Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016605
V. Borzov, E. Damaskinsky
We consider special linear combinations of classical Chebyshev polynomials (of the 2nd kind) generating a class of polynomials related to “local perturbations” of the coefficients of the discrete Schrödinger equation. These polynomials are called the generalized Chebyshev polynomials. Namely, we find an explicit expression of the coefficients of this linear combination (connection coefficients) using the coefficients of the recurrence relations defining generalized Chebyshev polynomials. This report is a continuation of authors’ work [1].
{"title":"Some identities for generalized Chebyshev polynomials","authors":"V. Borzov, E. Damaskinsky","doi":"10.1109/DD46733.2019.9016605","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016605","url":null,"abstract":"We consider special linear combinations of classical Chebyshev polynomials (of the 2nd kind) generating a class of polynomials related to “local perturbations” of the coefficients of the discrete Schrödinger equation. These polynomials are called the generalized Chebyshev polynomials. Namely, we find an explicit expression of the coefficients of this linear combination (connection coefficients) using the coefficients of the recurrence relations defining generalized Chebyshev polynomials. This report is a continuation of authors’ work [1].","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"21 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":"123466038","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/DD46733.2019.9016418
V. Filatova, L. Pestov, Valeria A. Sedaikina, A. Danilin
The work is devoted to the problem of finding small inclusions in the breast tissue by boundary measurements of acoustic waves generated by sources located on the boundary. In this work, we describe some results of simulations of this problem in 3D. The simulations include the solution of direct and inverse problems. We calculate acoustic waves for a specific breast model (direct problem) [1, 2]. Our approach, proposed in [3, 4], is based on visualization of inclusions and unknown inner boundary between fat and glandular tissues and determination of sound speeds in inclusions using kinematic argument.
{"title":"Breast ultrasound tomography problem: 3D simulation","authors":"V. Filatova, L. Pestov, Valeria A. Sedaikina, A. Danilin","doi":"10.1109/DD46733.2019.9016418","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016418","url":null,"abstract":"The work is devoted to the problem of finding small inclusions in the breast tissue by boundary measurements of acoustic waves generated by sources located on the boundary. In this work, we describe some results of simulations of this problem in 3D. The simulations include the solution of direct and inverse problems. We calculate acoustic waves for a specific breast model (direct problem) [1, 2]. Our approach, proposed in [3, 4], is based on visualization of inclusions and unknown inner boundary between fat and glandular tissues and determination of sound speeds in inclusions using kinematic argument.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"2 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":"132231603","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/DD46733.2019.9016587
N.V. Kharuk, V. Zalipaev, D. Gulevich
In this paper, bound excitons are studied in the frame work of the time-dependent density-functional theory (TDDFT). Two 1D systems are considered: the Kronig–Penney model and a smooth periodic potential. Within the two-band approximation, we study the dependence of the number of bound excitons on the type of exchange-correlation kernels. Two simple approximations are used: the short-ranged contact xc kernel and the long-ranged (or ‘soft-Coulomb’) one. As a result, one or two bound ecxitons are produced, depending on the system.
{"title":"Exciton spectrum within the time-dependent density-functional theory in two models of one-dimensional periodic potential","authors":"N.V. Kharuk, V. Zalipaev, D. Gulevich","doi":"10.1109/DD46733.2019.9016587","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016587","url":null,"abstract":"In this paper, bound excitons are studied in the frame work of the time-dependent density-functional theory (TDDFT). Two 1D systems are considered: the Kronig–Penney model and a smooth periodic potential. Within the two-band approximation, we study the dependence of the number of bound excitons on the type of exchange-correlation kernels. Two simple approximations are used: the short-ranged contact xc kernel and the long-ranged (or ‘soft-Coulomb’) one. As a result, one or two bound ecxitons are produced, depending on the system.","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":"132382795","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/DD46733.2019.9016598
P. Petrov, Matthias Ehrhardt
A wide-angle mode parabolic equation is obtained from the horizontal refraction equation by using the rational-linear approximation of the square-root operator. A finite-difference scheme for the numerical solution of the derived equation is developed. The scheme is based on the standard Crank–Nicolson method and fully-discrete transparent boundary conditions which allow for an accurate simulation of sound propagation on an unbounded domain.
{"title":"Wide-angle mode parabolic equation with transparent boundary conditions and its applications in shallow water acoustics","authors":"P. Petrov, Matthias Ehrhardt","doi":"10.1109/DD46733.2019.9016598","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016598","url":null,"abstract":"A wide-angle mode parabolic equation is obtained from the horizontal refraction equation by using the rational-linear approximation of the square-root operator. A finite-difference scheme for the numerical solution of the derived equation is developed. The scheme is based on the standard Crank–Nicolson method and fully-discrete transparent boundary conditions which allow for an accurate simulation of sound propagation on an unbounded domain.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"26 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":"134541318","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/DD46733.2019.9016567
M. Yavorsky, D. Vikulin, E. Barshak, B. Lapin, C. Alexeyev
The propagation of linearly polarized optical vortices of unit topological charge through circular optical fibers endowed with a propagating fundamental flexural acoustic wave is considered. A novel polarization-dependent optical vortex transformation is shown, in which the sign of the topological charge (and orbital angular momentum) of an outgoing vortex beam is determined by the direction of the incident linear polarization. This effect can be used for implementing a fast dynamic continuous control of both the orbital angular momentum and the intensity of outcoming vortex beams.
