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Embedding formulae for scattering by three-dimensional structures. (English) Zbl 1231.74230
Summary: The far-field diffraction behaviour for canonical scattering problems involving corners or by sectors, in three-dimensions, is considered. The far-field results are obtained using ideas based upon embedding formulae and therefore complement and extend existing results. Specific geometries such as the flat cone (a sector) and a corner formed by a solid octant are considered in detail. The formulae derived for the diffraction behaviour are also computed in special cases and compared with known results.

MSC:
74J20 Wave scattering in solid mechanics
76Q05 Hydro- and aero-acoustics
35P25 Scattering theory for PDEs
78A45 Diffraction, scattering
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[1] Keller, J.B., The geometric theory of diffraction, J. opt. soc. am., 52, 116-130, (1962)
[2] Osipov, A.V.; Norris, A.N., The malyuzhinets theory for scattering from wedge boundaries: a review, Wave motion, 29, 313-340, (1999) · Zbl 1074.76611
[3] Noble, B., Methods based on the wiener – hopf technique, (1958), Pergamon Press
[4] Jones, D.S., Acoustic and electromagnetic waves, (1986), Oxford University Press
[5] Felsen, L.B.; Marcuvitz, N., Radiation and scattering of waves, (1973), Prentice-Hall · Zbl 0050.41802
[6] Kraus, L.; Levine, L.M., Diffraction by an elliptic cone, Commun. pure appl. math., 14, 49-68, (1961) · Zbl 0096.30502
[7] Blume, S.; Uschkerat, U., The radar cross-section of the semi infinite elliptic cone – numerical evaluation, Wave motion, 22, 311-326, (1995) · Zbl 0968.35526
[8] Smyshlyaev, V.P., Diffraction by conical surfaces at high frequencies, Wave motion, 12, 329-339, (1990) · Zbl 0721.73011
[9] Smyshlyaev, V.P., The high-frequency diffraction of electromagnetic waves by cones of arbitrary cross sections, SIAM J. appl. math., 53, 670-688, (1993) · Zbl 0778.35104
[10] Babich, V.M.; Dementév, D.B.; Samokish, B.A.; Smyshlyaev, V.P., On evaluation of the diffraction coefficients for arbitrary nonsingular directions of a smooth convex cone, SIAM J. appl. math., 60, 536-573, (2000) · Zbl 0992.78016
[11] Bonner, B.D.; Graham, I.G.; Smyshlyaev, V.P., The computation of conical diffraction coefficients in high-frequency acoustic wave scattering, SIAM J. numer. anal., 43, 1202-1230, (2005) · Zbl 1104.65115
[12] Shanin, A.V., Modified smyshlyaev’s formulae for the problem of diffraction of a plane wave by an ideal quarter plane, Wave motion, 41, 79-93, (2005) · Zbl 1189.35056
[13] Craster, R.V.; Shanin, A.N., Embedding formulae for diffraction by rational wedge and angular geometries, Proc. roy. soc. lond. A, 461, 2227-2242, (2005) · Zbl 1206.35075
[14] Williams, M.H., Diffraction by a finite strip, Quart. J. mech. appl. math., 35, 103-124, (1982) · Zbl 0482.73024
[15] Gautesen, A.K., On the green’s function for acoustical diffraction by a strip, J. acoust. soc. am., 74, 600-604, (1983) · Zbl 0525.73021
[16] Martin, P.A.; Wickham, G.R., Diffraction of elastic waves by a penny-shaped crack: analytical and numerical results, Proc. roy. soc. lond. A, 390, 91-129, (1983) · Zbl 0537.73017
[17] Linton, C.M.; McIver, P., Handbook of mathematical techniques for wave/structure interactions, (2001), Chapman-Hall CRC Press · Zbl 0989.76001
[18] Biggs, N.R.T.; Porter, D.; Stirling, D.S.G., Wave diffraction through a perforated breakwater, Quart. J. mech. appl. math., 53, 375-391, (2000) · Zbl 0963.76013
[19] Biggs, N.R.T.; Porter, D., Wave diffraction through a perforated barrier of non-zero thickness, Quart. J. mech. appl. math., 54, 523-547, (2001) · Zbl 1017.76013
[20] Biggs, N.R.T.; Porter, D., Wave scattering by a perforated duct, Quart. J. mech. appl. math., 55, 249-272, (2002) · Zbl 1076.35086
[21] Biggs, N.R.T.; Porter, D., Wave scattering by an array of perforated breakwaters, IMA J. appl. math., 70, 908-936, (2005) · Zbl 1151.35409
[22] Craster, R.V.; Shanin, A.V.; Doubravsky, E.M., Embedding formulae in diffraction theory, Proc. roy. soc. lond. A, 459, 2475-2496, (2003) · Zbl 1092.78504
[23] Skelton, E.A.; Craster, R.V.; Shanin, A.V., Embedding formulae for diffraction by non-parallel slits, Quart. J. mech. appl. math., 61, 93-116, (2008) · Zbl 1132.74020
[24] Biggs, N.R.T., A new family of embedding formulae for diffraction by wedges and polygons, Wave motion, 43, 517-528, (2006) · Zbl 1231.78023
[25] Shanin, A.V., Coordinate equations for a problem on a sphere with a cut associated with diffraction by an ideal quarter plane, Quart. J. mech. appl. math., 58, 289-308, (2005) · Zbl 1072.35065
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