411 research outputs found
On the determination of the boundary impedance from the far field pattern
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 incident wave. We introduce a potential for which the far
field patterns in specially selected directions represent its Fourier
coefficients. The boundary impedance is then calculated from the potential by
an explicit formula or from the WKB approximation. Numerical examples are given
to demonstrate efficiency of the approaches. We also discuss the validity of
the WKB approximation in determining the impedance of an obstacle.Comment: 10 pages, 4 figure
Resonance regimes of scattering by small bodies with impedance boundary conditions
The paper concerns scattering of plane waves by a bounded obstacle with
complex valued impedance boundary conditions. We study the spectrum of the
Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic
behavior of the solutions of the scattering problem. The study includes the
case when is an eigenvalue or a resonance. The transformation from the
impedance to the Dirichlet boundary condition as impedance grows is described.
A relation between poles and zeroes of the scattering matrix in the non-self
adjoint case is established. The results are applied to a problem of scattering
by an obstacle with a springy coating. The paper describes the dependence of
the impedance on the properties of the material, that is on forces due to the
deviation of the boundary of the obstacle from the equilibrium position
The effect of disorder on the wave propagation in one-dimensional periodic optical systems
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 exponent on the frequency and
magnitude of the disorder . It is shown that in the bulk of the bands
, while near the band edges it has the order . This dependence is illustrated by numerical simulations.Comment: 15 pages, 4 figure
Propagation and dispersion of Bloch waves in periodic media with soft inclusions
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 satisfied at the boundary. The leading terms of Bloch
waves, their dispersion relations, and cutoff frequencies are rigorously
derived. Our approach reveals the existence of exceptional wave vectors for
which Bloch waves are comprised of clusters of perturbed plane waves that
propagate in different directions. We demonstrate that for these exceptional
wave vectors, no Bloch waves propagate in any one specific direction.Comment: 20 pages, 1 figur
Clusters of Bloch waves in three-dimensional periodic media
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 is fixed. We derive and rigorously justify
the dispersion relation for general frequencies and show that there are
exceptional frequencies for which the solution is a cluster of waves
propagating in different directions with different frequencies so that the
dispersion relation cannot be defined uniquely. Examples are provided for the
spherical inclusions.Comment: 28 pages, 1 figur
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