An analytical expression for a Rayleigh wave propagating along the surface of a nonhomogenous elastic body (the cases of anisotropic medium and of isotropic medium) of arbitrary shape is obtained using the boundary layer method. The transport equations give possibility to obtain a formula for the amplitude of the wave and the ones for Berry phase.
{"title":"Boundary layer approach to the theory of localized waves","authors":"V. M. Babich, N. Kirpichnikova","doi":"10.1109/DD.2003.238127","DOIUrl":"https://doi.org/10.1109/DD.2003.238127","url":null,"abstract":"An analytical expression for a Rayleigh wave propagating along the surface of a nonhomogenous elastic body (the cases of anisotropic medium and of isotropic medium) of arbitrary shape is obtained using the boundary layer method. The transport equations give possibility to obtain a formula for the amplitude of the wave and the ones for Berry phase.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"336 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":"127575503","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}
New analytical results are presented for the problem of a plane acoustic wave scattering by a flat cone (a quarter plane) with Dirichlet boundary conditions. The results are obtained within a general framework developed by author for the strip/slit diffraction problem. These results include (i) embedding formulae representing the diffraction coefficient in the factorized form through the edge Green's functions depending separately on the direction of incidence and scattering, and (ii) the coordinate equations for the auxiliary functions that reduce the partial differential problem to a boundary problem for a system of ordinary differential equations. The new approach can be treated as a generalization of the separation of variables technique.
{"title":"To the problem of diffraction by an ideal flat cone (quarter-plane)","authors":"A. Shanin","doi":"10.1109/DD.2003.238233","DOIUrl":"https://doi.org/10.1109/DD.2003.238233","url":null,"abstract":"New analytical results are presented for the problem of a plane acoustic wave scattering by a flat cone (a quarter plane) with Dirichlet boundary conditions. The results are obtained within a general framework developed by author for the strip/slit diffraction problem. These results include (i) embedding formulae representing the diffraction coefficient in the factorized form through the edge Green's functions depending separately on the direction of incidence and scattering, and (ii) the coordinate equations for the auxiliary functions that reduce the partial differential problem to a boundary problem for a system of ordinary differential equations. The new approach can be treated as a generalization of the separation of variables technique.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"1996 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":"132228585","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 consider the problem of waves propagation from non uniformly moving sources in electromagnetic dielectric waveguides. Asymptotic formulas for mode components of electromagnetic field have been obtained in which the large parameter /spl lambda//spl Gt/1 characterizes a large distance between moving source and receiver and smallness of acceleration of the source.
{"title":"Nonuniformly moving source in electromagnetic waveguides","authors":"V. Rabinovich, I.M. Sanches","doi":"10.1109/DD.2003.238232","DOIUrl":"https://doi.org/10.1109/DD.2003.238232","url":null,"abstract":"In this paper, we consider the problem of waves propagation from non uniformly moving sources in electromagnetic dielectric waveguides. Asymptotic formulas for mode components of electromagnetic field have been obtained in which the large parameter /spl lambda//spl Gt/1 characterizes a large distance between moving source and receiver and smallness of acceleration of the source.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"128 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":"125383959","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}
The results of numerical simulation on restoration of parameters of local in-homogeneities are considered. Studying of restoration of elastic inhomogeneities and inhomogeneities of electrical conductivity is implemented using elastic and electromagnetic wave fields correspondingly. The direct problem for the Lame and Maxwell equations is solved by the finite difference method. Restoration of parameters is implemented by the diffraction tomography method in the time domain with the help of the first-order Born approximation. In electromagnetic case we study restoration of local inhomogeneity of electrical conductivity using the sounding by diffusion electromagnetic field.
{"title":"Numerical simulation in diffraction tomography with elastic and electromagnetic sounding signals","authors":"Y. Kiselev, V. Troyan","doi":"10.1109/DD.2003.238179","DOIUrl":"https://doi.org/10.1109/DD.2003.238179","url":null,"abstract":"The results of numerical simulation on restoration of parameters of local in-homogeneities are considered. Studying of restoration of elastic inhomogeneities and inhomogeneities of electrical conductivity is implemented using elastic and electromagnetic wave fields correspondingly. The direct problem for the Lame and Maxwell equations is solved by the finite difference method. Restoration of parameters is implemented by the diffraction tomography method in the time domain with the help of the first-order Born approximation. In electromagnetic case we study restoration of local inhomogeneity of electrical conductivity using the sounding by diffusion electromagnetic field.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"44 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":"125918303","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 consider the resonance effects in quantum waveguides and layers with Neumann boundary conditions coupled through small windows. Asymptotics of the resonances (quasi eigenvalues) are obtained. Also the scattering problems for the cases of one and two coupling windows are considered.
{"title":"Laterally coupled waveguides with Neumann boundary condition: formal asymptotic expansions","authors":"L.V. Gortinskaya, I. Popov, E.S. Tesovskaya","doi":"10.1109/DD.2003.238132","DOIUrl":"https://doi.org/10.1109/DD.2003.238132","url":null,"abstract":"We consider the resonance effects in quantum waveguides and layers with Neumann boundary conditions coupled through small windows. Asymptotics of the resonances (quasi eigenvalues) are obtained. Also the scattering problems for the cases of one and two coupling windows are considered.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"44 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":"133357211","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 approaches to solution of the two-dimensional Helmholtz equation with a "wave number" are proposed. The results can be applied both in numerical areas of physics and in the theory of nonlinear equations. The first approach is based on the requirement of the covariance of equation under the generalized Darboux transformation (Moutard transformation). It allows to construct a new solution of equation, using a given initial solution of the equation. Simultaneously we obtain the "dressing" relation for the "wave number". The simplest examples of the approach are considered in detail. In the second approach the Green-Oauchy formula (the /spl part/~ -method) is applied to reduce the solution of the equation to the solution of a system of singular integral equations.
{"title":"Two approaches for Helmholtz equation: generalized Darboux transformation and the method of /spl part/~-problem","authors":"E. Gutshabash","doi":"10.1109/DD.2003.238133","DOIUrl":"https://doi.org/10.1109/DD.2003.238133","url":null,"abstract":"Two approaches to solution of the two-dimensional Helmholtz equation with a \"wave number\" are proposed. The results can be applied both in numerical areas of physics and in the theory of nonlinear equations. The first approach is based on the requirement of the covariance of equation under the generalized Darboux transformation (Moutard transformation). It allows to construct a new solution of equation, using a given initial solution of the equation. Simultaneously we obtain the \"dressing\" relation for the \"wave number\". The simplest examples of the approach are considered in detail. In the second approach the Green-Oauchy formula (the /spl part/~ -method) is applied to reduce the solution of the equation to the solution of a system of singular integral equations.","PeriodicalId":332604,"journal":{"name":"International Seminar Day on Diffraction, 2003. Proceedings.","volume":"15 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":"125301098","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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