Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016422
A. Kirpichnikova, N. Kirpichnikova
We construct shadow creeping waves in the problem of a plane wave diffraction by a smooth axially symmetric prolate body of revolution for both Dirichlet and Neumann boundary conditions. Using Fock’s asymptotics as the initial data for the creeping wave amplitude, the theory of residues allows us to present the wave field in the main approximation.
{"title":"Creeping waves in the shadow region with the Dirichlet and Neumann conditions","authors":"A. Kirpichnikova, N. Kirpichnikova","doi":"10.1109/DD46733.2019.9016422","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016422","url":null,"abstract":"We construct shadow creeping waves in the problem of a plane wave diffraction by a smooth axially symmetric prolate body of revolution for both Dirichlet and Neumann boundary conditions. Using Fock’s asymptotics as the initial data for the creeping wave amplitude, the theory of residues allows us to present the wave field in the main approximation.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"138 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127448414","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 : 2019-06-01DOI: 10.1109/DD46733.2019.9016596
E.V. Vybornyi
We consider a model quantum Hamiltonian of a charge in a resonance electromagnetic trap. Using the operator averaging method, we obtain an effective quantum operator that asymptotically describes the anharmonic part of the Hamiltonian. We show that the operator becomes a second-order difference operator in a specially chosen quantum action-angle representation. Using the discrete WKB method for this difference equation, we obtain the semiclassical WKB asymptotics of the spectrum and stationary states of the charge.
{"title":"On discrete WKB methods for resonance electromagnetic traps","authors":"E.V. Vybornyi","doi":"10.1109/DD46733.2019.9016596","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016596","url":null,"abstract":"We consider a model quantum Hamiltonian of a charge in a resonance electromagnetic trap. Using the operator averaging method, we obtain an effective quantum operator that asymptotically describes the anharmonic part of the Hamiltonian. We show that the operator becomes a second-order difference operator in a specially chosen quantum action-angle representation. Using the discrete WKB method for this difference equation, we obtain the semiclassical WKB asymptotics of the spectrum and stationary states of the charge.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123086384","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 : 2019-06-01DOI: 10.1109/DD46733.2019.9016464
A. Smirnov
The paper presents a method for constructing hyperelliptic integrals that are reducible to elliptic. Picard–Fuchs equations for integrals of known reducible hyperelliptic differentials are found. Numerous examples of reducible hyperelliptic integrals of the first and the second kind, and examples of Picard–Fuchs equations that have solutions in the form of hyperelliptic integrals are given.
{"title":"Covering of elliptic curves and Fuchsian equations","authors":"A. Smirnov","doi":"10.1109/DD46733.2019.9016464","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016464","url":null,"abstract":"The paper presents a method for constructing hyperelliptic integrals that are reducible to elliptic. Picard–Fuchs equations for integrals of known reducible hyperelliptic differentials are found. Numerous examples of reducible hyperelliptic integrals of the first and the second kind, and examples of Picard–Fuchs equations that have solutions in the form of hyperelliptic integrals are given.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124400451","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 : 2019-06-01DOI: 10.1109/DD46733.2019.9016586
V. Farafonov, V. Ustimov, M. V. Sokolovskaya, V. Il’in
Problem of light scattering by a layered particle with non-confocal spheroidal boundaries of the layers is typically considered in a framework of numerical methods. We suggest a rigorous method of solving this problem and apply it to a similar (but more simple) electrostatic problem. We discuss advantages of the method and demonstrate that it provides new approximations useful for a fast solution of the problem.
{"title":"Solution of the electrostatic problem for a core-mantle particle with non-confocal spheroidal boundaries of the mantle","authors":"V. Farafonov, V. Ustimov, M. V. Sokolovskaya, V. Il’in","doi":"10.1109/DD46733.2019.9016586","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016586","url":null,"abstract":"Problem of light scattering by a layered particle with non-confocal spheroidal boundaries of the layers is typically considered in a framework of numerical methods. We suggest a rigorous method of solving this problem and apply it to a similar (but more simple) electrostatic problem. We discuss advantages of the method and demonstrate that it provides new approximations useful for a fast solution of the problem.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"216 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122390035","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 : 2019-06-01DOI: 10.1109/DD46733.2019.9016558
A. Ivanov, P. Panteleeva
We study a $1tfrac{1}{2}$-degrees of freedom Hamiltonian system with a potential $U(x,varepsilon t) = tfrac{1}{2}(varphi (varepsilon t)x^2 - x^4)$ slowly varying with time. It is assumed that the factor φ(τ) is a periodic function with simple zeroes on its period. Using WKB-method together with a modification of the Melnikov method, we prove that in the adiabatic limit a cascade of bifurcations, occuring when the factor φ passes through the zero value, leads to the existence of transversal homoclinic intersections and multibump trajectories of the system.
