Consider the Dirichlet-to-Neumann operator N in the exterior problem for the 2D Helmholtz equation outside a bounded domain with smooth boundary. Using parametrization of the boundary by normalized arclength, we treat N as a pseudodifferential operator on the unit circle. We study its discrete symbol. We put, forward a conjecture on the universal behaviour, independent of shape and curvature of the boundary, of the symbol as the wavenumber k /spl rarr/ /spl infin/. The conjecture is motivated by an explicit formula for circular boundary, and confirmed numerically for other shapes. It also agrees, on a physical level of rigor, with Kirchhoff's approximation. The conjecture, if true, opens new ways in numerical analysis of diffraction in the range of moderately high frequencies.
{"title":"Symbol of the Dirichlet-to-Neumann operator in 2D diffraction problems with large wavenumber","authors":"M. Kondratieva, S. Sadov","doi":"10.1109/DD.2003.238180","DOIUrl":"https://doi.org/10.1109/DD.2003.238180","url":null,"abstract":"Consider the Dirichlet-to-Neumann operator N in the exterior problem for the 2D Helmholtz equation outside a bounded domain with smooth boundary. Using parametrization of the boundary by normalized arclength, we treat N as a pseudodifferential operator on the unit circle. We study its discrete symbol. We put, forward a conjecture on the universal behaviour, independent of shape and curvature of the boundary, of the symbol as the wavenumber k /spl rarr/ /spl infin/. The conjecture is motivated by an explicit formula for circular boundary, and confirmed numerically for other shapes. It also agrees, on a physical level of rigor, with Kirchhoff's approximation. The conjecture, if true, opens new ways in numerical analysis of diffraction in the range of moderately high frequencies.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117159081","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}
This paper describes the waves formed by the sources on expanding circular frames. The solution is constructed by means of Smirnov method of incomplete separation of variables. The circular source expanding with a velocity that is greater than the velocity of light may be realized by means of the pulse of hard radiation with the conical front and the absorptive plane. The constructed scalar solutions can be used for electromagnetic waves.
{"title":"Waves generated by sources on expanding circular frames","authors":"V. Borisov","doi":"10.1109/DD.2003.238129","DOIUrl":"https://doi.org/10.1109/DD.2003.238129","url":null,"abstract":"This paper describes the waves formed by the sources on expanding circular frames. The solution is constructed by means of Smirnov method of incomplete separation of variables. The circular source expanding with a velocity that is greater than the velocity of light may be realized by means of the pulse of hard radiation with the conical front and the absorptive plane. The constructed scalar solutions can be used for electromagnetic waves.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134493604","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}
All accelerating part of a linear collider is considered. To maximize the accelerating gradient, profiles of amplifying radial channels of a. supercollider are required to be optimized. A spectral problem - to find profiles of waveguide channels providing zero eigenvalue for Helmholtz type operator under corresponding boundary conditions - is settled. A constructive algorithm for this zero eigenvalue problem basing on the method of discrete sources together with singular value decomposition technique is developed. To check on the possibilities of this numerical algorithm, an analytical test problem is suggested. Several types of boundary profiles for amplifying waveguide channels are considered. Optimal parameters for these profiles are obtained.
{"title":"Singular value decomposition as a tool for solving of spectral problems arisen in supercollider simulation","authors":"Y. Bogomolov, E. S. Semenov, A.D. Yunakovsky","doi":"10.1109/DD.2003.238128","DOIUrl":"https://doi.org/10.1109/DD.2003.238128","url":null,"abstract":"All accelerating part of a linear collider is considered. To maximize the accelerating gradient, profiles of amplifying radial channels of a. supercollider are required to be optimized. A spectral problem - to find profiles of waveguide channels providing zero eigenvalue for Helmholtz type operator under corresponding boundary conditions - is settled. A constructive algorithm for this zero eigenvalue problem basing on the method of discrete sources together with singular value decomposition technique is developed. To check on the possibilities of this numerical algorithm, an analytical test problem is suggested. Several types of boundary profiles for amplifying waveguide channels are considered. Optimal parameters for these profiles are obtained.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126570802","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}
This article is concerned with the transmission of sound along a two-dimensional duct with a dissipative component that has one wave-bearing surface. Harmonic time dependence, e/sup -i/spl omega/t/ is assumed throughout and the boundary value problem is posed in terms of nondimensional variables. In this article, it is shown how the system of equations obtained through mode matching may be recast so that they do not depend on the roots of the dispersion relation. Numerical results demonstrating some of the transmission features of the silencer are also presented. The boundary value problem describing the propagation of sound through a duct with a finite length, flexible-walled silencer is presented. It is possible to calculate the reflected and transmitted power for a dissipative silencer with wave-bearing boundaries without solving the dispersion relation.
