25,022 research outputs found
Topological Sensitivity Based Far-Field Detection of Elastic Inclusions
The aim of this article is to present and rigorously analyze topological
sensitivity based algorithms for detection of diametrically small inclusions in
an isotropic homogeneous elastic formation using single and multiple
measurements of the far-field scattering amplitudes. A cost functional is
considered and a location indicator is constructed from its topological
derivative. The performance of the indicator is analyzed in terms of the
topological sensitivity for location detection and stability with respect to
measurement and medium noises. It is established that the location indicator
does not guarantee inclusion detection and achieves only a low resolution when
there is mode-conversion in an elastic formation. Accordingly, a weighted
location indicator is designed to tackle the mode-conversion phenomenon. It is
substantiated that the weighted function renders the location of an inclusion
stably with resolution as per Rayleigh criterion.Comment: 31 pages, 1 figur
Nearly cloaking the elastic wave fields
In this work, we develop a general mathematical framework on regularized
approximate cloaking of elastic waves governed by the Lam\'e system via the
approach of transformation elastodynamics. Our study is rather comprehensive.
We first provide a rigorous justification of the transformation elastodynamics.
Based on the blow-up-a-point construction, elastic material tensors for a
perfect cloak are derived and shown to possess singularities. In order to avoid
the singular structure, we propose to regularize the blow-up-a-point
construction to be the blow-up-a-small-region construction. However, it is
shown that without incorporating a suitable lossy layer, the regularized
construction would fail due to resonant inclusions. In order to defeat the
failure of the lossless construction, a properly designed lossy layer is
introduced into the regularized cloaking construction . We derive sharp
asymptotic estimates in assessing the cloaking performance. The proposed
cloaking scheme is capable of nearly cloaking an arbitrary content with a high
accuracy
Separable potential model for interactions at low energies
The effective separable meson-baryon potentials are constructed to match the
equivalent chiral amplitudes up to the second order in external meson momenta.
We fit the model parameters (low energy constants) to the threshold and low
energy data. In the process, the -proton bound state problem is
solved exactly in the momentum space and the 1s level characteristics of the
kaonic hydrogen are computed simultaneously with the available low energy
cross sections. The model is also used to describe the
mass spectrum and the energy dependence of the amplitude.Comment: 31 pages, v2 - added corrections to make it compatible with the
published versio
The (1535) and (1650) Resonances in Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory
The wave meson-baryon scattering is analyzed for the strangeness S=0
sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral
Symmetry. Four channels have been considered: , , ,
. The needed two particle irreducible matrix amplitude is taken from
lowest order Chiral Perturbation Theory in a relativistic formalism and low
energy constants are fitted to the elastic phase-shifts and the and cross section data. The position of
the complex poles in the second Riemann sheet of the scattering amplitude
determine masses and widths of the (1535) and (1650)
resonances, in reasonable agreement with experiment. A good overall description
of data, from threshold up to 2 GeV, is achieved keeping in mind that
the two pion production channel has not been included.Comment: 35 pages, LaTeX + 7 ps-figure files. Some minor mistakes have been
corrected for and a new appendix discussing the matching to HBChPT has been
also adde
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