Scattering Calculations with Wavelets

We show that the use of wavelet bases for solving the momentum-space scattering integral equation leads to sparse matrices which can simplify the solution. Wavelet bases are applied to calculate the K-matrix for nucleon-nucleon scattering with the s-wave Malfliet-Tjon V potential. We introduce a new method, which uses special properties of the wavelets, for evaluating the singular part of the integral. Analysis of this test problem indicates that a significant reduction in computational size can be achieved for realistic few-body scattering problems.Comment: 26 pages, Latex, 6 eps figure

Application of wavelets to singular integral scattering equations

The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties of wavelets are used to derive an efficient method for evaluating the singular integrals. The accuracy and efficiency of the wavelet transforms is demonstrated by solving the two-body T-matrix equation without partial wave projection. The resulting matrix equation which is characteristic of multiparticle integral scattering equations is found to provide an efficient method for obtaining accurate approximate solutions to the integral equation. These results indicate that wavelet transforms may provide a useful tool for studying few-body systems.Comment: 11 pages, 4 figure

Flaw Detection and Characterization in Ceramics with the Scanning Laser Acoustic Microscope (SLAM)

The high resolving power coupled with the real time capability of the SLAM make it a useful technique for characterization of materials including ceramics. The elastic structure of·ceramics is often dependent upon the details of the fabrication process, e.g., sintering, hot pressing, amount of. binder, etc .. Accordingly, acoustic micrographs and acoustic interferograms which reveal characteristic sonic transmission patterns and sonic velocity variations, respectively, can be used to nondestructively evaluate ceramics to ensure material uniformity. In addition, the ability to nondestructively detect flaws and inclusions is important in fracture toughness studies and in the evaluation of finished components

High Resolutional Real Time Acoustic Microscopy

A commercially available scanning-laser-acoustic-microscope {SLAM) has been developed which provides new and unique analytical capabilities for materials science and non-destructive testing. By employing 100 MHz acoustic waves to create images, the elastic microstructure of complex materials is visualized directly. The acoustic micrographs which contain 2 x 104 image points, are displayed on a real time TV monitor. The sample remains accessible to the investigator during the procedure and stressing fixtures can be employed. Dynamic activities can be recorded either on movie film or video tape. There are two acoustic imaging modes which appear to be essential for flaw and defect characterization. The first mode displays the acoustic transmission level through the sample (normal mode) and the second mode displays fringes related to the acoustic phase (interference mode). The presence of a defect within a sample may be evidenced by a change in transmission level or a change in phase or both. The nature of the defect (e.g. high density inclusion or void) can be determined through the combined analysis of the interference and normal mode micrographs. The SLAM technique has been applied to a wide variety of materials including ceramics, metals, glasses, polymers, etc. Defect localization down to 25 μm has been achieved. Samples can be systematically searched, area by area, by simply repositioning the part on the stage of the microscope and observing the acoustic image on the TV monitor

Velocity Fluctuations in Dynamical Fracture: the Role of Microcracks

We address the velocity fluctuations of fastly moving cracks in stressed materials. One possible mechanism for such fluctuations is the interaction of the main crack with micro cracks (irrespective whether these are existing material defects or they form during the crack evolution). We analyze carefully the dynamics (in 2 space dimensions) of one macro and one micro crack, and demonstrate that their interaction results in a {\em large} and {\em rapid} velocity fluctuation, in qualitative correspondence with typical velocity fluctuations observed in experiments. In developing the theory of the dynamical interaction we invoke an approximation that affords a reduction in mathematical complexity to a simple set of ordinary differential equations for the positions of the cracks tips; we propose that this kind of approximation has a range of usefulness that exceeds the present context.Comment: 7 pages, 7 figure

Acoustic Microscopy of Ceramics

The scanning laser acoustic microscope (SLAM) is applied to the problem of nondestructive testing of ceramic materials. The employment of a very high resolution ultrasonic imaging instrument provides capabilities which supplement ultrasonic pulse-echo testing. In addition, by means of showing a picture of the flaw, the SLAM technique provides its own capabilities which alleviate some of the limitations of other techniques. Flaws of various types are documented in this paper

High Mortality of a Population of Cowbirds Wintering at Columbus, Ohio

High mortality was experienced during two heavy rainfalls by a wintering population of Cowbirds in Columbus, Ohio. Their death was associated with a soaking of their feathers, and their inability to fly and to remain on their perches in the roost. Causes of death may be associated with the lowering of their body temperature, enhanced by bathing in streams containing detergents

Scanning Laser Acoustic Microscope Visualization of Solid Inclusions in Silicon Nitride

The Scanning Laser Acoustic Microscope (SLAM) operating at a frequency of 100 MHz is used to characterize solid inclusions in silicon nitride. Ten, seven millimeter thick discs, with 100 and 400 micron implanted inclusions are analyzed. We find that the images of a solid inclusion are characterized by a bright high transmission central zone, a well defined dark boundary and a characteristic diffraction ring pattern. These image features differentiate solid inclusions from pores and voids which may also be encountered in the samples. The images of the implanted flaws were generally found to be larger than anticipated. This can be understood in terms of the divergence of the sound due to diffraction and due to lens action of the curved boundary of the flaw. Our initial observations suggest that accurate estimates of defect size may be obtaiRable from a more complete analysis of SLAM micrographs

Differentiation of Various Flaw Types in Ceramics Using the Scanning Laser Acoustic Microscope

High frequency acoustic imaging represents a powerful technique for the nondestructive evaluation of optically opaque materials. In this report the Scanning Laser Acoustic Microscope (SLAM) is used to detect and characterize flaws in ceramics. SLAM micrographs showing typical examples of cracks, laminar flaws, porosity and solid inclusions. are presented. The various flaw types are easily differentiated on the basis of their characteristic acoustic signatures. The importance of an imaging approach to the nondestructive evaluation of ceramics is demonstrated