3,219 research outputs found
Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics
Scattering theory has had a major roll in twentieth century mathematical
physics. Mathematical modeling and algorithms of direct,- and inverse
electromagnetic scattering formulation due to biological tissues are
investigated. The algorithms are used for a model based illustration technique
within the microwave range. A number of methods is given to solve the inverse
electromagnetic scattering problem in which the nonlinear and ill-posed nature
of the problem are acknowledged.Comment: 61 pages, 5 figure
Uniqueness and factorization method for inverse elastic scattering with a single incoming wave
The first part of this paper is concerned with the uniqueness to inverse
time-harmonic elastic scattering from bounded rigid obstacles in two
dimensions. It is proved that a connected polygonal obstacle can be uniquely
identified by the far-field pattern over all observation directions
corresponding to a single incident plane wave. Our approach is based on a new
reflection principle for the first boundary value problem of the Navier
equation. In the second part, we propose a revisited factorization method to
recover a rigid elastic body with a single far-field pattern
Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets
We start by a review of the chronology of mathematical results on the
Dirichlet-to-Neumann map which paved the way towards the physics of
transformational acoustics. We then rederive the expression for the
(anisotropic) density and bulk modulus appearing in the pressure wave equation
written in the transformed coordinates. A spherical acoustic cloak consisting
of an alternation of homogeneous isotropic concentric layers is further
proposed based on the effective medium theory. This cloak is characterised by a
low reflection and good efficiency over a large bandwidth for both near and far
fields, which approximates the ideal cloak with a inhomogeneous and anisotropic
distribution of material parameters. The latter suffers from singular material
parameters on its inner surface. This singularity depends upon the sharpness of
corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak
becomes more and more singular when the number of vertices increases if it is
star shaped. We thus analyse the acoustic response of a non-singular spherical
cloak designed by blowing up a small ball instead of a point, as proposed in
[Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The
multilayered approximation of this cloak requires less extreme densities
(especially for the lowest bound). Finally, we investigate another type of
non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev.
Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.Comment: Latex, 21 pages, 7 Figures, last version submitted to Wave Motion.
OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110)
Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic
optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices;
(160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility;
(230.3205) Invisibility cloak
On the numerical solution of the three-dimensional inverse obstacle scattering problem
AbstractThe inverse problem under consideration is to determine the shape of an impenetrable sound-soft obstacle from the knowledge of a time-harmonic incident plane acoustic wave and far-field or near-field measurements of the scattered wave. We present a method for the approximate solution which avoids the solution of the corresponding direct problem and stabilizes the ill-posed inverse problem by reformulating it as a nonlinear optimization problem. The numerical implementation of the method is described and some three-dimensional examples of reconstructions are given
Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions
We investigate a time harmonic acoustic scattering problem by a penetrable
inclusion with compact support embedded in the free space. We consider cases
where an observer can produce incident plane waves and measure the far field
pattern of the resulting scattered field only in a finite set of directions. In
this context, we say that a wavenumber is a non-scattering wavenumber if the
associated relative scattering matrix has a non trivial kernel. Under certain
assumptions on the physical coefficients of the inclusion, we show that the
non-scattering wavenumbers form a (possibly empty) discrete set. Then, in a
second step, for a given real wavenumber and a given domain D, we present a
constructive technique to prove that there exist inclusions supported in D for
which the corresponding relative scattering matrix is null. These inclusions
have the important property to be impossible to detect from far field
measurements. The approach leads to a numerical algorithm which is described at
the end of the paper and which allows to provide examples of (approximated)
invisible inclusions.Comment: 20 pages, 7 figure
- …