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341. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/grating5.pdf
DIFFRACTION OF A PLANE WAVE BY TWO IDEAL STRIPS by Andrey V. Shanin (Department of Physics, Acoustics, Moscow State University, Leninskie Gory, Moscow 119992, Russia ) Summary The problem of scattering of a plane wave by two strips lying in one plane and having ideal boundary conditions is studied. ... The results listed above are obtained by applying two independent approaches: the Wiener-Hopf functional equations approach and the diffraction (Schwarzschild's) series approach. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/grating5.pdf -- 364.4 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/grating5.pdf -- 364.4 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/grating5.pdf -- 364.4 Кб -- 14.03.2011
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342. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/impetr_a.pdf
Excitation of wave field in a triangle with impedance boundary Andrey V.Shanin Introduction Here we consider the problem of excitation of wave field in equilateral triangular area with impedance boundary conditions. ... Fourier transform of the field on the boundary is the unknown function of this equation. ... Boundary conditions have the impedance form u - iuk0 sin = , n (2) where sin is a parameter, and are known functions that correspond to forces on the boundary. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/impetr_a.pdf -- 139.7 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/impetr_a.pdf -- 139.7 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/impetr_a.pdf -- 139.7 Кб -- 14.03.2011
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343. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/inclined.pdf
Emb edding formulae for diffraction by wedge and angular geometries B y R. V. Craster1 A. V. Shanin 1 2 2 Department of Mathematics, Imperial Col lege of Science, Technology ... London SW7 2BZ, U.K. Department of Physics (Acoustics Division), Moscow State University, 119992, Leninskie Gory, Moscow, Russia Embedding is the process of taking the far field directivity from a diffraction problem (or problems) involving line sources or multipoles placed at a sharp ... The Wedge, pp. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/inclined.pdf -- 177.4 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/inclined.pdf -- 177.4 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/inclined.pdf -- 177.4 Кб -- 14.03.2011
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344. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/p212.pdf
... Дмв МЕК ? ... ДНЕ ДОЕ мд{ Дм гз К ОН КК п йР К ? ... Й ДЕ ?Й Й мИ йДм н Е ДЕ м м ? ... Д ЕК -й в И йз Дмб ЗМ нЕ ? ... йДмб мб МЕ ? ... КЙ Й Й Й Й Й Й Й К Й йДмб - М МЕ ?аб йДм М МЕ И И И К Й Й Й Й ПК Й Й Й ? ... лДм н ЕИ м - мб н З гД м- НО Е ДН Е Й Й МК Й И ООН ? ... МЕ ЦДнЕ И л б вЗН Дм б - мв Е кв Дмб - М МЕ ЦД м - мб - ? ... Юбв ? ... ДнЕ ДШЗ ? ... Еа ЦДнЕ ДнЕ ШЗ ? ... Еа ЦДнЕ зОа ЗН зОаЗО ДнЕ ДнЕ Д ПЕ Е зб Дн И Е Ш- Дмб-Н н ? ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/p212.pdf -- 322.9 Кб -- 30.12.2012
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/p212.pdf -- 322.9 Кб -- 30.12.2012
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/p212.pdf -- 322.9 Кб -- 30.12.2012
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345. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/p258.pdf
Zapiski nauqnyh seminarov POMI Tom 275, 2001 g. A. V. Xanin K ZADAQE O DIFRAKCII NA WELI. NEKOTORYE SVO STVA R DA XVARCXIL^DA Vvedenie Zadaqa difrakcii na polose ili weli privlekaet vnimanie issledovatele u e bolee sta let. ... V to rabote integral~noe uravnenie, k kotoromu svodits zadaqa difrakcii, zamen ets paro obyknovennyh differencial~nyh uravneni . ... Bylo pokazano, qto rexeni podobnyh zadaq udovletvor t differencial~nym uravneni m s racional~nymi ko fficientami. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/p258.pdf -- 260.9 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/p258.pdf -- 260.9 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/p258.pdf -- 260.9 Кб -- 14.03.2011
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346. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/perehody.pdf
To commutative factorization of algebraic matrices Andrey V. Shanin1 , Eugeny M. Doubravsky2 Russia, 119899, Moscow, Moscow State University, Department of Physics, 2 Department of Mechanics and Mathematics October 4, 2005 Abstract The problem of matrix factorization motivated by diffraction or elasticity is studied. ... 7 3.4 Bypass matrices and reformulation of factorization problem Let G be an algebraic matrix, and let W be the set of words associated with this matrix. ... Consider matrix M (k ). ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/perehody.pdf -- 279.0 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/perehody.pdf -- 279.0 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/perehody.pdf -- 279.0 Кб -- 14.03.2011
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347. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/polosa3.pdf
Three Theorems Concerning Diffraction by a Strip or a Slit Andrey V. Shanin Abstract The problem of diffraction on a strip or a slit is under consideration. A functional equation of Wiener-Hopf type is derived; analytical restrictions are imposed on unknown functions. The solution of functional problem (the spectrum of the scattered field) is proved to be a solution of an ordinary differential equation (ODE) with rational coefficients known up to several numerical constants. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/polosa3.pdf -- 368.1 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/polosa3.pdf -- 368.1 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/polosa3.pdf -- 368.1 Кб -- 14.03.2011
