V. Philippov, N. Kirpichnikova, A. S. Kirpichnikova
A problem of diffraction of creeping waves on a point of transition of a convex boundary to a convex boundary is investigated. It is assumed that at the point of a jump of curvature, the tangent to the boundary is continuous and its derivative has a jump. An expression for the edge wave is obtained and investigated.
{"title":"Effects of diffraction of a creeping wave from a line of jump of curvature","authors":"V. Philippov, N. Kirpichnikova, A. S. Kirpichnikova","doi":"10.1109/DD.1999.816187","DOIUrl":"https://doi.org/10.1109/DD.1999.816187","url":null,"abstract":"A problem of diffraction of creeping waves on a point of transition of a convex boundary to a convex boundary is investigated. It is assumed that at the point of a jump of curvature, the tangent to the boundary is continuous and its derivative has a jump. An expression for the edge wave is obtained and investigated.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132720963","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 study the following initial-boundary value problem for the nonlocal Whitham equation u/sub t/+N(u)+Ku=0, (x,t) /spl isin/R/sup +//spl times/R/sup +/, u(x,0)=u~(x), x/spl isin/R/sup +/, where the nonlinearity is N(u)=u/sub x/u and K is the pseudodifferential operator on the half-line of order /spl alpha/ satisfying 1
{"title":"On the local and global existence of solutions to the nonlocal Whitham equation on half-line","authors":"N. Hayashi, E. Kaikina","doi":"10.1109/DD.1999.816186","DOIUrl":"https://doi.org/10.1109/DD.1999.816186","url":null,"abstract":"We study the following initial-boundary value problem for the nonlocal Whitham equation u/sub t/+N(u)+Ku=0, (x,t) /spl isin/R/sup +//spl times/R/sup +/, u(x,0)=u~(x), x/spl isin/R/sup +/, where the nonlinearity is N(u)=u/sub x/u and K is the pseudodifferential operator on the half-line of order /spl alpha/ satisfying 1</spl alpha/<2 and some dissipative conditions. We prove that if the initial data are such that x/sup /spl delta//u~/spl isin/L/sup 1/, with /spl delta//spl isin/(0, 1/2 ) and the norm /spl par/u~/spl par/X/sup +//spl par/x/sup /spl delta//u~/spl par/(L/sup 1/) is sufficiently small, where X={/spl psi//spl isin/(L/sup 1/), /spl psi/'/spl isin/L/sup 1/;/spl par//spl psi//spl par/x=/spl par//spl psi//spl par/(L/sup 1/)+/spl par//spl psi//sub x//spl par/(L/sup 1/)</spl infin/}, then there exists a unique solution u/spl isin/C ([0, +/spl infin/); L/sup 2/)/spl cap/C(R/sup +/, H/sup 1/) of the initial-value problem (1), where H/sup k/ is the Sobolev space with norm /spl par//spl phi//spl par/(H/sup k/)=/spl par/(1-/spl part//sub 2//sup x/)k/2/spl phi//spl par/(L/sup 2/). We also study large time asymptotics of the solutions.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130759866","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}
Investigates the process of confluence of two circular polarized waves in one linear polarized wave propagating in an ordinary inhomogeneous electromagnetic medium.
研究了在普通非均匀电磁介质中传播的两个圆极化波汇合成一个线性极化波的过程。
{"title":"Electromagnetic waves propagation in a weakly chiral medium","authors":"V.S. Buldyrev, T. Molokova","doi":"10.1109/DD.1999.816179","DOIUrl":"https://doi.org/10.1109/DD.1999.816179","url":null,"abstract":"Investigates the process of confluence of two circular polarized waves in one linear polarized wave propagating in an ordinary inhomogeneous electromagnetic medium.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124150054","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}
It is known that in a cracked layer consisting of alternating fluid and elastic layers and located inside an elastic medium an interference slow wave propagates. It was shown that a number of phenomena observed on crosshole sounding of the media with oil-collectors can be explained by the initiation of a slow wave. Interest in slow waves is related to different geophysical applications (volcanic activity, wave propagation in oil-bearing rocks and so on). A slow wave is a surface wave, the amplitude of which decreases exponentially in both directions away from the layer. The energy of the propagating wave is partially trapped by the elastic medium and, for sufficiently low frequencies, this part of the energy can be significant. A wave of the same nature arises in a fluid layer sandwiched between two elastic halfspaces. At its incidence on a borehole intersecting the cracked or fluid layer, the slow wave excites intricate interference oscillations in the borehole which are related to the response of the elastic medium with a fluid-filled borehole to the incident pertubation. We solve this problem in the low frequency approximation for /spl lambda//spl Gt/a, where /spl lambda/ is a wavelength, and a is the radius of the borehole. Earlier the problem of the excitation of a tube wave in a fluid-filled borehole by the Rayleigh wave propagating along the free surface of an elastic half-space was considered. The problem of slow wave diffraction at a borehole is more complicated because of the dispersion of the phase velocity of the slow wave. In this case we are unable to provide the solution in the time domain in an explicit form and the inverse Fourier transform must be applied.
