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

Application of multivariable complex analysis

• R.C.Assier, A.V.Shanin, Analytical continuation of two-dimensional wave fields // To appear in RSPA (2021) arXiv:2008.10673
• R.C.Assier, A.V.Shanin, Diffraction by a quarter–plane. Analytical continuation of spectral functions // QJMAM, V.72, N.1, P.51-85 (2019) (Open access)
• R.C.Assier, A.V.Shanin, Towards a multivariable Wiener-Hopf method, A mini-course in Isaac Newton Institute (Cambridge), Seminar "Bringing pure and applied analysis together via Wiener-Hopf Technique" Lecture 1 , Lecture 2 , Lecture 3 , Lecture 4 , Lecture 5

Lattices. Analytical approach and numerical techniques

• A.V.Shanin, A.I.Korolkov, Diffraction by a Dirichlet right angle on a discrete planar lattice // Submitted to Wave Motion arXiv preprint
• A.V.Shanin, A.I.Korolkov, Sommerfeld-type integrals for discrete diffraction problems // Wave Motion, V.97, 102606 (2020) DOI:10.1016/j.wavemoti.2020.102606 arXiv preprint
• J.Poblet-Puig, A.V.Shanin, A New Numerical Method for Solving the Acoustic Radiation Problem // Acoustical Physics, V.64, N.2, P.252-259 (2018) arXiv preprint
• J.Poblet-Puig, A.V.Shanin, A boundary algebraic formulation for plane strain elastodynamic scattering // SIAM Journal on Applied Mathematics, V.78, N.2, P.1256-1282 (2018)
• J.Poblet-Puig, V.Yu.Valyaev, A.V.Shanin, Suppression of spurious frequencies in scattering problems by means of boundary algebraic and combined field equations // J. Int. Eq. Appl., V.27, N.2, P.233-272 (2015)
• J.Poblet-Puig, V.Yu.Valyaev, A.V.Shanin, Boundary element method based on preliminary discretization â æóðíàëå Mathematical Models and Computer Simulations, V.6, N.2, P.172-182. (2014)

Waveguides and resonators

• M.A.Mironov, A.V.Shanin, A.I.Korolkov, K.S.Kniazeva, Exchange pulse related to phase synchronism in gas-plate structure // Submitted to Journ. Sound Vibr. arXiv preprint
• A.V.Shanin, K.S.Knyazeva, A.I.Korolkov Riemann surface of dispersion diagram of a multilayer acoustical waveguide Wave Motion, V.83. P.148-172. DOI: 10.1016/j.wavemoti.2018.09.010 arXiv preprint
• A.V.Shanin, Precursor wave in a layered waveguide, JASA, 141, PP. 346-356, 2017. arXiv preprint
• A.V.Shanin, A.I.Korolkov, Diffraction of a mode close to its cut-off by a transversal screen in a planar waveguide, Wave Motion, 68, PP. 218-241, 2017.
• A.I.Korolkov, S.A.Nazarov, A.V.Shanin, Stabilizing solutions at thresholds of the continuous spectrum and anomalous transmission of waves, ZAMM, 96, PP. 1245-1260, 2016.
• S.A. Nazarov, A.V. Shanin, Trapped modes in angular joints of 2D waveguides, Applicable Analysis, 93, PP. 572-582, 2014.
• 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.
• Dorofeev M.S., Shanin A.V. Resonances in a discrete system of variable length // Acoustical Physics V. 55, N 3, pp 307-314 (2009)
• 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)
• 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).

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

• R.C.Assier, A.V.Shanin, Analytical continuation of two-dimensional wave fields // To appear in RSPA (2021) arXiv:2008.10673
• A.V.Shanin, A.I.Korolkov, Diffraction by an impedance strip II. Solving Riemann–Hilbert problems by OE–equation method, QJMAM, 68, PP. 341-362, 2015, arXiv preprint
• A.V.Shanin, A.I.Korolkov, Diffraction by an impedance strip I. Reducing diffraction problem to Riemann-Hilbert problems, QJMAM, 68, PP. 321-339, 2015, arXiv preprint
• 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).
• 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).
• 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).
• 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)
• 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, 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, 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, To the problem of diffraction on a slit. Some properties of Schwarzschild's series // Zapiski seminarov POMI, V.275, ñ.258-285 (2001), in Russian, (PDF file, Russian version) (PDF file, English version)
• 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, 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, 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, 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)

Research on conical problems

• R.C.Assier, A.V.Shanin, Diffraction by a quarter–plane. Analytical continuation of spectral functions // QJMAM, V.72, N.1, P.51-85 (2019) (Open access)
• V.Yu.Valyaev, A.V.Shanin, Measurement of the Diffraction Coefficient of a Trihedral Cone with Homogeneous Neumann Boundary Conditions // PIERS Proceedings, Toyama 2018, DOI:10.23919/PIERS.2018.8597926
• 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
• 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
• A.V. Shanin, Diffraction series on a sphere and conical asymptotics // Proceedings of Days on Diffraction'2011, June 2010, S.Pb. PDF file
• 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)
• 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.
• 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., Diffraction by a flat cone // Int. Sem. "Days on Diffraction 2003", 2003, June 22-27, S.Pb. (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)
• 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)
• S.A.Nazarov, A.V. Shanin, Trapped modes in angular joints of 2D waveguides // Applicable Analysis. V.93, N 3 (2014) 572-582.
• 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)
• 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)

Integral equation formalism for the parabolic equation of diffraction theory

• A.I.Korolkov, A.V.Shanin, A.A.Belous, Diffraction by an Elongated Body of Revolution with Impedance Boundaries: the Boundary Integral Parabolic Equation Method // Acoustical Physics, V.65, N.4, P.340-347
• A.V.Shanin, A.I.Korolkov, Diffraction by an elongated body of revolution. A boundary integral equation based on the parabolic equation, Wave Motion, V. 85, N.1, P.176-190. DOI: 10.1016/j.wavemoti.2018.10.006 arXiv preprint
• A.I.Korolkov, A.V.Shanin, The parabolic equation method and the Fresnel approximation in the application to Weinstein's problems, Journal of Mathematical Sciences, 214, PP. 302-321, 2016.
• A.I.Korolkov, A.V.Shanin, High-frequency diffraction by an impedance segment at oblique incidence // Acoustical phyiscs, V. 62, No. 6, PP. 651-658 (2016)
• A.I.Korolkov, A.V.Shanin, High-frequency plane wave diffraction by an ideal strip at oblique incidence: Parabolic equation approach // Acoustical Physics, V.62, N.4, P.405-413

Research on matrix factorization

• 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.
• A.V.Shanin, An ODE-based approach to some Riemann--Hilbert problems motivated by wave diffraction arXiv preprint
• A.V.Shanin, E.M.Doubravsky, Criteria for commutative factorization of a class of algebraic matrices arXiv preprint

Embedding formulae

• 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
• 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, Embedding formulae for diffraction by non-parallel slits // Quart. Journ. Mech. Appl.Math. V. 61. N.1, pp 93-116 (2008). (manuscript, 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)
• 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 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, 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)

• 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, 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, 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 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 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, On wave excitation in a wedge-shaped region // Acoustical Physics, 1996, 42, 5, 612-617.

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.