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348. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/polosa_dd.pdf
DAY on DIFFRACTION'98 1 An Extension of Wiener-Hopf Metho d: Ordinary Differential Equations Asso ciated with Diffraction Problems Andrey V. Shanin Department of Physics, Moscow State University, Russia e-mail: shanin@ort.ru The problem of plane wave scattering on a strip or a set of strips situated in one plane is under consideration. A functional equation of Wiener-Hopf type with analytical restrictions on unknown functions is derived. ... Let for example U+ (k ) and W (k ) be such functions. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/polosa_dd.pdf -- 114.0 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/polosa_dd.pdf -- 114.0 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/polosa_dd.pdf -- 114.0 Кб -- 14.03.2011
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349. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/proc02.pdf
... The far-field diffraction pattern is a function of these directions. ... For example, if the obstacle is a planar crack in the medium, the auxiliary problems are associated with the excitation of the field by a point source located asymptotically close to the edge of the crack. ... The solution of the auxiliary diffraction problem (in 3D) depends on only three variables: the position of the crack edge, where the source is located and the two angles which determine the direction of the scattering. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/proc02.pdf -- 191.4 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/proc02.pdf -- 191.4 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/proc02.pdf -- 191.4 Кб -- 14.03.2011
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350. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/prsla02.pdf
... Here we construct a general approach to formulating and using embedding formulae, we do this using complementary approaches: overly singular states, and a physical interpretation in terms of sources. ... For example, if the obstacle is a planar crack in the medium, then the auxiliary problems are associated with the excitation of the field by a point source located asymptotically close to the edge of the crack. ... That is, has overly singular behaviour at the edge. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/prsla02.pdf -- 312.7 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/prsla02.pdf -- 312.7 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/prsla02.pdf -- 312.7 Кб -- 14.03.2011
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351. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/pseudodif.pdf
... In contrast to the approach developed in [7], which is based on a differential operator, here a pseudo-differential, i.e., a non-local operator is applied to the wave field. Using this non-local operator a new embedding formula is derived for scattering by a single wedge. ... Using the integral formula for Bessel functions represent the function v as a linear combination of plane waves: v (r, ) = J (k0 r)ei = 1 2 e ik0 r cos( -) i ( - /2) e d (35) where contour is shown in Fig. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/pseudodif.pdf -- 198.7 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/pseudodif.pdf -- 198.7 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/pseudodif.pdf -- 198.7 Кб -- 14.03.2011
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352. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/sepvar.pdf
... According to this method, the initial Helmholtz equation is replaced by a system of matrix equations of order 1. ... 1 Intro duction Separation of variables (SV) is the most powerful technique for finding exact solutions of the problems related to partial differential equations. ... The main idea of the method is to reduce the diffraction problem, which involves the Helmholtz equation, boundary, edge and radiation conditions, to an ordinary differential equation (ODE) of a 1 rather simple form. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/sepvar.pdf -- 259.8 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/sepvar.pdf -- 259.8 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/sepvar.pdf -- 259.8 Кб -- 14.03.2011
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353. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/shwaan1.pdf
To the problem of diffraction on a slit: Some properties of Schwarzschild's series A.V.Shanin Abstract We study the diffraction series (Schwarzschild's series) to solve the problem of diffraction on a slit with ideal boundary conditions. Uing this series we derive the representation obtained earlier by M.Williams and the differential equations for the unknown functions. ... The sequence of successive diffraction on the edges can be continued, thus giving the terms u1212.. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/shwaan1.pdf -- 201.8 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/shwaan1.pdf -- 201.8 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/shwaan1.pdf -- 201.8 Кб -- 14.03.2011
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354. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/trubochki.pdf
... The pap er presents a metho d of finding the disp ersion diagrams, and an inequality for the numb er of mo des, linking the numb er of mo des with the top ological prop erties of the system. node H closednode 1 Introduction cell w1 p1 w2 p2 w3 p3 input terminals opennode Consider an infinite periodic set of tubes filled with compressible lossless linear gas (or liquid). ... The tubes are connected with each other by small nodes. ... There can be dead ends (i.e. closed nodes), or open nodes. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/trubochki.pdf -- 144.1 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/trubochki.pdf -- 144.1 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/trubochki.pdf -- 144.1 Кб -- 14.03.2011
