40 research outputs found
High frequency limit of the Transport Cross Section and boundedness of the Total Cross Section in scattering by an obstacle with impedance boundary conditions
The scalar scattering of the plane wave by a strictly convex obstacle with
impedance boundary conditions is considered. The uniform boundedness of the
Total Cross Section for all values of frequencies is proved. The high frequency
limit of the Transport Cross Section is founded and presented as a classical
functional of the variational theory
Radiating and non-radiating sources in elasticity
In this work, we study the inverse source problem of a fixed frequency for
the Navier's equation. We investigate that nonradiating external forces. If the
support of such a force has a convex or non-convex corner or edge on their
boundary, the force must be vanishing there. The vanishing property at corners
and edges holds also for sufficiently smooth transmission eigenfunctions in
elasticity. The idea originates from the enclosure method: The energy identity
and new type exponential solutions for the Navier's equation.Comment: 17 page
Spectral properties of the Dirichlet-to-Neumann operator for exterior Helmholtz problem and its applications to scattering theory
We prove that the Dirichlet-to-Neumann operator (DtN) has no spectrum in the
lower half of the complex plane. We find several application of this fact in
scattering by obstacles with impedance boundary conditions. In particular, we
find an upper bound for the gradient of the scattering amplitude and for the
total cross section. We justify numerical approximations by providing bounds on
difference between theoretical and approximated solutions without using any a
priory unknown constants
Explicit representation of the green's function for the three-dimensional exterior Helmholtz equation
We construct a sequence of solutions of the exterior Helmholtz equation such that their restrictions form
an orthonormal basis on a given surface. The dependence of the coefficients of these functions on the
coefficients of the surface are given by an explicit algebraic formula. In the same way, we construct an
explicit normal derivative of the Dirichlet Greenâs function. We also construct the Dirichlet-to-Neumann
operator. We prove that the normalized coefficients are uniformly bounded from zero.PTDC/MAT/72840/2006CEOCFCTFEDER/ POCT