hig.sePublications
Change search
Link to record
Permanent link

Direct link
BETA
Shestopalov, Yury
Alternative names
Publications (10 of 82) 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)000444790500002 ()2-s2.0-85050078848 (Scopus ID)
Available from: 2018-08-15 Created: 2018-08-15 Last updated: 2018-10-15Bibliographically approved
Shestopalov, Y., Sheina, E. & Smirnov, A. (2018). Development of Numerical Techniques for Forward and Inverse Waveguide Scattering Problems. In: : . Paper presented at AT-RASC 2018, 2nd URSI Atlantic Radio Science Meeting,28 May - 1 June 2018, Gran Canaria,Spain.
Open this publication in new window or tab >>Development of Numerical Techniques for Forward and Inverse Waveguide Scattering Problems
2018 (English)Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

Development of the methods and algorithms [1, 2] are considered for the numerical solution to the forward problem of the electromagnetic wave scattering by inhomogeneous dielectric inclusions in a waveguide of rectangular cross section and inverse problem of reconstructing parameters of the dielectric inclusions from the values of the transmission coefficient of the scattered electromagnetic wave. The codes are developed implementing an FDTD method that employs the PML-layer technique. Numerical modeling and simulations are performed for the analysis of the wave propagation in waveguides of rectangular cross section loaded with parallel-plane layered media (layered dielectric diaphragms) and such diaphragms containing cubic dielectric inclusions. Validation is carried out of the results of calculations using closed-form solution [3] to the canonical single-layer structure.

Progress in analytical - numerical investigations of the solutions to the forward and inverse waveguide problems are largely based on a recent discovery [4] of the singularities and extrema in the complex domain of the transmission coefficient of layered dielectric diaphragms. In fact, the knowledge of the location of singularity and extrema sets of the scattering matrix allows one to justify correct determination of real or complex permittivity of each layer of the diaphragm by specifying domains in the complex plane where the transmission coefficientis one-to-one; that is, the domains that do not contain singularities and where unique permittivity reconstruction is therefore possible. Forthe forward problem of the scattering of a normal waveguide mode by a single-and three-layer diaphragms with a dielectric cube, it is shown [1, 2] that variation in the values of the transmission coefficient can be up to two orders of magnitude less than that of the permittivity of the inclusion. Taking into account this result and the presence of singularities, improvements are proposed of the numerical method, algorithms and codes implementing the calculations. The results of modeling and computations are validated by comparing with experimental and measurement data [3]. The requirements are formulated that should be imposed on the accuracy of computations and measurements necessary to reconstruct numerically permittivity of the inclusion from the amplitude and phase of the transmitted wave with the prescribed accuracy.

1. E. Sheina, A. Smirnov,Y. Shestopalov,and M.Ufimtsev,“FDTD solution of reconstructing permittivity of a dielectric inclusion in a waveguide taking into account measurement inaccuracy,”Progress in Electromagnetics Research Symposium (PIERS),St Petersburg, Russia, 2017, pp. 3188-3195, doi:10.1109/PIERS.2017.8262306.

2.E. Sheina, A. Smirnov, and Y. Shestopalov, “Influence of standing waves on the solution of the inverse problem ofreconstructing parameters of a dielectric inclusion in a waveguide,”URSI Int. Symposium on Electromagnetic Theory (EMTS), Espoo, Finland, 2016,pp. 643-646, doi:10.1109/URSI-EMTS.2016.7571479.

3. Yu. G. Smirnov, Yu. V. Shestopalov, and E. D. Derevyanchuk, “Inverse problem method for complex permittivity reconstruction of layered media in a rectangular waveguide,”Physica Status Solidi(C), 11,5-6, 2014,pp. 969–974, doi:10.1002/pssc.201300697.

4. Y. Shestopalov, “Resonant states in waveguide transmission problems,”PIER B,64: pp.119-143, 2015, doi: 10.2528/PIERB15083001.

