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1.
A series of multiple diffracted fields in a high-frequency asymptotic expansion of the solution to the problem of grazing
scattering of a plane wave by a smooth periodic boundary is summed in the case of appearance of Wood's anomalies. Bibliography:
8 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 87–100, 1990.
Translated by V. V. Zalipaev. 相似文献
2.
V. V. Zalipaev 《Journal of Mathematical Sciences》2000,102(4):4195-4202
In the present paper, the high-frequency diffraction of a plane wave by a right-angle step discontinuity in an impedance plane
is analyzed with the help of the uniform geometric theory of diffraction, beginning with the Maluzhenets solution. The principal
term of an asymptotic solution of the problem, which is uniform with respect to the angle of incidence of the plane wave and
the angle of observation, is derived. The excitation of primary and multiply diffracted fields radiated from the upper edge,
as well as surface waves, is considered (the lower edge does not radiate cylindrical or surface waves owing to a right-angle
step). For simplicity, the details of computation are given here for a right-angle step discontinuity. A similar procedure
is applied to other examples with more complicated geometry. Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 97–108.
Translated by V. V. Zalipaev. 相似文献
3.
4.
V. V. Zalipaev 《Journal of Mathematical Sciences》2000,102(4):4203-4219
The two-dimensional problem of the scattering of a plane wave by a periodic perfectly conducting grating, an echelette with
a right angle, is considered in the case of a high-frequency approximation (the wavelength is assumed to be small as compared
with the period of the grating). The situation where the incident plane wave glides along one of the faces of a wedge is discussed.
A ray-optical solution of the problem (a shortwave asymptotic result) is derived by the method of summing multiple diffracted
fields, which is well known in the geometric theory of diffraction. The main result of this paper consists of obtaining simple
formulas for the efficiency en of a diffraction order with maximal value of en, derived in the shortwave approximation. Numerical results are presented, and important optical properties obtained by asymptotic
analysis are described. Bibliography: 10 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 109–135.
Translated by V. V. Zalipaev. 相似文献
5.
Zalipaev V. V.; Movchan A. B.; Jones I. S. 《The Quarterly Journal of Mechanics and Applied Mathematics》2007,60(4):457-471
Planar elasticity problems are considered for thin domains fixedalong a small part of the end region boundary. The analysisinvolves two small parameters: the normalized thickness of thebody and the normalized length of the fixed part of the boundary.The aim of the paper is to derive an asymptotic approximationof the solution to a boundary-value problem in such a domainand, in particular, analyze the effective boundary conditions,which occur for the leading-order terms of the asymptotics.We include applications for problems of both anti-plane shearand plane strain elasticity. 相似文献
6.
V. V. Zalipaev 《Journal of Mathematical Sciences》1995,73(3):342-352
High-frequency asymptotic expansion of the coefficients of radiating plane waves in the problem of grazing scattering of a
plane wave on a smooth periodic boundary is derived. Bibliography: 8 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 71–86, 1990.
Translated by V. V. Zalipaev. 相似文献
7.
We developed semiclassical method and show that any smooth potential in graphene describing elongated a quantum dot or wire may behave as a barrier or as a trapping well or as a double barrier potential, Fabry–Perot structure, for 1D Schrödinger equation. The energy spectrum of quantum wires has been found and compared with numerical simulations. We found that there are two types of localized states, stable and metastable, having finite life time. These life times are calculated, as is the form of the localized wave functions which are exponentially decaying away from the wire in the perpendicular direction. 相似文献
8.
The short-wavelength asymptotic behavior of the field near a reflecting boundary (the Fock zone and the neighborhood of the limit ray) is constructed for the problem of the diffraction of a plane wave by a smooth periodic boundary.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Seklova AN SSSR, Vol. 173, pp. 60–86, 1990. 相似文献
9.
The diffraction problem of the penumbral field by a smooth convex contour is solved. New equations are obtained in the Fok region and in the vicinity of the limiting ray. Relations are provided on their basis for multiple diffraction of the penumbral field by humps of a periodic boundary.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 165, pp. 59–90, 1987. 相似文献
10.
Zalipaev V 《Optics letters》1997,22(1):1-3
The problem of plane-wave scattering by an echelette grating with a right angle is considered in the case of high-frequency approximation (the wavelength is assumed to be small compared with the period of grating). We present the results of short-wave asymptotic analysis for a ray optical solution to the problem that was derived on the basis of the method of summation of multiple diffracted fields that is well known in the geometric theory of diffraction. A new effect of perfect blazing for an echelette grating in the high-frequency approximation is also discussed. 相似文献