Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

Digging for Treasure - Unique Fate and Transport Study

In 1970, scientists at the National Bureau of Standards (NBS), now called the National Institute of Standards and Testing (NIST), implemented the most ambitious and comprehensive long-term corrosion behavior test for stainless steels in soil environments. This study had historic significance since the NBS 1957 landmark corrosion textbook compiled by Romanoff did not include stainless steels, and this 1970 research set forth to complete the missing body of knowledge. To conduct the test, NIST scientists buried 6,324 coupons from stainless steel types, specialty alloys, composite configurations, multiple material forms, and treatment conditions at six distinctive soil-type sites throughout the country. Between 1971 and 1980, four sets of coupons were removed from six sites to establish 1-year, 2-year, 4-year, and 8-year corrosion rates data sets for different soil environments. The fifth and last set of coupons (approximately 200 at each site) remains undisturbed after 32-years, providing a virtual buried treasure of material and subsurface scientific data. These buried coupons and the surrounding soils represent an analog to the condition of buried waste and containers. Heretofore, the samples were simply pulled from the soil, measured for mass loss and the corrosion rate determined while the subsurface/fate and transport information was not considered nor gathered. Funded through an Environmental Management Science Program (EMSP) proposal, the Idaho National Engineering and Environmental Laboratory (INEEL) operated for the U.S. Department of Energy by Bechtel-BWXT Idaho, LLC (BBWI), is chartered to restart this corrosion test and concurrently capture the available subsurface/fate and transport information. Since the work of retrieving the buried metal coupons is still in the planning stage, this paper outlines the interdisciplinary team of scientists and engineers and defines the benefits of this research to long-term stewardship, subsurface science, and infrastructure protection programs

Measurement of two-component flow using ultrasonic flowmeters

Calibration of transit-time and Doppler ultrasonic flowmeters under two-component flow conditions has been conducted on 400 mm (16-in.) pipe. Testing covered total flows of 0.19 to 1.89 m{sup 3}/s (3000 to 30,000 gpm) and void fractions up to 40%. Both flowmeter types of accurately measured total volumetric flow over a portion of their ranges. Pipe average void fraction, based on a three-beam gamma densitometer, was used to determine water component flow under stratified flow conditions, with similar results. 2 refs

A 3D extension to cortex like mechanisms for 3D object class recognition

We introduce a novel 3D extension to the hierarchical visual cortex model used for prior work in 2D object recognition. Prior work on the use of the visual cortex standard model for the explicit task of object class recognition has solely concentrated on 2D imagery. In this paper we discuss the explicit 3D extension of each layer in this visual cortex model hierarchy for use in object recognition in 3D volumetric imagery. We apply this extended methodology to the automatic detection of a class of threat items in Computed Tomography (CT) security baggage imagery. The CT imagery suffers from poor resolution and a large number of artefacts generated through the presence of metallic objects. In our examination of recognition performance we make a comparison to a codebook approach derived from a 3D SIFT descriptor and demonstrate that the visual cortex method out-performs in this imagery. Recognition rates in excess of 95% with minimal false positive rates are demonstrated in the detection of a range of threat item

A comparison of 3D interest point descriptors with application to airport baggage object detection in complex CT imagery

We present an experimental comparison of 3D feature descriptors with application to threat detection in Computed Tomography (CT) airport baggage imagery. The detectors range in complexity from a basic local density descriptor, through local region histograms and three-dimensional (3D) extensions to both to the RIFT descriptor and the seminal SIFT feature descriptor. We show that, in the complex CT imagery domain containing a high degree of noise and imaging artefacts, a specific instance object recognition system using simpler descriptors appears to outperform a more complex RIFT/SIFT solution. Recognition rates in excess of 95% are demonstrated with minimal false-positive rates for a set of exemplar 3D objects

Aggregatibacter actinomycetemcomitans Cytolethal Distending Toxin Induces Apoptosis in Nonproliferating Macrophages by a Phosphatase-Independent Mechanism▿

Aggregatibacter actinomycetemcomitans strains that express cytolethal distending toxin (Cdt) are associated with localized aggressive periodontitis. However, the in vivo targets of Cdt in the human oral cavity have not been firmly established. Here, we demonstrate that A. actinomycetemcomitans Cdt kills proliferating and nonproliferating U937 monocytic cells at a comparable specific activity, approximately 1.5-fold lower than that against the Cdt-hypersensitive Jurkat T-cell line. Cdt functioned both as a DNase and a phosphatidylinositol 3-phosphate (PIP3) phosphatase, and these activities were distinguished by site-specific mutagenesis of the active site residues of CdtB. Using these mutants, we determined that the DNase activity of CdtB is required for cell cycle arrest and caspase-dependent induction of apoptosis in proliferating U937 cells. In contrast, Cdt holotoxin induced apoptosis by a mechanism independent of caspase- and apoptosis-inducing factor in nonproliferating U937 cells. Furthermore, apoptosis of nonproliferating U937 cells was unaffected by the Cdt mutant possessing reduced phosphatase activity or by the addition of a specific PIP3 phosphatase inhibitor, suggesting that the induction of apoptosis is independent of phosphatase activity. These results indicate that Cdt intoxication of proliferating and nonproliferating U937 cells occurs by distinct mechanisms and suggest that macrophages may also be potential in vivo targets of Cdt