National Category
Mathematics Other Engineering and Technologies
Identifiers
urn:nbn:se:hig:diva-28319 (URN)
Conference
AT-RASC 2018, 2nd URSI Atlantic Radio Science Meeting,28 May - 1 June 2018, Gran Canaria,Spain
Available from: 2018-10-15 Created: 2018-10-15 Last updated: 2018-10-15Bibliographically 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: 2018-10-15Bibliographically approved
Shestopalov, Y. & Kuzmina, E. (2018). On Recent Findings in the Theory of Complex Waves in Open Metal-Dielectric Waveguides. In: : . Paper presented at AT-RASC 2018, 2nd URSI Atlantic Radio Science meeting, 29 May - 1 June 2018, Gran Canaria, Spain.
Open this publication in new window or tab >>On Recent Findings in the Theory of Complex Waves in Open Metal-Dielectric Waveguides
2018 (English)Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

Theory of complex waves (see e.g. [1] and references therein) accumulated a big volume of results. However, its biggest drawback remains which brakes significantly the development of the theory: absence of rigorous proofs of the existence of complex waves. In this respect, studies of complex waves in open metal-dielectric waveguides has been essentially enhanced when two new families of symmetric (angle-independent) complex waves have been identified [2, 3] in a dielectric rod (DR) and Goubau line (GL) with homogeneous dielectric cover: surface complex waves occurring as perturbations of real surface waves caused by the presence of lossy dielectric, and pure complex waves which have no counterpart in the set of real waves. Existence of the latter family of complex waves has been shown using a special technique and the proof [3] of the existence of an infinite set of complex roots of the dispersion equation (DE) describing waves in DR and GL.

In this work, a development of the analytical and numerical methods [2, 3] are considered for the analysis of the electromagnetic wave propagation in metal-dielectric waveguides with multi-layered dielectric filling. The first step constitutes extension of the results obtained for symmetric complex waves in DR and GLto the case of non-symmetric (angle-dependent) waves, and the second step, to multi-layered dielectric covers. Both steps are accomplished using specific forms of DEs obtained in [3]by construction analytical continuation of the functions involved in DEs to multi-sheet Riemann surfaces of the spectral parameter and applying appropriate generalization the techniques [4]forfinding complex roots of the DEs.

Calculation ofnon-symmetric complex waves employs numerical solution of the DEs with the help of parameter differentiation in the complex domain using multi-parameter setting and analysis of implicit functions of several complex variables [5] and reduction [2, 3] to numerical solution of auxiliary Cauchy problems.

1. A. S. Raevskiiand S. B. Raevskii, Complex Waves, Radiotekhnika, Moscow, 2010.

2. E. Kuzmina and Y. Shestopalov, “Waves in a lossyGoubau line,”10th European Conf. on Antennas and Propagation (EuCAP), Davos, Switzerland, 2016, doi: 10.1109/EuCAP.2016.7481368.

3. E. Kuzmina and Y. Shestopalov, “Complex waves in a dielectric rod and Goubau line,” 19th Int. Conf. on Electromagneticsin Advanced Applications (ICEAA), Verona, Italy, 2017, pp. 963-966, doi: 10.1109/ICEAA.2017.8065417.

4. Y. Shestopalov, “Resonant states in waveguide transmission problems,”PIER B,64: pp.119-143, 2015, doi: 10.2528/PIERB15083001.

5.Y. Shestopalov,“On unique solvability of multi-parameter waveguide inverse problems, ”19th Int. Conf. on Electromagnetics in Advanced Applications (ICEAA), Verona, Italy, 2017, pp. 372-376, doi: 10.1109/ICEAA.2017.8065253.

National Category
Other Engineering and Technologies Mathematics
Identifiers
urn:nbn:se:hig:diva-28320 (URN)
Conference
AT-RASC 2018, 2nd URSI Atlantic Radio Science meeting, 29 May - 1 June 2018, Gran Canaria, Spain
Available from: 2018-10-15 Created: 2018-10-15 Last updated: 2018-10-15Bibliographically approved
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), Article ID 1507083.
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 1, article id 1507083Article 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: 2018-10-15Bibliographically 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
Organisations

Search in DiVA

Show all publications