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355. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/ursi1.pdf
... The main feature of the modified Smyshlyaev's formula is that it uses the edge Green's functions instead of the usual Green's function on a sphere with a cut. ... The embedding formula expresses the diffraction coefficient in terms of the edge Green's functions. ... We assume that both Green's functions are found in consideration of the boundary, edge, vertex and radiation conditions formulated for the initial diffraction problem. ... Introduce the edge Green functions for the Neumann problem. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/ursi1.pdf -- 278.5 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/ursi1.pdf -- 278.5 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/ursi1.pdf -- 278.5 Кб -- 14.03.2011
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356. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/ursi2.pdf
... U4 of the coordinate equations. ... A The explicit form of the co ordinate equations coefficients of the coordinate equations (5) are , Y11 Y2 Y = 13 Y1 Y14 15 Y21 Y22 Y23 Y24 Y31 Y32 Y33 Y34 Y41 Y42 , Y43 Y44 The explicit expressions for the as follows ... X4 X= 1 3 3 3 3 X1 X2 X3 X4 4 4 4 4 X1 X2 X3 X4 (35) Figure 6: 3D graph of Re [v 1 ] for = 20 + i where 1 X1 1 X2 1 X3 1 X4 1 1 cos - 2(C1 + E1 ) sin , 2 sin2 ) 2(1 - cos 1 E 1 cos - C2 sin = - cos cos ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/ursi2.pdf -- 421.3 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/ursi2.pdf -- 421.3 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/ursi2.pdf -- 421.3 Кб -- 14.03.2011
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357. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/valyaev10.pdf
... Their approach is to extract the far-field using properties of the Laplace-Beltrami operator on the unit sphere and the far field is represented as a contour integral involving the spherical Green's function of the Laplace-Beltrami operator. ... The canonical problem requires an edge Green's function with, in two (three) dimensions, a line (point) source placed on the sharp edges. ... The angle between the edges is . ... The edge Green's the fields of monopole and dipole f the z -edge of the cone. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/valyaev10.pdf -- 286.5 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/valyaev10.pdf -- 286.5 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/valyaev10.pdf -- 286.5 Кб -- 14.03.2011
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358. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/weinstein09.pdf
... 70, No. 4, pp. 12011218 c 2009 Society for Industrial and Applied Mathematics WEINSTEIN'S DIFFRACTION PROBLEM: EMBEDDING FORMULA AND SPECTRAL EQUATION IN PARABOLIC APPROXIMATION ANDREY V. SHANIN Abstract. A short-wave problem of reflection and radiation by an open end of a two-dimensional planar waveguide is studied. ... A recently developed approach based on the embedding formula and the "spectral" equation for the directivity of an edge Green's function is applied to the problem. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/weinstein09.pdf -- 284.6 Кб -- 14.03.2011
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/weinstein09.pdf -- 284.6 Кб -- 14.03.2011
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/weinstein09.pdf -- 284.6 Кб -- 14.03.2011
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359. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/weinstein2_eng.pdf
Diffraction of a high-frequency grazing wave by a grating with a complicated period A. V. Shanin January 3, 2013 Abstract A 2D problem of propagation of a plane wave on a branched surface with a periodic set of branch points is studied. ... The branched surface consists of the "main" sheet and an infinite number of "auxiliary" sheets. ... 75) 24 main sheet y uin q x Figure 4: Two-sheet branched surface for the model problem Compute the field to the right of the branch point, i.e. for x > 0. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/weinstein2_eng.pdf -- 152.4 Кб -- 03.01.2013
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/weinstein2_eng.pdf -- 152.4 Кб -- 03.01.2013
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/weinstein2_eng.pdf -- 152.4 Кб -- 03.01.2013
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360. http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/zapiski14a_eng.pdf
... Edge Green functions are introduced. The embedding formula and the spectral equation for the edge Green functions are derived. ... This formula expresses the scattering co ecients in terms of the directivities of the edge Green functions. ... One can see that the edge Green functions are generated by p oint sources. ... 5 Embedding formula An emb edding formula links the scattering co ecients of the initial problem with the directivities of the edge Green functions. ... 2 shown in Fig. ... Fig. ...
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Ссылки http://acoustics.phys.msu.su/teachers/shanin_files/~shanin/papers/zapiski14a_eng.pdf -- 369.8 Кб -- 05.12.2014
[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/zapiski14a_eng.pdf -- 369.8 Кб -- 05.12.2014
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[ Текст ] Ссылки http://acoustics.phys.msu.ru/teachers/shanin_files/~shanin/papers/zapiski14a_eng.pdf -- 369.8 Кб -- 05.12.2014
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