{"title":"Multibump trajectories of adiabatically perturbed periodic Hamiltonian systems with pitchfork bifurcations","authors":"A. Ivanov, P. Panteleeva","doi":"10.1109/DD46733.2019.9016558","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016558","url":null,"abstract":"We study a $1tfrac{1}{2}$-degrees of freedom Hamiltonian system with a potential $U(x,varepsilon t) = tfrac{1}{2}(varphi (varepsilon t)x^2 - x^4)$ slowly varying with time. It is assumed that the factor φ(τ) is a periodic function with simple zeroes on its period. Using WKB-method together with a modification of the Melnikov method, we prove that in the adiabatic limit a cascade of bifurcations, occuring when the factor φ passes through the zero value, leads to the existence of transversal homoclinic intersections and multibump trajectories of the system.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130857634","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 : 2019-06-01DOI: 10.1109/DD46733.2019.9016515
L. Goray, A. Dashkov, V. Asadchikov, B. Roshchin, A. Muslimov, V. Kanevsky
Grazing incidence X-ray reflectometry (GIXRR) and fluorescence (GIXRF) analysis of the metallic-coated diffraction grating has been conducted. The grating has the sinusoidal-type groove profile derived from the atomic-force microscopy measurements. Using the developed methods of GIXRR and GIXRF, we theoretically and experimentally investigate angular dependences of the specular reflected and emitted radiation intensity of the Al-coated 400 mm grating with a Cr adhesion layer of the thickness of ~2 nm on the SiO2 substrate working in extreme conical and classical diffraction mounts for the incident wavelength of ~0.1541 nm and the grazing-incidence angle range of ~0.05–0.5 deg. The specular reflectance (the 0-th order efficiency) as well as the specular fluorescence intensity have been found from solutions of the respective vector Helmholtz equations. In order to determine the fluorescence intensity, we have used the approach based on a method of fundamental parameters using the reciprocity theorem.
对金属涂层衍射光栅进行了掠入射x射线反射(GIXRR)和荧光(GIXRF)分析。光栅具有原子力显微镜测量得到的正弦波型凹槽轮廓。利用发展的GIXRR和GIXRF方法，本文从理论和实验两方面研究了在入射波长为~0.1541 nm、掠射入射角范围为~0.05 ~ 0.5°时，在SiO2衬底上镀有厚度为~2 nm的Cr涂层的400 mm al光栅的镜面反射和发射辐射强度与角的依赖关系，得到了镜面反射率(0阶效率)和镜面荧光强度从各自向量亥姆霍兹方程的解中得到。为了确定荧光强度，我们采用了基于互易定理的基本参数方法。
{"title":"Grazing-incidence X-ray reflectometry and fluorescence analysis of the metallic-coated sinusoidal diffraction grating","authors":"L. Goray, A. Dashkov, V. Asadchikov, B. Roshchin, A. Muslimov, V. Kanevsky","doi":"10.1109/DD46733.2019.9016515","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016515","url":null,"abstract":"Grazing incidence X-ray reflectometry (GIXRR) and fluorescence (GIXRF) analysis of the metallic-coated diffraction grating has been conducted. The grating has the sinusoidal-type groove profile derived from the atomic-force microscopy measurements. Using the developed methods of GIXRR and GIXRF, we theoretically and experimentally investigate angular dependences of the specular reflected and emitted radiation intensity of the Al-coated 400 mm grating with a Cr adhesion layer of the thickness of ~2 nm on the SiO2 substrate working in extreme conical and classical diffraction mounts for the incident wavelength of ~0.1541 nm and the grazing-incidence angle range of ~0.05–0.5 deg. The specular reflectance (the 0-th order efficiency) as well as the specular fluorescence intensity have been found from solutions of the respective vector Helmholtz equations. In order to determine the fluorescence intensity, we have used the approach based on a method of fundamental parameters using the reciprocity theorem.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"150 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134410726","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 : 2019-06-01DOI: 10.1109/DD46733.2019.9016450
A. Tagirdzhanov, A. Kiselev
As is well known, time-harmonic “complex sources” wavefields that show a Gaussian-type localization, are solutions of inhomogeneous Helmholtz equation where source functions are supported by certain antennas with a circular edge. We address energy density of a “complex source” wavefield in a neighborhood of the edge of the antenna and show that it is nonintegrable.
