Zobrazeno 1 - 10
of 170
pro vyhledávání: '"Shanin, A. V."'
This work is motivated by an attempt to construct a two-dimensional analogue of the Wiener--Hopf method. It is supposed that understanding the branching structure of unknown functions will provide insight into the form in which these functions can be
Externí odkaz:
http://arxiv.org/abs/2412.02481
We propose a general procedure to study double integrals arising when considering wave propagation in periodic structures. This method, based on a complex deformation of the integration surface to bypass the integrands' singularities, is particularly
Externí odkaz:
http://arxiv.org/abs/2402.08076
We apply the stationary phase method developed in (Assier, Shanin \& Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written as a double Fourier transform of an unknown spectral function. We make
Externí odkaz:
http://arxiv.org/abs/2310.18031
A contribution to the mathematical theory of diffraction. Part I: A note on double Fourier integrals
We consider a large class of physical fields $u$ written as double inverse Fourier transforms of some functions $F$ of two complex variables. Such integrals occur very often in practice, especially in diffraction theory. Our aim is to provide a close
Externí odkaz:
http://arxiv.org/abs/2204.02729
A modification of the saddle point method is proposed for computation of non-stationary wave processes (pulses) in waveguides. The dispersion diagram of the waveguide is continued analytically. A set of possible saddle points on the dispersion diagra
Externí odkaz:
http://arxiv.org/abs/2103.06537
Autor:
Shanin, A. V., Korolkov, A. I.
A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld transformant of the
Externí odkaz:
http://arxiv.org/abs/2009.03355
Autor:
Assier, Raphael C., Shanin, Andrey V.
Publikováno v:
Proc. Roy. Soc. A, 477:2020081, 2021
Wave fields obeying the 2D Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing ideal boundary
Externí odkaz:
http://arxiv.org/abs/2008.10673
Problems of pulse excitation in an acoustic waveguide with a flexible wall and in an acoustic half-space with a flexible wall are studied. In both cases the flexible wall is described by a thin plate equation. The solutions are written as double Four
Externí odkaz:
http://arxiv.org/abs/2007.12687
A thin two-layered waveguide is considered. The governing equations for this waveguide is a matrix Klein--Gordon equation of dimension~2. A formal solution of this system in the form of a double integral can be obtained by using Fourier transformatio
Externí odkaz:
http://arxiv.org/abs/2006.14990
Autor:
Assier, Raphaël C., Shanin, Andrey V.
In our previous work (Assier \& Shanin, QJMAM, 2019), we gave a new spectral formulation in two complex variables associated with the problem of plane-wave diffraction by a quarter-plane. In particular, we showed that the unknown spectral function sa
Externí odkaz:
http://arxiv.org/abs/2004.08700