Euler-Bessel and Euler-Fourier Transforms

We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible \zed-valued functions to continuous $\real$-valued functions over a vector space. Core contributions include: the definition of the topological Bessel transform; a relationship in terms of the logarithmic blowup of the topological Fourier transform; and a novel Morse index formula for the transforms. We then apply the theory to problems of target reconstruction from enumerative sensor data, including localization and shape discrimination. This last application utilizes an extension of spatially variant apodization (SVA) to mitigate sidelobe phenomena

Ultrasound Nondestructive Evaluation (NDE) Imaging with Transducer Arrays and Adaptive Processing

This paper addresses the challenging problem of ultrasonic non-destructive evaluation (NDE) imaging with adaptive transducer arrays. In NDE applications, most materials like concrete, stainless steel and carbon-reinforced composites used extensively in industries and civil engineering exhibit heterogeneous internal structure. When inspected using ultrasound, the signals from defects are significantly corrupted by the echoes form randomly distributed scatterers, even defects that are much larger than these random reflectors are difficult to detect with the conventional delay-and-sum operation. We propose to apply adaptive beamforming to the received data samples to reduce the interference and clutter noise. Beamforming is to manipulate the array beam pattern by appropriately weighting the per-element delayed data samples prior to summing them. The adaptive weights are computed from the statistical analysis of the data samples. This delay-weight-and-sum process can be explained as applying a lateral spatial filter to the signals across the probe aperture. Simulations show that the clutter noise is reduced by more than 30 dB and the lateral resolution is enhanced simultaneously when adaptive beamforming is applied. In experiments inspecting a steel block with side-drilled holes, good quantitative agreement with simulation results is demonstrated

Atmospheric Deposition of Mercury and Lead Contamination to Soils Across and Elevation Gradient in Vermont, USA

Atmospheric deposition, rather than inputs from local point sources, is the primary mechanism contributing to high levels of mercury in the northeastern United States, particularly in remote high elevation watersheds. However, no studies have yet been published on the effect of elevation on mercury concentrations in soils and vegetation, despite well-known increases in concentrations of other heavy metals at high elevations. In this study I examine the effects of three deposition mechanisms known to cause higher lead levels at higher elevations: 1) orographic precipitation, 2) increasing amounts coniferous vegetation with elevation, and 3) the onset of occult deposition. This study finds that these mechanisms do cause significant increases of mercury at higher elevations. Furthermore, these processes produce an abrupt increase in mercury amounts above the elevation of average cloud base height and the elevation at which vegetation becomes fully coniferous. These effects are clearest in organic horizon soils. From the lowest elevation site of 540 meters to the site located at I 034 meters, mercury amounts increase by nearly six-fold, from 1.36 mg/m2 to 7.65 mg/m2 . The threshold response of mercury to the onset of occult deposition and the change in vegetation leads to 1.49 times more mercury at the 986 meter site ( 4.85 mg/m2 Hg) than at the 934 meter site (3 .25 mg/m2 Hg) and 2.13 times more mercury at the 861 meter site (3 .0 I mg/m2 Hg) than at the 801 meter site ( 1.41 mg/m2 Hg). Thus, this study uncovers high elevation pools of mercury caused by magnification of anthropogenic contamination through three key atmospheric deposition processes. These pools represent potential for long-term contamination of lower elevation soils and watersheds, even in the absence of new mercury inputs.Geolog