Pub Date : 2022-05-30DOI: 10.1109/DD55230.2022.9961053
S. Sadov, G. Kalachev
We discuss some facts and open problems related to maximizers of convolution operators with kernels in $L_{q}(mathbb{R}^{n})$ from the perspective of our existence theorem (Sbornik Mathematics, 2019). The results on evaluation of $L_{p}rightarrow L_{p^{prime}}$ norms of the Laplace transform, which motivated this research, are reported.
{"title":"On maximizers of convolution operators in $L_{p}(mathbb{R}^{n})$","authors":"S. Sadov, G. Kalachev","doi":"10.1109/DD55230.2022.9961053","DOIUrl":"https://doi.org/10.1109/DD55230.2022.9961053","url":null,"abstract":"We discuss some facts and open problems related to maximizers of convolution operators with kernels in $L_{q}(mathbb{R}^{n})$ from the perspective of our existence theorem (Sbornik Mathematics, 2019). The results on evaluation of $L_{p}rightarrow L_{p^{prime}}$ norms of the Laplace transform, which motivated this research, are reported.","PeriodicalId":125852,"journal":{"name":"2022 Days on Diffraction (DD)","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121265390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-30DOI: 10.1109/DD55230.2022.9961048
R. Feshchenko, A. Popov
In this paper, exact transparent boundary conditions (TBC) for the 2D Helmholtz equation are reported. Their properties, as well as the transition to the limiting case of the narrow-angle TBC for the 2D parabolic equation are discussed. A finite-difference implementation of thus derived one-directional evolutionary type TBC is developed and a fully discrete exact transparent boundary condition is obtained. A number of numerical experiments is conducted in the free space demonstrating how the derived TBC can be used to correctly describe wide-angle wave scattering problems. In the last section, the analysis is extended to the problems involving the back-scattering encountered in the reflection optics and ground penetrating radar.
{"title":"Exact transparent boundary conditions for the 2D Helmholtz equation","authors":"R. Feshchenko, A. Popov","doi":"10.1109/DD55230.2022.9961048","DOIUrl":"https://doi.org/10.1109/DD55230.2022.9961048","url":null,"abstract":"In this paper, exact transparent boundary conditions (TBC) for the 2D Helmholtz equation are reported. Their properties, as well as the transition to the limiting case of the narrow-angle TBC for the 2D parabolic equation are discussed. A finite-difference implementation of thus derived one-directional evolutionary type TBC is developed and a fully discrete exact transparent boundary condition is obtained. A number of numerical experiments is conducted in the free space demonstrating how the derived TBC can be used to correctly describe wide-angle wave scattering problems. In the last section, the analysis is extended to the problems involving the back-scattering encountered in the reflection optics and ground penetrating radar.","PeriodicalId":125852,"journal":{"name":"2022 Days on Diffraction (DD)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126745384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-30DOI: 10.1109/DD55230.2022.9960960
A. Mikhaylov, V. Mikhaylov
We introduce the Hilbert space of analytic functions associated with the multidimensional wave equation in a bounded domain. This space can be considered as a generalization of the de Branges space for first order canonical systems.
{"title":"On a special Hilbert space of functions associated with the multidimensional wave equation in a bounded domain","authors":"A. Mikhaylov, V. Mikhaylov","doi":"10.1109/DD55230.2022.9960960","DOIUrl":"https://doi.org/10.1109/DD55230.2022.9960960","url":null,"abstract":"We introduce the Hilbert space of analytic functions associated with the multidimensional wave equation in a bounded domain. This space can be considered as a generalization of the de Branges space for first order canonical systems.","PeriodicalId":125852,"journal":{"name":"2022 Days on Diffraction (DD)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125993044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-30DOI: 10.1109/DD55230.2022.9961038
V. Zalipaev, L. Leibov, A. Ismagilov, B. Nasedkin, N. Petrov, A. Tcypkin
Computational aspects of ghost imaging diffraction modelling based on broadband terahertz pulsed radiation, modulated by a random phase screen, are discussed. An image generated by transmission of an incident Gauss-Hermite beam passing through a 2D inhomogeneous thin film is the main subject of our study. The modelling is performed in both the frequency and the time domains. The quality of the reconstructed images of a set of slots of different size is analysed for various modes of the incident Gauss-Hermite beams.
