3,157 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
Some Results on Inverse Scattering
A review of some of the author's results in the area of inverse scattering is
given. The following topics are discussed: 1) Property and applications, 2)
Stable inversion of fixed-energy 3D scattering data and its error estimate, 3)
Inverse scattering with ''incomplete`` data, 4) Inverse scattering for
inhomogeneous Schr\"odinger equation, 5) Krein's inverse scattering method, 6)
Invertibility of the steps in Gel'fand-Levitan, Marchenko, and Krein inversion
methods, 7) The Newton-Sabatier and Cox-Thompson procedures are not inversion
methods, 8) Resonances: existence, location, perturbation theory, 9) Born
inversion as an ill-posed problem, 10) Inverse obstacle scattering with
fixed-frequency data, 11) Inverse scattering with data at a fixed energy and a
fixed incident direction, 12) Creating materials with a desired refraction
coefficient and wave-focusing properties.Comment: 24p
Shape identification in inverse medium scattering problems with a single far-field pattern
Consider time-harmonic acoustic scattering from a bounded penetrable obstacle
embedded in a homogeneous background medium. The index
of refraction characterizing the material inside is supposed to be H\"older
continuous near the corners. If is a convex polygon, we
prove that its shape and location can be uniquely determined by the far-field
pattern incited by a single incident wave at a fixed frequency. In dimensions
, the uniqueness applies to penetrable scatterers of rectangular type
with additional assumptions on the smoothness of the contrast. Our arguments
are motivated by recent studies on the absence of non-scattering wavenumbers in
domains with corners. As a byproduct, we show that the smoothness conditions in
previous corner scattering results are only required near the corners
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