Reconstruction of the Electromagnetic Wavefield from Scattering Data

Inverse scattering theory concerns itself with determining the properties of a scatterer (e.g., the spatial variation of the scatterer’s dielectric constant and conductivity) from measured scattering data. Two general approaches to this problem exist. The first approach is a direct variational method. One starts by computing the scattering amplitude for some assumed properties of the scatterer. The resulting theoretical scattering amplitude is compared with the measured scattering data. If these results differ, then one varies the properties of the assumed scatterer and recomputes the scattered field for the new properties. This process is truncated when the measured and computed fields agree to a specified accuracy. The properties of the assumed scatterer are then supposed to coincide to within some accuracy with the unknown scatterer which generated the measured data

Ultrasonic Signals from Worst-Case Hard-Alpha Inclusions Beneath a Random Rough Surface

Up to the present time, the detection of hard alpha inclusions in commercial titanium products or in billets has relied on the presence of associated voids and cracks, which due to their sharp edges are good acoustic reflectors at high frequencies. The detection problem becomes much harder, if cracks and voids are absent, since the acoustic impedance of a hard alpha inclusion is at least an order of magnitude smaller. The problem appears to call for the use of high frequency focused probes. However, one cannot use arbitrarily high frequencies for at least three reasons: (1) grain scattering due to the microstructure of titanium, (2) attenuation of the beam due to surface roughness and most importantly (3) the nature of the flaw as discussed below

Oil and Gas Platforms in the Gulf of Mexico: Their Relationship to Fish and Fisheries

There are over 2300 standing oil and gas platforms in the northern Gulf of Mexico (GOM). It has been argued that platforms provide reef-like habitat that increases the growth and survival rates of fishes by increasing prey availability and affording shelter for protection from predators, provide additional spawning substrate, and by acting as a visual attractant for organisms not otherwise dependent upon hard bottom. Platforms differ from most natural habitats, and from traditional artificial reefs, in that their vertical profile extends upward through the water column into the photic zone and the sea surface. Increased habitat quality on, or immediately around, oil and gas platforms are thought to be derived from increased in situ food production associated with encrustation by fouling organisms. In this chapter, we address the issue of how to evaluate the role of artificial reefs by first establishing levels of evaluation for individual fish species found on oil and gas platforms in the GOM. The levels of evaluation relate to the amount and adequacy of the available information, which was populated with an extensive literature and data search. Three levels of assessment are established, analogous to the levels of analysis established National Oceanographic and Atmospheric Administration (NOAA) Fisheries for identification of Essential Fish Habitat. More than 1300 documents, including reports, stock assessments, other gray literature, and papers published in the primary literature, were used to complete this chapter. When available, published literature was the preferred source of information

On the Effects of a Finite Aperture on the Inverse Born Approximation

One of the most important effects of complex part geometry is that the available entrance and exit angles for ultrasound are limited. We will present a study of the Inverse Born Approximation in which we have data for incident (and exit) directions confined to a conical aperture. Modeling the direct problem by the Born Approximation, we obtained analytical results for (1) a weak spherical inclusion, and (2) a penny shaped crack (modeled by an oblate spheroid). General results are: (a) the value of the characteristic function γ is constant in the interior of the flaw, but reduced in value; (b) the discontinuity at the boundary of the flaw occurs over the “lighted” portion of the flaw; (c) this discontinuity is contrasted by a region where γ is negative; and (d) new non-physical discontinuities and non-analyticities appear in the reconstructed characteristic function. These general features also appear in numerical calculations which use as input strong scattering data from a spherical void and a flat penny shaped crack in Titanium. The numerical results can be straightforwardly interpreted in terms of the analytical calculation mentioned above, indicating that they will be useful in the study of realistic flaws. We conclude by discussing the stabilization of the aperture limited inversion problem and the removal of non-physical features in the reconstruction

Effects of Acoustic Scattering at Rough Surfaces on the Sensitivity of Ultrasonic Inspection

Ultrasonic inspection of ordinary samples with more or less rough surfaces is an everyday problem in industrial NDE. Contact techniques require flat or other regular (e. g., cylindrical) surfaces of negligible roughness with respect to the acoustic wavelength. Immersion techniques are less susceptible to surface topography, but they still require that the surface radius be larger than the beam diameter and the surface roughness be comparable or less than the wavelength in the immersion fluid. This difference is due to the fact that in immersion inspection surface irregularities do not significantly reduce the energy transmission into the specimen but rather randomize the field through incoherent scattering. Figure 1 shows the schematic diagram of ultrasonic inspection of a rough specimen by the immersion method. The probability of detection of a given flaw is ultimately limited by the signal-to-noise ratio produced at the receiver. The flaw signal results from coherent reflection from a single, relatively large and strong scatterer. In comparison, the noise is incoherent scattering from a large number of randomly distributed, relatively small and weak scatterers such as material inhomogeneities or geometrical irregularities. Surface roughness can substantially reduce the signal-to-noise ratio with respect to an otherwise similar smooth sample. First, surface roughness attenuates the coherent flaw signal much more than the incoherent material noise [1,2]. Second, surface roughness increases the overall noise level by adding another incoherent component to the material noise. This paper discusses the adverse effect of the excess surface noise on ultrasonic flaw detection in rough samples

Stable Tearing and Buckling Responses of Unstiffened Aluminum Shells with Long Cracks