{"title":"Computational aspects of ghost imaging diffraction in broadband terahertz range","authors":"V. Zalipaev, L. Leibov, A. Ismagilov, B. Nasedkin, N. Petrov, A. Tcypkin","doi":"10.1109/DD55230.2022.9961038","DOIUrl":"https://doi.org/10.1109/DD55230.2022.9961038","url":null,"abstract":"Computational aspects of ghost imaging diffraction modelling based on broadband terahertz pulsed radiation, modulated by a random phase screen, are discussed. An image generated by transmission of an incident Gauss-Hermite beam passing through a 2D inhomogeneous thin film is the main subject of our study. The modelling is performed in both the frequency and the time domains. The quality of the reconstructed images of a set of slots of different size is analysed for various modes of the incident Gauss-Hermite beams.","PeriodicalId":125852,"journal":{"name":"2022 Days on Diffraction (DD)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117312266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-30DOI: 10.1109/DD55230.2022.9960959
A. Kovtanyuk, A. Chebotarev, T. Seleznev, R. Lampe
The analysis of an optimization algorithm for solving an inverse problem for the cerebral oxygen transport model is carried out. A theorem on the solvability of the optimal control problem is presented, an optimality system is constructed, and the convergence of approximate solutions to the solution of the inverse problem is proved. The results of numerical simulation are presented.
{"title":"Cerebral oxygen transport model with unknown surface sources","authors":"A. Kovtanyuk, A. Chebotarev, T. Seleznev, R. Lampe","doi":"10.1109/DD55230.2022.9960959","DOIUrl":"https://doi.org/10.1109/DD55230.2022.9960959","url":null,"abstract":"The analysis of an optimization algorithm for solving an inverse problem for the cerebral oxygen transport model is carried out. A theorem on the solvability of the optimal control problem is presented, an optimality system is constructed, and the convergence of approximate solutions to the solution of the inverse problem is proved. The results of numerical simulation are presented.","PeriodicalId":125852,"journal":{"name":"2022 Days on Diffraction (DD)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131166378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-30DOI: 10.1109/DD55230.2022.9961013
E. Glushkov, N. Glushkova, O. Ermolenko, A. Tatarinov
This work is a continuation of research presented at the last year DD meeting and partly published in [1], [2] and papers cited therein. Computer models for analytically based simulation of ultrasonic guided wave (GW) propagation in multilayer bone phantoms have been developed and used for systematic numerical analysis of GW propagation depending on phantoms' structure aimed to identify signs predicting osteoporosis. Now we have focused on developing reliable methods of processing experimental data to extract GW characteristics that can be used in the objective functions constructed for the inverse problem solution. Minimization of the objective functions in the space of waveguide's elastic constants and thicknesses yields its effective material parameters indicating a change in the strength properties.
{"title":"Extracting guided wave characteristics of bone phantoms from ultrasonometric data for osteoporosis diagnosis","authors":"E. Glushkov, N. Glushkova, O. Ermolenko, A. Tatarinov","doi":"10.1109/DD55230.2022.9961013","DOIUrl":"https://doi.org/10.1109/DD55230.2022.9961013","url":null,"abstract":"This work is a continuation of research presented at the last year DD meeting and partly published in [1], [2] and papers cited therein. Computer models for analytically based simulation of ultrasonic guided wave (GW) propagation in multilayer bone phantoms have been developed and used for systematic numerical analysis of GW propagation depending on phantoms' structure aimed to identify signs predicting osteoporosis. Now we have focused on developing reliable methods of processing experimental data to extract GW characteristics that can be used in the objective functions constructed for the inverse problem solution. Minimization of the objective functions in the space of waveguide's elastic constants and thicknesses yields its effective material parameters indicating a change in the strength properties.","PeriodicalId":125852,"journal":{"name":"2022 Days on Diffraction (DD)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131199885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-30DOI: 10.1109/dd55230.2022.9961006
{"title":"Proceedings of the International Conference Days on Diffraction 2022","authors":"","doi":"10.1109/dd55230.2022.9961006","DOIUrl":"https://doi.org/10.1109/dd55230.2022.9961006","url":null,"abstract":"","PeriodicalId":125852,"journal":{"name":"2022 Days on Diffraction (DD)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127820588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-30DOI: 10.1109/DD55230.2022.9960977
A. Maslovskaya, L. Moroz
The paper proposes a time-fractional modified model of thermal wave propagation in ferroelectrics. To solve the initial-boundary value problem for a partial differential equation numerically, an implicit computational scheme was derived using a finite-difference approximation of the time-fractional Caputo derivative. The constructed numerical scheme was implemented in Matlab. The designed computer program was used to conduct simulations of the space-time thermal distribution in typical ferroelectrics associated with the dynamical pyroelectric measurements. This approach allows us to provide more adequate modelling of heat conductivity processes in complex physical systems due to the variation of regimes by means of changes in the fractal dynamical dimension.
