We consider the question which potentials in the action of a (1+1) dimensional scalar field theory allowing for spontaneous symmetry breaking have quantum fluctuations corresponding to reflectionless scattering data. The general problem of restoration from known scattering data is formulated and a number of explicit examples is given. Only certain sets of reflectionless scattering data correspo...

Cosmic rays from deep space are continuously striking the Earth’s atmosphere. The result is a shower of particles of various sorts, travelling in various directions at nearly the speed of light. Some of these particles are so unstable that they decay before reaching the Earth’s surface. Others are less energetic and are absorbed by the atmosphere. Muons, on the other hand, are not so unstable a...

We apply the ℓ 1 minimizing technique of compressive sensing (CS) to non-linear quadratic observations. For the example of coherent X-ray scattering we provide the formulae for a Kalman filter approach to quadratic CS and show how to reconstruct the scattering data from their spatial intensity distribution.

This work explores potential methods for use in the detection and classification of defects within crystal structures via analysis of diffuse scattering data generated by single crystal neutron scattering experiments. The proposed defect detection methodology uses machine learning and image processing techniques to perform image texture analysis on neutron diffraction patterns generated by neut...

A new method for finding small inhomogeneities from surface scattering data is proposed and mathematically justified. The method allows one to find small holes and cracks in metallic and other objects from the observation of the acoustic field scattered by the objects.

Based on perturbation theory and the Born approximation, a volume scattering model is developed, which is capable of simulating the backscattered field and time series due to 3-D volumetric bottom inhomogeneities. The model predictions compare favorably to experimental data avdable btween 250 and 650 Hz. INTRODUCTION As part of the Acoustic Reverberation Special Research Program (A RSRP), low-f...

Our approach is to develop spectral models of short waves on the sea surface for use in the multiscale model that will include effects of bound waves and raindrops. These models are being developed by analyzing previous experimental results, obtained both by us and by others, studying previous theoretical work, conducting new experiments in the University of Miami wind wave tank, and attempting...

The Newton-Sabatier method for solving inverse scattering problem with fixed-energy phase shifts for a sperically symmetric potential is discussed. It is shown that this method is fundamentally wrong in the sense that its foundations are wrong: in general it cannot be carried through because its basic integral equation may be not solvable for some r > 0 and in this case the method breaks down; ...

In this paper, we are concerned with the identification of complex obstacles from the scattering data for the acoustic problem. The complex obstacle is characterized by its shape and the boundary values of the impedance coefficient. We establish pointwise formulas which can be used to reconstruct the shape of the obstacle and give explicitly the values of the surface impedance as a function of ...

We consider K − nucleon elastic and inelastic scattering in isospin symmetric nuclear matter. It is found that the proper description of the Λ(1405) resonance structure in nuclear matter requires a self-consistent approach. Then the Λ(1405) resonance mass remains basically unchanged, however, the resonance acquires an increased decay width as nuclear matter is compressed. The elastic and inelas...