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Shestopalov, Yury
Alternative names
Publications (10 of 108) Show all publications
Smirnov, Y., Smolkin, E. & Shestopalov, Y. (2019). Diffraction of a TE-Polarized Wave by a Nonlinear Goubau Line. Radio Science, 54(1), 151-157
Open this publication in new window or tab >>Diffraction of a TE-Polarized Wave by a Nonlinear Goubau Line
2019 (English)In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 54, no 1, p. 151-157Article in journal (Refereed) Published
Abstract [en]

The diffraction of a cylindrical wave by a nonlinear metal-dielectric waveguide filled with nonlinear medium is considered. Two widely used types of nonlinearities (Kerr nonlinearity and nonlinearity with saturation) are considered. The problem is to find amplitudes of the reflected and the transmitted fields when the amplitude of the incident field is known. The analytical and numerical solution techniques are developed. Numerical results are presented. ©2019. American Geophysical Union. All Rights Reserved.

Place, publisher, year, edition, pages
Blackwell Publishing Ltd, 2019
Keywords
nonlinear waveguide, numerical method, TE polarization, the diffraction problem, Dielectric waveguides, Numerical methods, Analytical and numerical solutions, Diffraction problem, Kerr nonlinearity, Nonlinear metals, Nonlinear waveguides, Numerical results, TE polarizations, Transmitted field, Diffraction
National Category
Mathematics Other Engineering and Technologies
Identifiers
urn:nbn:se:hig:diva-30478 (URN)10.1029/2018RS006629 (DOI)000458731300012 ()2-s2.0-85060646358 (Scopus ID)
Projects
Largescale
Funder
Swedish Institute
Note

Funding agencies:

- Ministry of Education and Science of the Russian Federation Grant no. 1.894.2017/4.6

- University of Gavle, Sweden  

Available from: 2019-08-09 Created: 2019-08-09 Last updated: 2019-08-09Bibliographically approved
Khulbe, M., Tripathy, M. R., Parthasarathy, H., Shestopalov, Y. & Lagovsky, B. (2019). Inverse Scattering and Imaging Using Second Order Optical Nonlinearities. In: 2019 6th International Conference on Signal Processing and Integrated Networks, SPIN 2019: . Paper presented at 6th International Conference on Signal Processing and Integrated Networks, SPIN 2019, 7-8 March 2019, Noida, India (pp. 1086-1089). IEEE
Open this publication in new window or tab >>Inverse Scattering and Imaging Using Second Order Optical Nonlinearities
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2019 (English)In: 2019 6th International Conference on Signal Processing and Integrated Networks, SPIN 2019, IEEE, 2019, p. 1086-1089Conference paper, Published paper (Refereed)
Abstract [en]

In this paper a mathematical technique is developed to find the parameters of a medium in terms of its scattered electromagnetic fields. Optical nonlinearity plays an important role in finding the scattering parameters of a medium. Using perturbation theory and nonlinear inverse scattering techniques with first order, second order and third order optical nonlinearity we find scattered electromagnetic fields. Using error minimization techniques parameters are estimated in term of permittivity and permeability up to second order. © 2019 IEEE.

Place, publisher, year, edition, pages
IEEE, 2019
Keywords
Inverse scattering, least square estimation techniques, Optical nonlinearity, parameter extraction, permeability, permittivity, RF imaging, Electromagnetic fields, Electromagnetic wave diffraction, Mechanical permeability, Parameter estimation, Perturbation techniques, Signal processing, Least square estimation, Perturbation theory, Scattered electromagnetic fields, Second order optical nonlinearity, Third-order optical nonlinearities, Nonlinear optics
National Category
Signal Processing
Identifiers
urn:nbn:se:hig:diva-30501 (URN)10.1109/SPIN.2019.8711652 (DOI)000470844100209 ()2-s2.0-85066895033 (Scopus ID)9781728113791 (ISBN)
Conference
6th International Conference on Signal Processing and Integrated Networks, SPIN 2019, 7-8 March 2019, Noida, India
Note

Funding agency:

- DST, New Delhi INT/RUS/RFBR/P-341 

Available from: 2019-08-15 Created: 2019-08-15 Last updated: 2019-08-22Bibliographically approved
Shestopalov, Y., Samokhin, A. & Samokhina, A. (2019). Iterative Gradient Descent Methods for Solving Linear Equations. Computational Mathematics and Mathematical Physics, 59(8), 1267-1274
Open this publication in new window or tab >>Iterative Gradient Descent Methods for Solving Linear Equations
2019 (English)In: Computational Mathematics and Mathematical Physics, ISSN 0965-5425, E-ISSN 1555-6662, Vol. 59, no 8, p. 1267-1274Article in journal (Refereed) Published
Abstract [en]

The paper presents the results on the use of gradient descent algorithms for constructing iterative methods for solving linear equations. A mathematically rigorous substantiation of the conver- gence of iterations to the solution of the equations is given. Numerical results demonstrating the effi- ciency of the modified iterative gradient descent method are presented.

