26 citations · 83 across the 13 of their papers we have counts for
14 papers
Embedding transmission problems for Maxwell's equations into elliptic theory
Yuri A. Godin, Boris Vainberg
We embed general boundary value problems for the time-harmonic Maxwell equations into the elliptic boundary value theory. This is achieved by introducing two new scalar functions t…
Spectral properties of operators and wave propagation in high-contrast media
Yuri A. Godin, Leonid Koralov, Boris Vainberg
The paper aims to study the spectral properties of elliptic operators with highly inhomogeneous coefficients and related issues concerning wave propagation in high-contrast media.…
Local gaps in three-dimensional periodic media
Yuri A. Godin, Boris Vainberg
We consider the propagation of acoustic waves in a medium with a periodic array of small inclusions of arbitrary shape. The inclusion size is much smaller than the array period…
Propagation and dispersion of Bloch waves in periodic media with soft inclusions
Yuri A. Godin, Boris Vainberg
We investigate the behavior of waves in a periodic medium containing small soft inclusions or cavities of arbitrary shape, such that the homogeneous Dirichlet conditions are satisf…
Clusters of Bloch waves in three-dimensional periodic media
Yuri A. Godin, Boris Vainberg
We consider acoustic wave propagation through a periodic array of the inclusions of arbitrary shape. The inclusion size is much smaller than the array period while the wavelength i…
Slowdown of group velocity in periodic waveguides
Yuri A. Godin, Boris Vainberg
We consider the propagation of acoustic, electromagnetic and elastic waves in a one-dimensional periodic two-component material. Accurate asymptotic formulas are provided for the g…
Dispersion of waves in two and three-dimensional periodic media
Yuri A. Godin, Boris Vainberg
We consider the propagation of acoustic time-harmonic waves in a homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavel…
Dispersive and effective properties of two-dimensional periodic media
Yuri A. Godin, Boris Vainberg
We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation…
Effective properties of periodic tubular structures
Yuri A. Godin
A method is described to calculate effective tensor properties of a periodic array of two-phase dielectric tubes embedded in a host matrix. The method uses Weierstrass' quasiperodi…
Effective complex permittivity tensor of a periodic array of cylinders
Yuri A. Godin
We determine the effective complex permittivity of a two-dimensional composite, consisting of an arbitrary doubly periodic array of identical circular cylinders in a homogeneous ma…
The effective conductivity of a periodic lattice of circular inclusions
Yuri A. Godin
We determine the effective conductivity of a two-dimensional composite consisting of a doubly periodic array of identical circular cylinders within a homogeneous matrix. We obtain…
The effect of disorder on the wave propagation in one-dimensional periodic optical systems
Yuri A. Godin, Stanislav Molchanov, Boris Vainberg
The influence of disorder on the transmission through periodic waveguides is studied. Using a canonical form of the transfer matrix we investigate dependence of the Lyapunov expone…
Lyapunov exponent of the random Schrödinger operator with short-range correlated noise potential
Yuri Godin, Stanislav Molchanov, Boris Vainberg
We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties of the process governed by the Schrödinger equation with the white…
On the determination of the boundary impedance from the far field pattern
Yuri A. Godin, Boris Vainberg
We consider the Helmholtz equation in the half space and suggest two methods for determining the boundary impedance from knowledge of the far field pattern of the time-harmonic inc…