{"title":"Computational techniques for time-fractional modeling of thermal wave propagation in ferroelectrics","authors":"A. Maslovskaya, L. Moroz","doi":"10.1109/DD55230.2022.9960977","DOIUrl":"https://doi.org/10.1109/DD55230.2022.9960977","url":null,"abstract":"The paper proposes a time-fractional modified model of thermal wave propagation in ferroelectrics. To solve the initial-boundary value problem for a partial differential equation numerically, an implicit computational scheme was derived using a finite-difference approximation of the time-fractional Caputo derivative. The constructed numerical scheme was implemented in Matlab. The designed computer program was used to conduct simulations of the space-time thermal distribution in typical ferroelectrics associated with the dynamical pyroelectric measurements. This approach allows us to provide more adequate modelling of heat conductivity processes in complex physical systems due to the variation of regimes by means of changes in the fractal dynamical dimension.","PeriodicalId":125852,"journal":{"name":"2022 Days on Diffraction (DD)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121275240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-30DOI: 10.1109/DD55230.2022.9960971
D. Dolinina, A. Yulin
A nonlinear active waveguide with periodically changed refractive index and periodically modulated effective gain is considered. The spontaneous symmetry breaking bifurcation of spatially uniform stationary states is investigated. The formation of nonlinear structures on the backgrounds with broken symmetry is demonstrated.
{"title":"Spontaneous symmetry breaking in a waveguide with periodic complex potential","authors":"D. Dolinina, A. Yulin","doi":"10.1109/DD55230.2022.9960971","DOIUrl":"https://doi.org/10.1109/DD55230.2022.9960971","url":null,"abstract":"A nonlinear active waveguide with periodically changed refractive index and periodically modulated effective gain is considered. The spontaneous symmetry breaking bifurcation of spatially uniform stationary states is investigated. The formation of nonlinear structures on the backgrounds with broken symmetry is demonstrated.","PeriodicalId":125852,"journal":{"name":"2022 Days on Diffraction (DD)","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127941446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-30DOI: 10.1109/DD55230.2022.9961039
E. Barshak, B. Lapin, D. Vikulin, C. Alexeyev, M. Yavorsky
We study the propagation of circularly polarized modes in a system of anisotropic and multihelical optical fibers. We demonstrate the transformation of circularly polarized mode in linearly polarized optical vortex. The topological charge of the output optical vortex is determined by the state of polarization of the input field. We show the transformation of angular momenta of circularly polarized light in each fiber of such a system. The parameters of the anisotropic and multihelical fibers are established to implement efficient transformation of the input field.
{"title":"Transformation of angular momentum of light in a system of anisotropic and multihelical optical fibers","authors":"E. Barshak, B. Lapin, D. Vikulin, C. Alexeyev, M. Yavorsky","doi":"10.1109/DD55230.2022.9961039","DOIUrl":"https://doi.org/10.1109/DD55230.2022.9961039","url":null,"abstract":"We study the propagation of circularly polarized modes in a system of anisotropic and multihelical optical fibers. We demonstrate the transformation of circularly polarized mode in linearly polarized optical vortex. The topological charge of the output optical vortex is determined by the state of polarization of the input field. We show the transformation of angular momenta of circularly polarized light in each fiber of such a system. The parameters of the anisotropic and multihelical fibers are established to implement efficient transformation of the input field.","PeriodicalId":125852,"journal":{"name":"2022 Days on Diffraction (DD)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117320685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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