Moscow State University, Department of Physics, Acoustics Division

Andrey V. Shanin

Education

• 1988 - Moscow 57th high school
• 1994 - M.Sc. Department of Physics, Moscow State University
• 1997 - Ph.D. Department of Physics, Moscow State University

Professional positions

• 1997-2000: Researcher, Department of Physics, Moscow State University
• 2000-2003: Senior researcher, Department of Physics, Moscow State University
• 2003-present: Reader, Department of Physics, Moscow State University

Research interests

Elastic wedges and functional equations

• A.V.Shanin, On wave excitation in a wedge-shaped region // Acoustical Physics, 1996, 42, 5, 612-617.
• A.V.Shanin, Excitation and scattering of a wedge wave in an obtuse elastic wedge close to 180 // Acoustical Physics, 1997, V. 43, N.3, pp. 344-349. (djvu, Russian)
• A.V.Shanin, Excitation of waves in a wedge-shaped region // Acoustical Physics, 1988, V.44. N.5, pp.592-597 (scanned PDF file, English version)
• A.V.Shanin, Excitation of wave field in a triangle area // Int. sem. "Days on Diffraction 97", proceedings pp. 205-210, 1997, june 3-5, S.Pb.
• A.V.Shanin, Excitation of wave field in a triangular area with impedance boundary Zapiski seminarov POMI, 1988, V.250, pp.300-318 (in Russian) (PDF file, English version)
• A.V.Shanin, V.V.Krylov, An approximate theory for waves in a thin elastic wedge immersed in liquid // Proc.Roy.Soc.L.A, V. 456, N 2001, 2179-2196 (2000) (PDF file)

• A.V.Shanin, Embedding formula for electromagnetic diffraction problem // Zapiski seminarov POMI, V.324, pp.247-261 (2001), in Russian, (PDF file, Russian version) (PDF file, English version)
• R.V.Craster, A.V.Shanin, Embedding formulae for planar cracks // Advanced research workshop "Surface waves in anisotropic and laminated bodies and defect detection", 7-9 February 2002, Moscow
• A.V.Shanin, R.V.Craster, Removable singular points for ordinary differential equations // Europ. J. Appl. Math V.13. N 6. pp. 617-639 (2002). (PDF file) (CUP)
• R.V.Craster, A.V. Shanin, E.M.Doubravsky, Embedding formulae in diffraction theory // Proc.Roy.Soc.Lond.A (2003) V.459, 2475-2496. (PDF file)
• R.V.Craster, A.V.Shanin, Embedding formula for diffraction by wedge and angular geometries // PRSLA, (2005) V.461, 2227-2242 (PDF file)
• E.A.Skelton, R.V.Craster, A.V.Shanin, Embedding formulae for diffraction by non-parallel slits // Quart. Journ. Mech. Appl.Math. V. 61. N.1, pp 93-116 (2008). (manuscript, PDF file)
• A.V.Shanin, R.V.Craster, Pseudo-differential operators for embedding formulae // Journ. Comp. Appl. Math. V.234, pp. 1637-1646 (2010) (manuscript, PDF file)
• E.A. Skelton, R.V. Craster, A.V. Shanin, V.Valyaev. Embedding formulae for scattering by three-dimensional structures. Wave Motion, Vol. 47 (2010) pp. 299–317. (manuscript, PDF file) doi:10.1016/j.wavemoti.2009.11.006

2D diffraction problems (strips etc), generalization of the Wiener-Hopf method, spectral equation method, coordinate equations

• A.V.Shanin, An extension of Wiener-Hoph method: Ordinary differential equations associated with diffraction problems // Proceedings of the Int. Sem. "Days on Diffraction 99", 1999, June 1-3, S.Pb., pp 176-182. (PDF file)
• A.V.Shanin, Three theorems concerning diffraction by a strip or a slit // Q.Jl Mech. Appl. Math. V. 54, No 1, pp. 107-137 (2001) (manuscript, PDF file)
• A.V.Shanin, S.V.Chernyshev, Diffraction by two ideal strips // Int. Sem. "Days on Diffraction 2001", May 29-31(2001), S.Pb. (PDF file)
• A.V.Shanin, Diffraction of a plane wave by two ideal strips // Q.Jl Mech. Appl. Math. V. 56, No 2, pp. 187-215 (2001) (manuscript, PDF file)
• A.V.Shanin, To the problem of diffraction on a slit. Some properties of Schwarzschild's series // Zapiski seminarov POMI, V.275, ß.258-285 (2001), in Russian, (PDF file, Russian version) (PDF file, English version)
• A.V.Shanin, On the connection between the Wiener-hopf method and the theory of ordinary differential equations // Electromagnetic waves and electronic systems 2002, V.7, N 7. (PDF file, English version)
• A.V.Shanin, Further progress in the coordinate equations theory // Int. Sem. "Days on Diffraction 2002", 2002, June 5-8, S.Pb. (PDF file)
• A.V.Shanin, A generalization of the separation of variables method for some 2D diffraction problems // Wave Motion, V.37, N.3, pp. 241-256 (2003) (manuscript, PDF) doi:10.1016/S0165-2125(02)00077-X
• A.V.Shanin, Diffraction by a flat cone // Int. Sem. "Days on Diffraction 2003", 2003, June 22-27, S.Pb. (PDF file)
• A.V.Shanin, E.M.Doubravsky. Acoustical scattering at a gap between two orthogonal, semi-infinite barriers: coordinate and spectral equations // Journ. Eng. Math., V. 59, N.4, 2007, pp.437-449. (manuscript, PDF file)
• Shanin A.V., Edge Green’s functions on a branched surface. Asymptotics of solutions of coordinate and spectral equations // Journal of Mathematical Sciences, V. 148, N5, pp. 769-783 (2008).
• Shanin A.V. Edge Green's functions on a branched surface. Statement of the problem of finding unknown constants// V. 155, N3, pp. 461-474 (2008).
• A.V. Shanin, V.Yu. Valyaev. Numerical procedure for solving the strip problem by the spectral equation // Journal of Computational Acoustics. V. 19, No 3, P. 269-290 (2011).
• A.V.Shanin, A.I.Korolkov, Diffraction by an impedance strip I. Reducing diffraction problem to Riemann-Hilbert problems, Submitted to QJMAM, arXiv preprint
• A.V.Shanin, A.I.Korolkov, Diffraction by an impedance strip II. Solving Riemann–Hilbert problems by OE–equation method, Submitted to QJMAM, arXiv preprint