The results of an analytical and experimental study of the nonlinear response of thin, unstiffened, aluminum cylindrical shells with a long longitudinal crack are presented. The shells are analyzed with a nonlinear shell analysis code that accurately accounts for global and local structural response phenomena. Results are presented for internal pressure and for axial compression loads. The effect of initial crack length on the initiation of stable crack growth and unstable crack growth in typical shells subjected to internal pressure loads is predicted using geometrically nonlinear elastic-plastic finite element analyses and the crack-tip-opening angle (CTOA) fracture criterion. The results of these analyses and of the experiments indicate that the pressure required to initiate stable crack growth and unstable crack growth in a shell subjected to internal pressure loads decreases as the initial crack length increases. The effects of crack length on the prebuckling, buckling and postbuckling responses of typical shells subjected to axial compression loads are also described. For this loading condition, the crack length was not allowed to increase as the load was increased. The results of the analyses and of the experiments indicate that the initial buckling load and collapse load for a shell subjected to axial compression loads decrease as the initial crack length increases. Initial buckling causes general instability or collapse of a shell for shorter initial crack lengths. Initial buckling is a stable local response mode for longer initial crack lengths. This stable local buckling response is followed by a stable postbuckling response, which is followed by general or overall instability of the shell

Solid-state metathesis reactions under pressure: A rapid route to crystalline gallium nitride

High pressure chemistry has traditionally involved applying pressure and increasing temperature until conditions become thermodynamically favorable for phase transitions or reactions to occur. Here, high pressure alone is used as a starting point for carrying out rapid, self-propagating metathesis reactions. By initiating chemical reactions under pressure, crystalline phases, such as gallium nitride, can be synthesized which are inaccessible when initiated from ambient conditions. The single-phase gallium nitride made by metathesis reactions under pressure displays significant photoluminescence intensity in the blue/ultraviolet region. The absence of size or surface-state effects in the photoluminescence spectra show that the crystallites are of micron dimensions. The narrow lines of the x-ray diffraction patterns and scanning electron microscopy confirm this conclusion. Brightly luminescent thin films can be readily grown using pulsed laser deposition

Live Trap Preference Among Grassland Mammals

In two independent studies, small mammals of grassland communities in eastern Kansas, when given a choice, preferred Fitch to Sherman live traps. Except for the harvest mice in the demographic study, the type of preferred trap and magnitude of selection was remarkably comparable, with microtines showing slight, and cricetines strong, preferences overall. The merits of each type of trap are compared, and related to season, weather, prior experience, and trap-associated mortality

The Effect of Cluster Environment on Galaxy Evolution in the Pegasus I Cluster

We present neutral hydrogen observations of 54 galaxies in the Pegasus Cluster. The observations include single-dish H I measurements, obtained with the Arecibo telescope for all 54 galaxies in the sample, as well as H I images obtained with the Very Large Array (VLA) for 10 of these. The Arecibo profiles reveal an overall H I deficiency in the cluster, with similar to 40% of the galaxies in the core of the cluster showing modest deficiencies of typically a factor of 2-3. The HI morphology of so me galaxies shows that the HI disk is smaller than the optical disk and slightly offset from the stars. We find a correlation between HI deficiency and the ratio of the HI disk size to optical disk size. More HI deficient galaxies have relatively smaller HI disks, a configuration that is usually attributed to an interaction between the interstellar medium (ISM) of the galaxy and the hot intracluster med ium (ICM). Such a result is surprising since the Pegasus cluster has a low level of X-ray emission, and a low velocity dispersion. The low velocity dispersion, coupled with the lack of a dense hot ICM indicate that ram pressure stripping should not play a significant role in this environment. In addition, two of the galaxies, NGC7604 and NGC7648, are morphologically peculiar. Their peculiarities indicate contradictory scenarios of what is triggering their unusual star formation. Hα imaging, along with long-slit spectroscopy of NGC7648 reveal morphological features which point to a recent tidal interaction. On the other hand, Hα imaging of NGC7604 reveals a strong episode of star formation concentrated into an asymmetric arc, preferentially located on one side of the galaxy. VLA HI mapping shows the HI also highly concentrated into that region, suggestive of a ram pressure event. Our data indicate that ISM-ICM interactions may play a role in a wider variety of environments than suggested by simple ram pressure arguments

Multiscale Modeling of Astrophysical Jets

We are developing the capability for a multi-scale code to model the energy deposition rate and momentum transfer rate of an astrophysical jet which generates strong plasma turbulence in its interaction with the ambient medium through which it propagates. We start with a highly parallelized version of the VH-1 Hydrodynamics Code (Coella and Wood 1984, and Saxton et al., 2005). We are also considering the PLUTO code (Mignone et al. 2007) to model the jet in the magnetohydrodynamic (MHD) and relativistic, magnetohydrodynamic (RMHD) regimes. Particle-in-Cell approaches are also being used to benchmark a wave-population models of the two-stream instability and associated plasma processes in order to determine energy deposition and momentum transfer rates for these modes of jet-ambient medium interactions. We show some elements of the modeling of these jets in this paper, including energy loss and heating via plasma processes, and large scale hydrodynamic and relativistic hydrodynamic simulations. A preliminary simulation of a jet from the galactic center region is used to lend credence to the jet as the source of the so-called the Fermi Bubble (see, e.g., Su, M. & Finkbeiner, D. P., 2012)*It is with great sorrow that we acknowledge the loss of our colleague and friend of more than thirty years, Dr. John Ural Guillory, to his battle with cancer