{"title":"Nonintegrability of the energy density of “complex sources” wavefields","authors":"A. Tagirdzhanov, A. Kiselev","doi":"10.1109/DD46733.2019.9016450","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016450","url":null,"abstract":"As is well known, time-harmonic “complex sources” wavefields that show a Gaussian-type localization, are solutions of inhomogeneous Helmholtz equation where source functions are supported by certain antennas with a circular edge. We address energy density of a “complex source” wavefield in a neighborhood of the edge of the antenna and show that it is nonintegrable.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114413952","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 : 2019-06-01DOI: 10.1109/DD46733.2019.9016427
G. Iovane, A. Nasedkin
This paper considers a piezoelectric transducer operating on torsional modes. The transducer consists of a piezoelectric cylinder rigidly coupled with an elastic twisted rod. Along the central axis in the cylinder and in the rod, there are the cylindrical hollows with the same radius. The piezoelectric cylinder is made of PZT ceramics, polarized in the circumferential direction. It has two electrodes at the end surfaces and it is rigidly fixed at the bottom end. When a harmonically varying voltage or electric current is applied to the electrodes, in the cylinder predominantly torsional oscillations are generated. The naturally twisted shape of the elastic rod promotes to an additional amplification of torsional vibrations. The analysis of the piezoelectric transducer was carried out in the ANSYS finite element package. A comparison was made of the amplitude-frequency characteristics of the transducer near the first modes of thickness oscillations for the cases of dense and porous PZT ceramics, for the cases of twisted and non-twisted forms of an elastic rod, and for the cases when the oscillations are excited by voltage or by current generators. The results of computational experiments have shown the highest efficiency of the transducer from porous piezoceramics with a twisted rod when the vibrations are excited by the electric current generator.
{"title":"Computer simulation of torsional transducer from porous piezoceramics with twisted rod","authors":"G. Iovane, A. Nasedkin","doi":"10.1109/DD46733.2019.9016427","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016427","url":null,"abstract":"This paper considers a piezoelectric transducer operating on torsional modes. The transducer consists of a piezoelectric cylinder rigidly coupled with an elastic twisted rod. Along the central axis in the cylinder and in the rod, there are the cylindrical hollows with the same radius. The piezoelectric cylinder is made of PZT ceramics, polarized in the circumferential direction. It has two electrodes at the end surfaces and it is rigidly fixed at the bottom end. When a harmonically varying voltage or electric current is applied to the electrodes, in the cylinder predominantly torsional oscillations are generated. The naturally twisted shape of the elastic rod promotes to an additional amplification of torsional vibrations. The analysis of the piezoelectric transducer was carried out in the ANSYS finite element package. A comparison was made of the amplitude-frequency characteristics of the transducer near the first modes of thickness oscillations for the cases of dense and porous PZT ceramics, for the cases of twisted and non-twisted forms of an elastic rod, and for the cases when the oscillations are excited by voltage or by current generators. The results of computational experiments have shown the highest efficiency of the transducer from porous piezoceramics with a twisted rod when the vibrations are excited by the electric current generator.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116517705","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 : 2019-06-01DOI: 10.1109/DD46733.2019.9016609
V. A. Akulichev, V. Bulanov, L. K. Bugaeva
Taking into account new experimental data on the distribution of bubbles in sea water, it is shown that the influence of a near-surface layer of bubbles on the structure of the spatial decay in the propagation of sound can be significant at fairly typical concentrations of bubbles in the near-surface layers of the ocean. In the presence of bubble clouds, a spatial restructuring of the field energy structure is observed, in which the main effect of the bubbles is concentrated at small distances, at the same time not affecting the sound attenuation at large distances.
{"title":"On the structure of the acoustic field in the sea containing a developed bubble layer near the surface","authors":"V. A. Akulichev, V. Bulanov, L. K. Bugaeva","doi":"10.1109/DD46733.2019.9016609","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016609","url":null,"abstract":"Taking into account new experimental data on the distribution of bubbles in sea water, it is shown that the influence of a near-surface layer of bubbles on the structure of the spatial decay in the propagation of sound can be significant at fairly typical concentrations of bubbles in the near-surface layers of the ocean. In the presence of bubble clouds, a spatial restructuring of the field energy structure is observed, in which the main effect of the bubbles is concentrated at small distances, at the same time not affecting the sound attenuation at large distances.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122732293","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 : 2019-06-01DOI: 10.1109/DD46733.2019.9016546
O. Trofimova, A. Kovtanyuk, I. Prokhorov
The paper considers a mathematical model of laser thermotherapy of biological tissue. The model is based on the radiation transfer equation and the heat equation. An algorithm for solving the problem, based on the use of a diffusion approximation with the release of the ballistic component of the radiation flux, was implemented. A numerical analysis of radiation and thermal processes occured under laser irradiation of biological tissue containing a tumor filled with a colloidal solution of gold nanoparticles was carried out. A significant contribution of the scattered radiation component to the temperature increase in the medium was recorded.
{"title":"Mathematical modeling of pulsed laser therapy","authors":"O. Trofimova, A. Kovtanyuk, I. Prokhorov","doi":"10.1109/DD46733.2019.9016546","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016546","url":null,"abstract":"The paper considers a mathematical model of laser thermotherapy of biological tissue. The model is based on the radiation transfer equation and the heat equation. An algorithm for solving the problem, based on the use of a diffusion approximation with the release of the ballistic component of the radiation flux, was implemented. A numerical analysis of radiation and thermal processes occured under laser irradiation of biological tissue containing a tumor filled with a colloidal solution of gold nanoparticles was carried out. A significant contribution of the scattered radiation component to the temperature increase in the medium was recorded.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121005340","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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