Connection Between Time- and Frequency-Domain Three-Dimensional Inverse Problems for the Schrödinger Equation

The use of inverse scattering methods in electromagnetic remote sensing, seismic exploration and ultrasonic imaging is rapidly expanding. For these cases which involve classical wave equations with variable velocity,1 no exact inversion methods exists for general three-dimensional (3d) scatterers. However, exact inversion methods (for example, those based on the Born series2 and the Newton-Marchenko equation2) do exist for the 3d Schrödinger equation. In this paper, these inversion methods for Schrödinger’s equation will be rewritten in a form which brings out certain analogies with classical wave equations. It is hoped these analogies will eventually contribute to a common exact inversion method for both types of equations

Applications of squeezed states: Bogoliubov transformations and wavelets to the statistical mechanics of water and its bubbles

The squeezed states or Bogoliubov transformations and wavelets are applied to two problems in nonrelativistic statistical mechanics: the dielectric response of liquid water, epsilon(q-vector,w), and the bubble formation in water during insonnification. The wavelets are special phase-space windows which cover the domain and range of L(exp 1) intersection of L(exp 2) of classical causal, finite energy solutions. The multiresolution of discrete wavelets in phase space gives a decomposition into regions of time and scales of frequency thereby allowing the renormalization group to be applied to new systems in addition to the tired 'usual suspects' of the Ising models and lattice gasses. The Bogoliubov transformation: squeeze transformation is applied to the dipolaron collective mode in water and to the gas produced by the explosive cavitation process in bubble formation

Periodic Composite Backing Filter for the Design of Ultrasonic Transducers

The transducer is the central element of acoustic and ultrasonic detection and characterization technologies [1–4]. Some commercial applications of these modalities include ultrasonic nondestructive evaluation NDE, medical diagnostics and undersea imaging.</p

A Perturbation Method for Inverse Scattering in Three-Dimensions Based on the Exact Inverse Scattering Equations

The detection and characterization of macroscopic flaws, such as cracks in solids are fundamental goals of nondestructive evaluation. Many inspection methods use scattered electromagnetic or ultrasonic waves. These methods rely explicitly on the development of inverse scattering theory. This theory seeks to determine the geometrical and material properties of flaws from scattering data.</p

An Application of Wavelet Signal Processing to Ultrasonic Nondestructive Evaluation

In this paper we present a flaw signature estimation approach which utilizes the Wiener filter [1–5] along with a wavelet based procedure [6–15] to achieve both deconvolution and reduction of acoustic noise. In related ealier work by Patterson et al. [6], the wavelet transform was applied to certain components of the Wiener filter, and coefficient chopping was used to reduce acoustic noise. In the approach that we present here, the wavelet transform is applied individually to the real part and to the imaginary part of the scattering amplitude estimate determined by application of a sub-optimal form of the Wiener filter. This wavelet transform takes the real and imaginary parts, respectively, from the typical Fourier frequency domain to a wavelet phase space. In this new space, the acoustic noise shows significant separation from the flaw signature making selective pruning of wavelet coefficients an effective means of reducing the acoustic noise. The final estimates of the real and imaginary parts of the scattering amplitude are determing via an inverse wavelet transform.</p

Connection Between Time- and Frequency-Domain Three-Dimensional Inverse Problems for the Schrödinger Equation

The use of inverse scattering methods in electromagnetic remote sensing, seismic exploration and ultrasonic imaging is rapidly expanding. For these cases which involve classical wave equations with variable velocity,1 no exact inversion methods exists for general three-dimensional (3d) scatterers. However, exact inversion methods (for example, those based on the Born series2 and the Newton-Marchenko equation2) do exist for the 3d Schrödinger equation. In this paper, these inversion methods for Schrödinger’s equation will be rewritten in a form which brings out certain analogies with classical wave equations. It is hoped these analogies will eventually contribute to a common exact inversion method for both types of equations.</p

An O(nlogn)-Time Algorithm for the Maximum Constrained Agreement Subtree Problem for Binary Trees

In nondestructive evaluation, one attempts to obtain information about the parameters of a medium by means of scattering experiments

Three Dimensional Inverse Scattering for the Classical Wave Equation with Variable Speed

In nondestructive evaluation, one attempts to obtain information about the parameters of a medium by means of scattering experiments.</p