{"title":"All-fiber polarization-dependent optical-vortex-controlling via acousto-optic interaction","authors":"M. Yavorsky, D. Vikulin, E. Barshak, B. Lapin, C. Alexeyev","doi":"10.1109/DD46733.2019.9016567","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016567","url":null,"abstract":"The propagation of linearly polarized optical vortices of unit topological charge through circular optical fibers endowed with a propagating fundamental flexural acoustic wave is considered. A novel polarization-dependent optical vortex transformation is shown, in which the sign of the topological charge (and orbital angular momentum) of an outgoing vortex beam is determined by the direction of the incident linear polarization. This effect can be used for implementing a fast dynamic continuous control of both the orbital angular momentum and the intensity of outcoming vortex beams.","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":"128696876","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/DD46733.2019.9016524
G. V. Tushavin, A. Trifanov, E. Trifanova, I.A. Shipitsyn
We studied the structure of invariant subspaces of effective Hamiltonian of phase light modulation process [1]. Hamiltonian generators satisfy the commutation relationships of SU(2) rotation group [2], thus we can derive their Bose operator representation by using Jordan mapping technique. However, due to the dimensionality of Fock space and additional symmetries of Bose operators, tasks of obtaining eigenbasis, as well as complete classification of invariant subspaces, become nontrivial. In this work, we obtain the relations between the bases of invariant subspaces and derive a classification of the last ones.
{"title":"Structure of invariant subspaces of the rotation group image under the Jordan mapping","authors":"G. V. Tushavin, A. Trifanov, E. Trifanova, I.A. Shipitsyn","doi":"10.1109/DD46733.2019.9016524","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016524","url":null,"abstract":"We studied the structure of invariant subspaces of effective Hamiltonian of phase light modulation process [1]. Hamiltonian generators satisfy the commutation relationships of SU(2) rotation group [2], thus we can derive their Bose operator representation by using Jordan mapping technique. However, due to the dimensionality of Fock space and additional symmetries of Bose operators, tasks of obtaining eigenbasis, as well as complete classification of invariant subspaces, become nontrivial. In this work, we obtain the relations between the bases of invariant subspaces and derive a classification of the last ones.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"16 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":"122359108","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/DD46733.2019.9016576
M. Lyalinov, S. V. Polyanskaya
In this work we study the scattering of a plane incident wave by a semi-infinite impedance sector. We develop an approach that enables us to compute different components in the far-field asymptotics. The method is based on the Sommerfeld integral representation of the scattered wave field, on the careful study of singularities of the integrand and on the asymptotic evaluation of the integral by means of the saddle point technique. In this way, we describe the waves reflected from the sector, diffracted by its edges or scattered by the vertex as well as the surface waves.
{"title":"The asymptotics of the wave field scattered by an impedance sector","authors":"M. Lyalinov, S. V. Polyanskaya","doi":"10.1109/DD46733.2019.9016576","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016576","url":null,"abstract":"In this work we study the scattering of a plane incident wave by a semi-infinite impedance sector. We develop an approach that enables us to compute different components in the far-field asymptotics. The method is based on the Sommerfeld integral representation of the scattered wave field, on the careful study of singularities of the integrand and on the asymptotic evaluation of the integral by means of the saddle point technique. In this way, we describe the waves reflected from the sector, diffracted by its edges or scattered by the vertex as well as the surface waves.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"101 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":"130923276","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/DD46733.2019.9016458
M. Popov
In this paper we present a new concept of theory of surface wave propagation along smooth, strictly convex surfaces imbedded in 3D Euclidian space. It is based, actually, on the extension of the locality principle which is well known in the short wave diffraction and propagation.
{"title":"On theory of surface wave propagation on smooth strictly convex surfaces embedded in ℝ3","authors":"M. Popov","doi":"10.1109/DD46733.2019.9016458","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016458","url":null,"abstract":"In this paper we present a new concept of theory of surface wave propagation along smooth, strictly convex surfaces imbedded in 3D Euclidian space. It is based, actually, on the extension of the locality principle which is well known in the short wave diffraction and propagation.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"9 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":"132020924","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/dd46733.2019.9016503
{"title":"[Front matter]","authors":"","doi":"10.1109/dd46733.2019.9016503","DOIUrl":"https://doi.org/10.1109/dd46733.2019.9016503","url":null,"abstract":"","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":"116748618","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/DD46733.2019.9016575
V. A. Es'kin, A. Kudrin
A method for constructing an orthogonal system of eigenwaves of a cluster of open cylindrical waveguides filled with a gyrotropic medium and located in free space is developed. A procedure for obtaining the discrete- and continuous-spectrum waves of such a guiding system is described.
{"title":"A method for constructing an orthogonal system of eigenwaves of a cluster of open gyrotropic cylindrical waveguides","authors":"V. A. Es'kin, A. Kudrin","doi":"10.1109/DD46733.2019.9016575","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016575","url":null,"abstract":"A method for constructing an orthogonal system of eigenwaves of a cluster of open cylindrical waveguides filled with a gyrotropic medium and located in free space is developed. A procedure for obtaining the discrete- and continuous-spectrum waves of such a guiding system is described.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"86 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":"134472628","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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