Keywords
systems of linear algebraic equations, gradient descent, iterative methods
National Category
Mathematics
Identifiers
urn:nbn:se:hig:diva-30718 (URN)10.1134/S0965542519080141 (DOI)
Available from: 2019-10-03 Created: 2019-10-03 Last updated: 2019-10-04Bibliographically approved
Shestopalov, Y., Smolkin, E. & Snegur, M. (2019). New Propagation Regimes of TE Waves in a Waveguide filled with a Nonlinear Dielectric Metamaterial. In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC): . Paper presented at URSI AP-RASC 2019, 09 - 15 March 2019, New Delhi, India. New Dehli: IEEE, Article ID 8738241.
Open this publication in new window or tab >>New Propagation Regimes of TE Waves in a Waveguide filled with a Nonlinear Dielectric Metamaterial
2019 (English)In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, article id 8738241Conference paper, Published paper (Refereed)
Abstract [en]

We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) metamaterial medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. 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
New Dehli: IEEE, 2019
Keywords
dielectric waveguides, differential equations, eigenvalues and eigenfunctions, electromagnetic wave propagation, optical metamaterials, optical waveguides, new propagation regimes, TE waves, nonlinear dielectric metamaterial, circular metal-dielectric waveguide, nonlinear metamaterial medium, Kerr nonlinearity, nonlinear transmission eigenvalue problem, ordinary differential equation, eigenvalues, problem correspond, propagation constants, auxiliary Cauchy problem, Electromagnetic waveguides, Dielectrics, Permittivity, Metamaterials, Electromagnetics, Electromagnetic scattering
National Category
Electrical Engineering, Electronic Engineering, Information Engineering Mathematics
Identifiers
urn:nbn:se:hig:diva-30555 (URN)10.23919/URSIAP-RASC.2019.8738241 (DOI)2-s2.0-85068617892 (Scopus ID)978-908-25987-5-9 (ISBN)978-908-25987-4-2 (ISBN)978-1-5386-8551-8 (ISBN)
Conference
URSI AP-RASC 2019, 09 - 15 March 2019, New Delhi, India
Available from: 2019-08-22 Created: 2019-08-22 Last updated: 2019-08-22Bibliographically approved
Shestopalov, Y. (2019). On a Method of Solution to Dispersion Equations in Electromagnetics. In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC): . Paper presented at URSI AP-RASC 2019, 09 - 15 March 2019, New Delhi, India. New Dehli, Article ID 8738297.
Open this publication in new window or tab >>On a Method of Solution to Dispersion Equations in Electromagnetics
2019 (English)In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli, 2019, article id 8738297Conference paper, Published paper (Refereed)
Abstract [en]

A possible general approach to the analysis of dispersion equations (DEs) of electromagnetics is presented. The method takes into account the known explicit forms of DEs describing eigenoscillations and normal waves in layered structures and is based on the development of the notion of generalized cylindrical polynomials. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the DE roots and validate iterative numerical solution techniques.

Place, publisher, year, edition, pages
New Dehli: , 2019
Keywords
eigenvalues and eigenfunctions, electromagnetism, iterative methods, oscillations, polynomials, wave equations, dispersion equations, electromagnetics, DEs describing eigenoscillations, normal waves, layered structures, generalized cylindrical polynomials, possible general approach, explicit forms, eigenoscillations, iterative numerical solution techniques, Mathematical model, Dispersion, Frequency modulation, Zinc, Waveguide theory
National Category
Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:hig:diva-30554 (URN)10.23919/URSIAP-RASC.2019.8738297 (DOI)2-s2.0-85068608591 (Scopus ID)978-908-25987-5-9 (ISBN)978-908-25987-4-2 (ISBN)978-1-5386-8551-8 (ISBN)
Conference
URSI AP-RASC 2019, 09 - 15 March 2019, New Delhi, India
Available from: 2019-08-22 Created: 2019-08-22 Last updated: 2019-09-04Bibliographically approved
Shestopalov, Y., Smolkin, E. & Smirnov, Y. (2019). On the existence of the nonlinear leaky TE-polarized waves in a metal–dielectric cylindrical waveguide. Wave motion, 91, Article ID 102378.
Open this publication in new window or tab >>On the existence of the nonlinear leaky TE-polarized waves in a metal–dielectric cylindrical waveguide
2019 (English)In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 91, article id 102378Article in journal (Refereed) Published
Abstract [en]

We consider propagation of leaky waves in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green’s function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. Conditions under which a finite number of waves can propagate are obtained and the intervals of localization of the corresponding propagation constants are determined. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. In numerical experiments, two types of nonlinearities are considered and compared: Kerr nonlinearity and nonlinearity with saturation. New propagation regimes are discovered.