{"title":"Acoustic transmission through a silencer with wave-bearing boundaries","authors":"I. M. Mohamed-Guled, J. B. Lawrie","doi":"10.1109/DD.2003.238184","DOIUrl":"https://doi.org/10.1109/DD.2003.238184","url":null,"abstract":"This article is concerned with the transmission of sound along a two-dimensional duct with a dissipative component that has one wave-bearing surface. Harmonic time dependence, e/sup -i/spl omega/t/ is assumed throughout and the boundary value problem is posed in terms of nondimensional variables. In this article, it is shown how the system of equations obtained through mode matching may be recast so that they do not depend on the roots of the dispersion relation. Numerical results demonstrating some of the transmission features of the silencer are also presented. The boundary value problem describing the propagation of sound through a duct with a finite length, flexible-walled silencer is presented. It is possible to calculate the reflected and transmitted power for a dissipative silencer with wave-bearing boundaries without solving the dispersion relation.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134545333","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}
In this paper, we give a general treatment of the propagation of nonlinear acceleration waves in approximately constrained elastic materials. By means of a suitable perturbative scheme, namely a Laurent expansion for the constitutive functions, we can derive the characteristic of acceleration waves, speeds and amplitudes, for elastic bodies with first and second-order poles. The theory is applied to St. Venant-Kirchhoff materials, which can be used to approximate rigid or incompressible bodies, to isotropic, anisotropic materials and to a model for unidirectionally fiber-reinforced composites.
{"title":"Nonlinear waves in approximately constrained materials","authors":"F. Pastrone, M. Tonon","doi":"10.1109/DD.2003.238229","DOIUrl":"https://doi.org/10.1109/DD.2003.238229","url":null,"abstract":"In this paper, we give a general treatment of the propagation of nonlinear acceleration waves in approximately constrained elastic materials. By means of a suitable perturbative scheme, namely a Laurent expansion for the constitutive functions, we can derive the characteristic of acceleration waves, speeds and amplitudes, for elastic bodies with first and second-order poles. The theory is applied to St. Venant-Kirchhoff materials, which can be used to approximate rigid or incompressible bodies, to isotropic, anisotropic materials and to a model for unidirectionally fiber-reinforced composites.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115217878","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}
Solution of the nonlinear wave equation with a small external force is investigated. The frequency of external force varies slowly and passes through resonance. The resonance generates a solitary packets of waves. Full asymptotic description of this process is presented.
{"title":"Generation of solitary packets of waves by resonance","authors":"S. Glebov, V. Lazarev, O. Kiselev","doi":"10.1109/DD.2003.238131","DOIUrl":"https://doi.org/10.1109/DD.2003.238131","url":null,"abstract":"Solution of the nonlinear wave equation with a small external force is investigated. The frequency of external force varies slowly and passes through resonance. The resonance generates a solitary packets of waves. Full asymptotic description of this process is presented.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123165825","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}
Transient, solutions of the inhomogeneous wave equation is constructed in terms of spherical harmonics. The source belongs to the spherical pulsating surface. The velocity of sphere is grater than the wavefront velocity. The possibility of description of electromagnetic waves by means of the scalar solution is discussed.
