Related papers: The $J$-matrix inverse scattering approach for cou…
This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…
We consider the small-angle multiple neutron scattering and a possibility of its model-free analysis by the inverse problem method. We show that the ill-defined problem is essentially regularized by use of a planar detector without a…
The inverse scattering problem, whose goal is to reconstruct an unknown scattering object from its scattered wave, is essential in fundamental wave physics and its wide applications in imaging sciences. However, it remains challenging to…
The Complex Scaling Method (CSM) provides scattering wave functions which regularize resonances and suggest a resolution of the identity in terms of such resonances, completed by the bound states and a smoothed continuum. But, in the case…
The aim of this paper is to introduce the Inverse Scattering Method for later studies of some problems in nonlinear dynamics, and describe the kink solution of the Sine Gordon Equation using the Inverse Scattering Method as a methodological…
The aim of this chapter is to make a review of the recent results using the Enclosure Method on inverse obstacle problems governed by the wave equation and the Maxwell system in time domain. We also describe some of unsolved problems…
This paper investigates the inverse scattering problems using sampling methods with near field measurements. The near field measurements appear in two classical inverse scattering problems: the inverse scattering for obstacles and the…
A new approach is described to the evaluation of the S-matrix in three-dimensional atom-diatom reactive quantum scattering theory. The theory is developed based on natural collision coordinates where progress along the reaction coordinate…
Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions. A relation between the exact energy eigenvalue in the box and the…
The coupled-channel technique augments a non-relativistic distorted wave born approximation scattering calculation to include a coupling to virtual states from the negative energy region. It has been found to be important in low energy…
We study restricted multiple three wave interaction system by the inverse scattering method. We develop the algebraic approach in terms of classical $r$-matrix and give an interpretation of the Poisson brackets as linear $r$-matrix algebra.…
We consider the problem of transmission of several distributed correlated sources over a multiple access channel (MAC) with side information at the sources and the decoder. Source-channel separation does not hold for this channel.…
In this work we consider the inverse elastic scattering problem by an inclusion in two dimensions. The elastic inclusion is placed in an isotropic homogeneous elastic medium. The inverse problem, using the third Betti's formula (direct…
We present a lattice method for determining scattering phase shifts and mixing angles for the case of an arbitrary number of coupled channels. Previous nuclear lattice effective field theory simulations were restricted to mixing of up to…
A multi-channel algebraic scattering theory, to find solutions of coupled-channel scattering problems with interactions determined by collective models, has been structured to ensure that the Pauli principle is not violated. Positive…
We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
The main objective of this paper is to give a rigorous treatment of Wigner's and Eisenbud's $R$-matrix method for scattering matrices of scattering systems consisting of two selfadjoint extensions of the same symmetric operator with finite…
Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions in all three directions. A relation between the exact energy eigenvalue in…
Inverse scattering problem is discussed for the Maxwell's equations. A reduction of the Maxwell's system to a new Fredholm second-kind integral equation with a {\it scalar weakly singular kernel} is given for electromagnetic (EM) wave…