Keywords
Goubau line, Leaky TE waves, Nonhomogeneous dielectric waveguide, Nonlinear permittivity, Numerical method
National Category
Physical Sciences
Identifiers
urn:nbn:se:hig:diva-30786 (URN)10.1016/j.wavemoti.2019.102378 (DOI)
Available from: 2019-10-14 Created: 2019-10-14 Last updated: 2019-10-14Bibliographically approved
Shestopalov, Y. & Shakhverdiev, A. (2019). Qualitative Analysis of Quadratic Polynomial Dynamical Systems Associated with the Modeling and Monitoring of Oil Fields. Lobachevskii Journal of Mathematics, 40(10), 1695-1710
Open this publication in new window or tab >>Qualitative Analysis of Quadratic Polynomial Dynamical Systems Associated with the Modeling and Monitoring of Oil Fields
2019 (English)In: Lobachevskii Journal of Mathematics, ISSN 1995-0802, E-ISSN 1818-9962, Vol. 40, no 10, p. 1695-1710Article in journal (Refereed) Published
Abstract [en]

The behavior and properties of solutions of two-dimensional quadratic polynomial dynamical system on the phase plane of variables and time are considered. A complete qualitative theory is constructed which includes the analysis of all singular points and the features of solutions depending on all parameters of the problem. A main result is that, with the discriminant criteria created on the basis of the growth model constructed in the present study, it is possible to formulate practical recommendations for regulating and monitoring the process of waterflooding and the development of an oil field.

Keywords
Polynomial quadratic dynamical system, qualitative theory, autonomous equation, singularities, qualitative analysis
National Category
Mathematics
Identifiers
urn:nbn:se:hig:diva-30719 (URN)10.1134/S1995080219100226 (DOI)
Available from: 2019-10-03 Created: 2019-10-03 Last updated: 2019-10-04Bibliographically approved
Lagovsky, B. A., Samokhin, A. B. & Shestopalov, Y. V. (2019). Regression Methods of Obtaining Angular Superresolution. In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC): . Paper presented at URSI AP-RASC 2019, 09 - 15 March 2019, New Delhi, India. New Dehli: IEEE, Article ID 8738539.
Open this publication in new window or tab >>Regression Methods of Obtaining Angular Superresolution
2019 (English)In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, article id 8738539Conference paper, Published paper (Refereed)
Abstract [en]

New methods of signal processing based on nonlinear regression methods are presented. They allow us to restore images of individual objects of group targets with superresolution at signal-to-noise ratios that are significantly lower than those provided by the known methods.

Place, publisher, year, edition, pages
New Dehli: IEEE, 2019
Keywords
Signal resolution, Image resolution, Signal to noise ratio, Image restoration, Radar, Inverse problems
National Category
Other Engineering and Technologies Mathematics
Identifiers
urn:nbn:se:hig:diva-30553 (URN)10.23919/URSIAP-RASC.2019.8738539 (DOI)2-s2.0-85068588586 (Scopus ID)978-908-25987-5-9 (ISBN)978-908-25987-4-2 (ISBN)978-1-5386-8551-8 (ISBN)
Conference
URSI AP-RASC 2019, 09 - 15 March 2019, New Delhi, India
Available from: 2019-08-22 Created: 2019-08-22 Last updated: 2019-08-22Bibliographically approved
Shestopalov, Y. (2019). Trigonometric and cylindrical polynomials and their applications in electromagnetics. Applicable Analysis
Open this publication in new window or tab >>Trigonometric and cylindrical polynomials and their applications in electromagnetics
2019 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504XArticle in journal (Refereed) Epub ahead of print
Abstract [en]

Development of the theory of trigonometric polynomials (TPs) is considered that involves generalization of the notion of TP and extension of the methods and results to cylindrical polynomials (CPs). On the basis of the proposed augmentation of TPs and CPs, a general approach is presented to the analysis of guided waves and resonances in electromagnetics and beyond. The method employs the known explicit forms of dispersion equations (DEs) describing eigenoscillations and normal waves in layered structures and is based on the development of the theory of generalized TPs and CPs performed in the study. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the TP and CP zeros and the DE roots and validate iterative numerical solution techniques.

Place, publisher, year, edition, pages
Taylor & Francis, 2019
Keywords
cylindrical polynomials; dispersion equation; zeros; electromagnetic waves
National Category
Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:hig:diva-30485 (URN)10.1080/00036811.2019.1584290 (DOI)2-s2.0-85062349423 (Scopus ID)
Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-12Bibliographically approved
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
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