{"title":"On transient waves produced by a source on superluminal pulsate sphere","authors":"I. Simonenko","doi":"10.1109/DD.2003.238234","DOIUrl":"https://doi.org/10.1109/DD.2003.238234","url":null,"abstract":"Transient, solutions of the inhomogeneous wave equation is constructed in terms of spherical harmonics. The source belongs to the spherical pulsating surface. The velocity of sphere is grater than the wavefront velocity. The possibility of description of electromagnetic waves by means of the scalar solution is discussed.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123472705","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}
An analytical solution of two-dimensional problem of finding frequencies and forms of natural oscillations of a cylindrical resonator having special form is constructed. The cross-section of a resonator consists of circle with adjacent concentric truncated sector. Two outside round and radial boundaries of the system are ideally rigid. The arc wall between two regions is a thin elastic cylindrical shell with the clamped edges. The adjacent cavities of the resonator are filled with various ideal compressible irrotational fluids. The effect of a natural frequencies lowering under diminution of sector radial size is confirmed.
{"title":"Free acoustic oscillations in cylindrical tube coupled with annular sector cavity","authors":"Y. Lavrov, V. V. Piotrovitch","doi":"10.1109/DD.2003.238183","DOIUrl":"https://doi.org/10.1109/DD.2003.238183","url":null,"abstract":"An analytical solution of two-dimensional problem of finding frequencies and forms of natural oscillations of a cylindrical resonator having special form is constructed. The cross-section of a resonator consists of circle with adjacent concentric truncated sector. Two outside round and radial boundaries of the system are ideally rigid. The arc wall between two regions is a thin elastic cylindrical shell with the clamped edges. The adjacent cavities of the resonator are filled with various ideal compressible irrotational fluids. The effect of a natural frequencies lowering under diminution of sector radial size is confirmed.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132918228","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}
We show a new phenomenon which has been found numerically for coherent electronic transmission through a mesoscopic quantum wire with a step structure. The motion of free electrons in the wire is ballistic with specular reflections from the Dirichlet boundaries. The wire allows only a few modes for electronic transmission. We have found numerically that the electric current shows periodic oscillations with small but nonnegligible amplitudes as a function of a system parameter. We explain that this is purely the effects of diffraction and constructive interference of transmitting electrons at the step structure of the wire.
{"title":"Numerical evidence of diffraction in electronic transmission through a stepped quantum wire","authors":"H. Ishio","doi":"10.1109/DD.2003.238177","DOIUrl":"https://doi.org/10.1109/DD.2003.238177","url":null,"abstract":"We show a new phenomenon which has been found numerically for coherent electronic transmission through a mesoscopic quantum wire with a step structure. The motion of free electrons in the wire is ballistic with specular reflections from the Dirichlet boundaries. The wire allows only a few modes for electronic transmission. We have found numerically that the electric current shows periodic oscillations with small but nonnegligible amplitudes as a function of a system parameter. We explain that this is purely the effects of diffraction and constructive interference of transmitting electrons at the step structure of the wire.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122683842","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}
Two-dimensional long wave nonlinear models are developed to describe the propagation of the rogue waves. It is shown that the simplest model corresponds to the Kadomtsev-Petviashvili equation, while the influence of the atmosphere movement and the current in the ocean on the generation of the rogue waves is resulted in derivation of new nonlinear integro-differential equation. Two mechanisms of the rogue wave formation are proposed on. the basis of the model equations. First is based on a resonant interaction of inclined plane solitary waves. According to the second one the rogue wave is single two-dimensionally localized travelling wave having the pit shape.
{"title":"Two-dimensional long wave nonlinear models for the rogue waves in the ocean","authors":"A. Porubov, I. Lavrenov, D. Shevchenko","doi":"10.1109/DD.2003.238231","DOIUrl":"https://doi.org/10.1109/DD.2003.238231","url":null,"abstract":"Two-dimensional long wave nonlinear models are developed to describe the propagation of the rogue waves. It is shown that the simplest model corresponds to the Kadomtsev-Petviashvili equation, while the influence of the atmosphere movement and the current in the ocean on the generation of the rogue waves is resulted in derivation of new nonlinear integro-differential equation. Two mechanisms of the rogue wave formation are proposed on. the basis of the model equations. First is based on a resonant interaction of inclined plane solitary waves. According to the second one the rogue wave is single two-dimensionally localized travelling wave having the pit shape.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128536246","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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