scholarly journals Stability on the one-dimensional inverse source scattering problem in a two-layered medium

2017 ◽  
Vol 98 (4) ◽  
pp. 682-692 ◽  
Author(s):  
Yue Zhao ◽  
Peijun Li
Keyword(s):  
Layered Medium ◽  
Scattering Problem ◽  
One Dimensional ◽  
The One

scholarly journals A logarithmic estimate for the inverse source scattering problem with attenuation in a two-layered medium

2020 ◽  
Vol 28 (4) ◽  
pp. 489-498
Author(s):  
Mozhgan N. Entekhabi ◽  
Ajith Gunaratne
Keyword(s):  
Layered Medium ◽  
Attenuation Factor ◽  
Scattering Problem ◽  
Stability Estimate ◽  
One Dimensional ◽  
Layer Medium ◽  
Multiple Frequencies ◽  
Logarithmic Estimate ◽  
The One ◽  
Logarithmic Stability

AbstractThe paper aims a logarithmic stability estimate for the inverse source problem of the one-dimensional Helmholtz equation with attenuation factor in a two layer medium. We establish a stability by using multiple frequencies at the two end points of the domain which contains the compact support of the source functions.

The direct and inverse problem in Newtonian scattering

1991 ◽  
Vol 118 (1-2) ◽  
pp. 119-131 ◽  
Author(s):  
M. A. Astaburuaga ◽  
Claudio Fernández ◽  
Víctor H. Cortés
Keyword(s):  
Inverse Problem ◽  
Phase Space ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Dimensional Case ◽  
Classical Particle ◽  
Scattering Operator ◽  
One Dimensional ◽  
The One

SynopsisIn this paper we study the direct and inverse scattering problem on the phase space for a classical particle moving under the influence of a conservative force. We provide a formula for the scattering operator in the one-dimensional case and we settle the properties of the potential that can be deduced from it. We also study the question of recovering the shape of the barriers which can be seen from −∞ and ∞. An example is given showing that these barriers are not uniquely determined by the scattering operator.

On the inversion and phase recovery of scattered electromagnetic amplitude data

1989 ◽  
Vol 426 (1871) ◽  
pp. 361-375 ◽  
Keyword(s):  
Electromagnetic Scattering ◽  
Transverse Electric ◽  
Complex Structure ◽  
Polarization State ◽  
Scattering Problem ◽  
Transverse Magnetic ◽  
One Dimensional ◽  
Amplitude Data ◽  
Transverse Magnetic Polarization ◽  
The One

The one-dimensional inverse electromagnetic scattering problem for the inversion of amplitude data of either linear polarization state is investigated. The method exploits the complex structure of the field scattered from a class of inhomogeneous dielectrics and enables the analytic signal to be reconstructed from measurements of the amplitude alone. The method is demonstrated and exemplified with experimental data in both transverse electric and transverse magnetic polarization states. The implications of the method as a means for regularization of scattered data are briefly discussed.

Analytical solution for the one-dimensional scattering problem

2011 ◽  
Vol 284 (23) ◽  
pp. 5457-5459 ◽  
Author(s):  
H. Eleuch ◽  
M. Sebawe Abdalla ◽  
Y.V. Rostovtsev
Keyword(s):  
Analytical Solution ◽  
Scattering Problem ◽  
One Dimensional ◽  
The One

scholarly journals Absolutely continuous spectrum of Dirac operators with square-integrable potentials

2014 ◽  
Vol 144 (3) ◽  
pp. 533-555
Author(s):  
Daniel Hughes ◽  
Karl Michael Schmidt
Keyword(s):  
Spectral Function ◽  
Continuous Spectrum ◽  
Scattering Problem ◽  
Dirac Operators ◽  
Mass Term ◽  
Absolutely Continuous Spectrum ◽  
Continuous Part ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
The One

We show that the absolutely continuous part of the spectral function of the one-dimensional Dirac operator on a half-line with a constant mass term and a real, square-integrable potential is strictly increasing throughout the essential spectrum (−∞, −1] ∪ [1, ∞). The proof is based on estimates for the transmission coefficient for the full-line scattering problem with a truncated potential and a subsequent limiting procedure for the spectral function. Furthermore, we show that the absolutely continuous spectrum persists when an angular momentum term is added, thus also establishing the result for spherically symmetric Dirac operators in higher dimensions.

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