{"title":"Slow wave diffraction at a borehole","authors":"P.V. Krauklis, L.A. Krauklis","doi":"10.1109/DD.1999.816191","DOIUrl":"https://doi.org/10.1109/DD.1999.816191","url":null,"abstract":"It is known that in a cracked layer consisting of alternating fluid and elastic layers and located inside an elastic medium an interference slow wave propagates. It was shown that a number of phenomena observed on crosshole sounding of the media with oil-collectors can be explained by the initiation of a slow wave. Interest in slow waves is related to different geophysical applications (volcanic activity, wave propagation in oil-bearing rocks and so on). A slow wave is a surface wave, the amplitude of which decreases exponentially in both directions away from the layer. The energy of the propagating wave is partially trapped by the elastic medium and, for sufficiently low frequencies, this part of the energy can be significant. A wave of the same nature arises in a fluid layer sandwiched between two elastic halfspaces. At its incidence on a borehole intersecting the cracked or fluid layer, the slow wave excites intricate interference oscillations in the borehole which are related to the response of the elastic medium with a fluid-filled borehole to the incident pertubation. We solve this problem in the low frequency approximation for /spl lambda//spl Gt/a, where /spl lambda/ is a wavelength, and a is the radius of the borehole. Earlier the problem of the excitation of a tube wave in a fluid-filled borehole by the Rayleigh wave propagating along the free surface of an elastic half-space was considered. The problem of slow wave diffraction at a borehole is more complicated because of the dispersion of the phase velocity of the slow wave. In this case we are unable to provide the solution in the time domain in an explicit form and the inverse Fourier transform must be applied.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124438527","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 an open quantum dot modeled by a straight hard-wall channel with a potential well. If this potential depends on the longitudinal variable only, the system exhibits embedded eigenvalues. They turn into resonances if the symmetry is violated, either by a magnetic field or by deformation of the well. We construct a perturbation theory of these resonances in the case of a weak perturbation and discuss other properties of the model.
{"title":"Magnetoresonances in quantum-dot resonators","authors":"P. Exner","doi":"10.1109/DD.1999.816182","DOIUrl":"https://doi.org/10.1109/DD.1999.816182","url":null,"abstract":"We consider an open quantum dot modeled by a straight hard-wall channel with a potential well. If this potential depends on the longitudinal variable only, the system exhibits embedded eigenvalues. They turn into resonances if the symmetry is violated, either by a magnetic field or by deformation of the well. We construct a perturbation theory of these resonances in the case of a weak perturbation and discuss other properties of the model.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125747069","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 classical TE/TM decomposition of electromagnetic fields and sources valid for isotropic and uniaxially anisotropic linear media is generalized to a class of linear bi-anisotropic media. It is shown that any field in the medium belonging to this class can be split into two individual parts with certain restrictions on their polarizations (the a-field and the b-field). Because of these restrictions, the fields are blind to certain parameter values of the medium. Thus, the original medium can be replaced by simpler effective media for the decomposed fields and, for these media, Green dyadics can be constructed in analytical form.
{"title":"Electromagnetic field and source decomposition in a class of linear media","authors":"I. Lindell, L. Ruotanen, F. Olyslager","doi":"10.1109/DD.1999.816193","DOIUrl":"https://doi.org/10.1109/DD.1999.816193","url":null,"abstract":"The classical TE/TM decomposition of electromagnetic fields and sources valid for isotropic and uniaxially anisotropic linear media is generalized to a class of linear bi-anisotropic media. It is shown that any field in the medium belonging to this class can be split into two individual parts with certain restrictions on their polarizations (the a-field and the b-field). Because of these restrictions, the fields are blind to certain parameter values of the medium. Thus, the original medium can be replaced by simpler effective media for the decomposed fields and, for these media, Green dyadics can be constructed in analytical form.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122252112","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}
On the basis of a unified theoretical formulation of resonances and resonance states in the rigged Hilbert spaces the spectral analysis of the Frobenius-Perron operators corresponding to some exactly solvable chaotic maps has been developed. Tent map and V-map as the simplest representatives of exactly solvable chaos have been studied in detail in the framework of the developed approach. In particular, an extension of the Frobenius-Perron resolvent to a suitable rigged Hilbert space has been constructed and the properties of the generalized spectral decomposition have been studied. Resonances and resonance projections for these maps have been calculated explicitly.