Research on conical problems

• Shanin A.V., Diffraction by a flat cone // Int. Sem. "Days on Diffraction 2003", 2003, June 22-27, S.Pb. (PDF file)
• Shanin A.V., Modified Smyshlyaev's formulae for the problem of diffraction of a plane wave by an ideal quarter-plane // Wave Motion, V.41, N1, pp. 79-93.
doi:10.1016/j.wavemoti.2004.05.005
• Shanin A.V., Coordinate equations for the Laplace-Beltrami problem on a sphere with a cut // QJMAM, 2005 (58) 2, 1-20 The preprint versions of two previous papers have been sent to URSI contest: Paper 1, PDF file, Paper 2, PDF file. Failed. Sad but true.
• Valyaev V.Yu, Shanin A.V. Derivation of modifed Smyshlyaev's formulae using integral transform of Kontorovich-Lebedev type // Int. Sem. "Days on Diffraction 2010", 2010, June 22-27, S.Pb. (PDF file)
• A.V. Shanin, Diffraction series on a sphere and conical asymptotics // Proceedings of Days on Diffraction'2011, June 2010, S.Pb. PDF file
• A.V.Shanin, Asymptotics of waves diffracted by a cone and diffraction series on a sphere // Zapiski Nauch Sem POMI RAN V.393, P. 234-258, 2011 PDF in Russian , English translation
• V.Valyaev, A.V.Shanin. Embedding formulae for Laplace-Beltrami problems on the sphere with a cut // Wave Motion 2012, V.49, N1, pp. 83-92. doi:10.1016/j.wavemoti.2011.07.004 manuscript, PDF

Embedding formula and spectral equation for Weinstein's class diffraction gratings. Processes in waveguides near the cut-off frequencies

• Shanin A.V. Weinstein's diffraction problem: embedding formula and spectral equation in parabolic approximation // SIAM Journ. Appl. Math. V.70. N4, pp.1201-1218 (2009) (PDF file)
• Shanin A.V. Diffraction of a high-frequency grazing wave by a grating with a complicated period (English translation of a paper published in Zap. nauch. sem. POMI RAN, 2012, 409, to appear in Journal of Mathematical Sciences) (PDF file)
• S.A.Nazarov, A.V. Shanin, Trapped modes in angular joints of 2D waveguides // Applicable Analysis. V.93, N 3 (2014) 572-582.
• A.I.Korolkov, A.V.Shanin, Diffraction by a grating consisting of absorbing screens of different height. New equations // Zap. Nauch. Sem. POMI, V. 422, P. 62-89 (2014), to be translated in J.Math.Sci. (PDF file)
• A.V.Shanin, A.I.Korolkov, Wave Reflection from a Diffraction Grating Consisting of Absorbing Screens: Description in Terms of the Wiener–Hopf–Fock Method // Acoust. Phys., V.60, N.5, P.624-632. (2014) (PDF file)

Waveguides and resonators (including nonlinear acoustics and room acoustics)

• O.V.Rudenko, A.V.Shanin, Nonlinear phenomena accompanying the development of oscillations excited in a layer of a linear dissipative medium by finite displacement of its boundary // Acoustical physics, V.46, No.3, pp.334-341 (2000).
• A.V. Shanin, M.S. Dorofeev, Wave modes in periodic systems of thin tubes, Proceedings of International conference “Days on Diffraction 08”, S.Pb, June 3-6, pp.163-168. (PDF file)
• Dorofeev M.S., Shanin A.V. Resonances in a discrete system of variable length // Acoustical Physics V. 55, N 3, pp 307-314 (2009)
• E. D. Shabalina, N. V. Shirgina, and A. V. Shanin. High Frequency Modes in a Two Dimensional Rectangular Room with Windows // Acoustical Physics, (2010), Vol. 56, No. 4, pp. 525–536.

Research on matrix factorization

• A.V.Shanin, E.M.Doubravsky, Criteria for commutative factorization of a class of algebraic matrices arXiv preprint
• A.V.Shanin, An ODE-based approach to some Riemann--Hilbert problems motivated by wave diffraction arXiv preprint
• A.V.Shanin, Wiener-Hopf matrix factorization using ordinary differential equations in the commutative case arXiv preprint
  Published as
  A.V.Shanin, Solution of Riemann-Hilbert problem related to Wiener-Hopf factorization problem using ordinary differential equations in the commutative case // Quart. Journ. Mech. Appl. Math. Vol. 66, No 4, pp. 533-555 (2013) doi:10.1093/qjmam/hbt017.

D.Sci. thesis (the defence took place on November 18, 2010)

It is entitled "New differential equations for the canonical diffraction problems" (PDF file, in Russian)

The abstract (30 pages) is here, in Russian also

Note

The right of distribution of each paper belongs to the publisher of corresponding Journal. However, usually I retain the right to post here a preprint or the final version of the paper, for educational purposes only. So if you want to use these materials for something else than education, please visit a library or the journal site.