylinder covered by a metamaterial layer. Advanced Electromagnetics (AEM), 7(2), 91-98
Open this publication in new window or tab >>Symmetric surface waves along a metamaterial dielectric waveguide and a perfectly conducting cylinder covered by a metamaterial layer
2018 (English)In: Advanced Electromagnetics (AEM), E-ISSN 2119-0275, Vol. 7, no 2, p. 91-98Article in journal (Refereed) Published
Abstract [en]

Existence of symmetric complex waves in a metamaterial dielectric rod and a perfectly conducting cylinder of circular cross section covered by a concentric layer of metamaterial, a metamaterial Goubau line, is proved. Analytical investigation and numerical solution of dispersion equations reveal several important properties of running waves inher- ent to open metal-metamaterial waveguides which have not been reported for waveguides filled with standard media.

Keywords
Complex waves, dispersion equation, metamaterial, Goubau line
National Category
Other Mathematics Other Physics Topics
Identifiers
urn:nbn:se:hig:diva-26994 (URN)10.7716/aem.v7i2.792 (DOI)2-s2.0-85047562255 (Scopus ID)
Available from: 2018-06-13 Created: 2018-06-13 Last updated: 2018-06-25Bibliographically approved
Smith, P. D., Vinogradova, E. D. & Shestopalov, Y. V. (2017). A regularized approach to the calculation of the propagation modes in a perturbed waveguide. In: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA): . Paper presented at 19th International Conference on Electromagnetics in Advanced Applications (ICEAA), 11-15 September 2017, Verona, Italy (pp. 1727-1730). , Article ID 8065627.
Open this publication in new window or tab >>A regularized approach to the calculation of the propagation modes in a perturbed waveguide
2017 (English)In: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2017, p. 1727-1730, article id 8065627Conference paper, Published paper (Refereed)
Abstract [en]

When a perfectly electrically conducting (PEC) waveguide is perturbed by the insertion of a PEC structure aligned with its axis, its propagation constants are perturbed. Two complementary approaches to the determination of change induced by the insert are described. The first provides an analytic estimate when the insert is a small flat strip. The second approach converts the underlying boundary value problem to a homogeneous Fredholm matrix equation in which the propagation constants are found from the roots of the determinant of the matrix and stable numerical processes may be employed to find the propagation constants. The second approach is not constrained by the size or shape of the inserts, and thus provides an independent estimate of the accuracy of the analytic estimate of perturbation to the propagation constants of the empty waveguide; it also determines the empty waveguide parameters themselves.

Keywords
Propagation constant, Integral equations, Eigenvalues and eigenfunctions, Kernel, Strips, Matrix converters, Transmission line matrix methods
National Category
Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:hig:diva-25435 (URN)10.1109/ICEAA.2017.8065627 (DOI)000426455500355 ()2-s2.0-85035079716 (Scopus ID)978-1-5090-4452-8 (ISBN)978-1-5090-4451-1 (ISBN)978-1-5090-4450-4 (ISBN)
Conference
19th International Conference on Electromagnetics in Advanced Applications (ICEAA), 11-15 September 2017, Verona, Italy
Available from: 2017-10-19 Created: 2017-10-19 Last updated: 2018-05-31Bibliographically approved
Kushnin, R., Semenjako, J. & Shestopalov, Y. (2017). Accelerated boundary integral method for solving the problem of scattering by multiple multilayered circular cylindrical posts in a rectangular waveguide. In: 2017 Progress In Electromagnetics Research Symposium - Fall (PIERS - FALL): . Paper presented at 2017 Progress In Electromagnetics Research Symposium - Spring, PIERS 2017, 22-25 May 2017, St. Petersburg, Russian Federation (pp. 3263-3271). Electromagnetics Academy
Open this publication in new window or tab >>Accelerated boundary integral method for solving the problem of scattering by multiple multilayered circular cylindrical posts in a rectangular waveguide
2017 (English)In: 2017 Progress In Electromagnetics Research Symposium - Fall (PIERS - FALL), Electromagnetics Academy , 2017, p. 3263-3271Conference paper, Published paper (Refereed)
Abstract [en]

An accelerated boundary integral method for the analysis of scattering of the dominant mode by multiple multi-layered full-height circular cylindrical posts in a rectangular waveguide is presented. After some transformations the surface integral equation is converted to a system of equations whose entries can be evaluated analytically yielding Schlömilch series. Slow convergence of these series is accelerated using the Ewald technique. The proposed method gives results that are comparable in terms of accuracy with other approaches, including those incorporated in solvers HFSS and CST Studio and outperforms them in terms of computation time, especially for posts with large electrical sizes. The efficiency of the proposed method is confirmed by the examples of H-plane cylinder bandpass filters design.

Place, publisher, year, edition, pages
Electromagnetics Academy, 2017
Series
Progress in Electromagnetics Research Symposium
Keywords
Bandpass filters, Rectangular waveguides, Boundary integral methods, Computation time, Cylindrical posts, Dominant mode, Multi-layered, Slow convergences, Surface integral equations, System of equations, Integral equations
National Category
Mathematics
Identifiers
urn:nbn:se:hig:diva-26729 (URN)10.1109/PIERS.2017.8262320 (DOI)000427596703053 ()2-s2.0-85044934518 (Scopus ID)9781509062690 (ISBN)978-1-5090-6270-6 (ISBN)
Conference
2017 Progress In Electromagnetics Research Symposium - Spring, PIERS 2017, 22-25 May 2017, St. Petersburg, Russian Federation
Projects
Project Largescale
Funder
Swedish Institute
Available from: 2018-06-04 Created: 2018-06-04 Last updated: 2018-06-04Bibliographically approved
Samokhin, A., Samokhina, A. & Shestopalov, Y. (2017). Analysis and solution method for problems of electromagnetic wave scattering on dielectric and perfectly conducting structures. Differential equations, 53(9), 1165-1173
Open this publication in new window or tab >>Analysis and solution method for problems of electromagnetic wave scattering on dielectric and perfectly conducting structures
2017 (English)In: Differential equations, ISSN 0012-2661, E-ISSN 1608-3083, Vol. 53, no 9, p. 1165-1173Article in journal (Refereed) Published
Abstract [en]

Problems of electromagnetic wave scattering on 3D dielectric structures in the presence of bounded perfectly conducting surfaces are reduced to a system of singular integral equations. We study this system mathematically and suggest a numerical solution method.

Keywords
Electromagnetic wave, scattering, singular integral equations
National Category
Computational Mathematics
Identifiers
urn:nbn:se:hig:diva-26991 (URN)10.1134/S0012266117090075 (DOI)
Funder
Swedish Institute
Available from: 2018-06-13 Created: 2018-06-13 Last updated: 2018-06-14Bibliographically approved
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