{"title":"Generalized spectral analysis of some exactly solvable chaotic maps","authors":"L. Dmitrieva, D.D. Gushin, Y. Kuperin","doi":"10.1109/DD.1999.816192","DOIUrl":"https://doi.org/10.1109/DD.1999.816192","url":null,"abstract":"On the basis of a unified theoretical formulation of resonances and resonance states in the rigged Hilbert spaces the spectral analysis of the Frobenius-Perron operators corresponding to some exactly solvable chaotic maps has been developed. Tent map and V-map as the simplest representatives of exactly solvable chaos have been studied in detail in the framework of the developed approach. In particular, an extension of the Frobenius-Perron resolvent to a suitable rigged Hilbert space has been constructed and the properties of the generalized spectral decomposition have been studied. Resonances and resonance projections for these maps have been calculated explicitly.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116737938","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}
Let U(t,/spl lambda/) be a solution of the Dirichlet problem y"+(/spl lambda/t-q(t))y=0 -1/spl les/t/spl les/1 y(-1)=0=y(x), with variable t on (-1,x), for fixed x, which satisfies the initial condition U(-1,/spl lambda/)=0, /spl part/U//spl part/t(-1,/spl lambda/)=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, the leading term of the asymptotic formula for /spl part/U//spl part//spl lambda/(x,/spl lambda//sub n/(x)),/spl lambda/'/sub n/(x) and /spl int//sub -1//sup x/ (/spl upsi/,/spl lambda//sub n/)d/spl upsi/ is obtained where /spl lambda//sub n/(x) is a negative eigenvalue of the Dirichlet problem on [-1,x] with fixed x<0.
{"title":"A research note on the second order differential equation","authors":"A. Jodayree Akbarfam, E. Pourreza","doi":"10.1109/DD.1999.816185","DOIUrl":"https://doi.org/10.1109/DD.1999.816185","url":null,"abstract":"Let U(t,/spl lambda/) be a solution of the Dirichlet problem y\"+(/spl lambda/t-q(t))y=0 -1/spl les/t/spl les/1 y(-1)=0=y(x), with variable t on (-1,x), for fixed x, which satisfies the initial condition U(-1,/spl lambda/)=0, /spl part/U//spl part/t(-1,/spl lambda/)=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, the leading term of the asymptotic formula for /spl part/U//spl part//spl lambda/(x,/spl lambda//sub n/(x)),/spl lambda/'/sub n/(x) and /spl int//sub -1//sup x/ (/spl upsi/,/spl lambda//sub n/)d/spl upsi/ is obtained where /spl lambda//sub n/(x) is a negative eigenvalue of the Dirichlet problem on [-1,x] with fixed x<0.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116922090","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}
Numerical simulation of the solution of the (2-D, SV) inverse problem on restoration of elastic parameters (/spl lambda/,/spl mu/) and mass density (/spl rho/) of local (/spl sim//spl lambda//sub p/) inhomogeneity by the diffraction tomography method based upon the first-order Born approximation is considered. The direct problem is solved by the finite difference method. For restoration of parameters of local inhomogeneities the algebraic methods and optimizing procedures are used. In the assumption of the linear relation between desired parameters an accuracy of their restoration is estimated by the numerical simulation.
{"title":"Restoration of elastic and velocity parameters in diffraction tomography","authors":"Y. Kiselev, V. Troyan","doi":"10.1109/DD.1999.816188","DOIUrl":"https://doi.org/10.1109/DD.1999.816188","url":null,"abstract":"Numerical simulation of the solution of the (2-D, SV) inverse problem on restoration of elastic parameters (/spl lambda/,/spl mu/) and mass density (/spl rho/) of local (/spl sim//spl lambda//sub p/) inhomogeneity by the diffraction tomography method based upon the first-order Born approximation is considered. The direct problem is solved by the finite difference method. For restoration of parameters of local inhomogeneities the algebraic methods and optimizing procedures are used. In the assumption of the linear relation between desired parameters an accuracy of their restoration is estimated by the numerical simulation.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134381816","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}
Considers an eigenfunction and an eigenvalue of a spectral problem on the whole axis for a 1D Schrodinger equation. Our goal would be to obtain recursive relations for matrix elements with a different number k and fixed n and m. Calculations are given using auxiliary differential equations and an integral transform. For an anharmonic oscillator, the basic equation is a specialization of the triconfluent Heun equation.
{"title":"Multipole matrix elements","authors":"S. Slavyanov","doi":"10.1109/DD.1999.816200","DOIUrl":"https://doi.org/10.1109/DD.1999.816200","url":null,"abstract":"Considers an eigenfunction and an eigenvalue of a spectral problem on the whole axis for a 1D Schrodinger equation. Our goal would be to obtain recursive relations for matrix elements with a different number k and fixed n and m. Calculations are given using auxiliary differential equations and an integral transform. For an anharmonic oscillator, the basic equation is a specialization of the triconfluent Heun equation.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130236085","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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