Dr. Yury Shestopalov
Faculty of Engineering and Sustainable Development, University of Gävle, 80176 Gävle, Sweden
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Academic Career Length
14Years (2013-Present)
(Calculated once Scilit publication data is synced: current year − year of first publication + 1)
Representative Publications
View All Publications27 March 2014 in physica status solidi (c)
Journal Article
23 November 2020 in Journal of Electromagnetic Waves and Applications
Journal Article
Yury ShestopalovProceeding from the scattered field expansion in cylindrical harmonics, we define partial invisibility or partial cloaking as suppression of finitely many lowest-order field harmonics. We show that for benchmark structures (a dielectric rod and a perfectly conducting cylinder of circular cross section covered by a concentric dielectric layer), such multiple suppression can be achieved. For this purpose, we prove the solvability and explicitly determine the solution of the corresponding equation system which provide vanishing of the lowest-order field expansion coefficients and the resulting simultaneous suppression of up to five lowest-order scattered harmonics. We investigate the character and qualitative properties of partial invisibility and partial cloaking by analyzing the scattered field patterns.
27 February 2019 in Applicable Analysis
Journal Article
Yury ShestopalovA 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.
Journal Article
Yury ShestopalovASAzizaga Shakhverdiev
Azizaga ShakhverdievA qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it possible to identify all feasible solution classes as well as the DS critical and singular points and solutions. The integrability of the considered DS family is established. Nine specific solution classes are identified. In each class, clear types of symmetry are determined and visualized and it is discussed how transformations between the solution classes create new types of symmetries. Visualization is performed as series of phase portraits revealing all possible catastrophic scenarios that result from the transition between the solution classes.
8 June 2021 in Radio Science
Journal Article
Yury ShestopalovA unified approach is developed for the analysis of singularities of the scattered field and vanishing of scattering harmonics. Rigorous proofs are presented of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder. The method employs a mathematically correct approach of the spectral theory of open structures involving generalized conditions at infinity when complex resonance frequencies may be considered. The result is obtained by verifying the existence of complex singularities of the series solution coefficients considered as functions of the problem parameters. The recently developed theory of generalized cylindrical polynomials (GCPs) is used that enables one to reduce determination of singularities (resonances) to finding zeros (real or complex) of a particular subfamily of GCPs.
15 October 2021 in Applicable Analysis
Journal Article
Yury ShestopalovWe consider eigenvalue problems for dielectric cylindrical scatterers of arbitrary cross with generalized conditions at infinity that enable one to take into account complex eigenvalues. The existence of resonance (scattering) frequencies associated with these eigenvalues is proved. The technique involves the determination of characteristic numbers (CNs) of the Fredholm operator-valued functions of the problems constructed using Green's potentials. Separating principal parts in the form of meromorphic operator pencils, we apply the operator generalization of Rouché's theorem to verify the occurrence of CNs in close proximities of the pencil poles. The results are illustrated in detail using the case of a dielectric cylinder of circular cross section.
About Me
Yury Shestopalov is Professor Emeritus of mathematics at the University of Gävle, Sweden. He completed a full university career from teaching assistant to professor and department head at Moscow State University (MSU), Karlstad University, and the University of Gävle (since 2013). Continuously teaching since 1977, he created and headed the department of computer science at the MSU Kolmogorov School (1992–1993) and initiated the Faculty of Higher Pedagogical Education at MSU. His main scientific contributions include the spectral theory of operators applied to mathematical methods for electromagnetics, inverse problems, wave propagation in nonlinear media, integral and partial differential equations, and numerical methods. Among his recent achievements are the complete description of the wave spectrum in inhomogeneously filled waveguides and the mathematical theory of inverse waveguide problems. Prof. Shestopalov has authored and co-authored six books (published in the USA and UK), over 100 articles in peer-reviewed journals, and more than 200 scientific works in total. He has supervised several PhD students who are now active professors. He actively coordinates international research projects across Sweden, the USA, Japan, Germany, Finland, Russia, and Ukraine. He has organized over 20 and participated in more than 60 international conferences, serving as Vice-Chairman of PIERS and a Programme Committee member of several URSI conferences.