An Entropy Stable Nodal Discontinuous Galerkin Method for the Two Dimensional Shallow Water Equations on Unstructured Curvilinear Meshes with Discontinuous Bathymetry

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretisation exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretisation of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem

A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes

We design a novel provably stable discontinuous Galerkin spectral element (DGSEM) approximation to solve systems of conservation laws on moving domains. To incorporate the motion of the domain, we use an arbitrary Lagrangian-Eulerian formulation to map the governing equations to a fixed reference domain. The approximation is made stable by a discretization of a skew-symmetric formulation of the problem. We prove that the discrete approximation is stable, conservative and, for constant coefficient problems, maintains the free-stream preservation property. We also provide details on how to add the new skew-symmetric ALE approximation to an existing discontinuous Galerkin spectral element code. Lastly, we provide numerical support of the theoretical results

LC-MS method development and comparison of sampling materials for the analysis of organic gunshot residues

This study aimed at comparing the efficiency of various sampling materials for the collection and subsequent analysis of organic gunshot residues (OGSR). To the best of our knowledge, it is the first time that sampling devices were investigated in detail for further quantitation of OGSR by LC-MS. Seven sampling materials, namely two "swab"-type and five "stub"-type collection materials, were tested. The investigation started with the development of a simple and robust LC-MS method able to separate and quantify molecules typically found in gunpowders, such as diphenylamine or ethylcentralite. The evaluation of sampling materials was then systematically carried out by first analysing blank extracts of the materials to check for potential interferences and determining matrix effects. Based on these results, the best four materials, namely cotton buds, polyester swabs, a tape from 3M and PTFE were compared in terms of collection efficiency during shooting experiments using a set of 9 mm Luger ammunition. It was found that the tape was capable of recovering the highest amounts of OGSR. As tape-lifting is the technique currently used in routine for inorganic GSR, OGSR analysis might be implemented without modifying IGSR sampling and analysis procedure

Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps

We use the behavior of the L2 norm of the solutions of linear hyperbolic equations with discontinuous coefficient matrices as a surrogate to infer stability of discontinuous Galerkin spectral element methods (DGSEM). Although the L2 norm is not bounded by the initial data for homogeneous and dissipative boundary conditions for such systems, the L2 norm is easier to work with than a norm that discounts growth due to the discontinuities. We show that the DGSEM with an upwind numerical flux that satisfies the Rankine-Hugoniot (or conservation) condition has the same energy bound as the partial differential equation does in the L2 norm, plus an added dissipation that depends on how much the approximate solution fails to satisfy the Rankine-Hugoniot jump

Organic gunshot residues: observations about sampling and transfer mechanisms

This work aimed at studying the sampling, storage, transfer and persistence of organic gunshot residue (OGSR), mainly stabilizers, using liquid chromatography hyphenated to mass spectrometry. Collection using swabs and stubs was compared through sequential sampling in terms of amount of residues left on the hand of a shooter. While stubs collected nearly all residues, swabs left about 50% of the residues on the hands. Moreover, the study of storage conditions after sampling showed that stubs were more stable than swabs and could be held at room temperature without significant compound loss up to two weeks. Then, shooting experiments were performed to evaluate transfer of OGSR. It was not possible to differentiate different brands of ammunition based on a single compound concentration. Moreover, a memory effect was identified when different ammunition was shot using the same firearm. Finally, various exposed skin surfaces and hair as well as clothing were sampled to estimate what surfaces might be the best targets for OGSR sampling by comparing results just after discharge and two hours after discharging a pistol. The results indicated that OGSR were more rapidly lost from hands than from clothing. Moreover, it was shown that the face and hair of a suspect might be contaminated through secondary transfer. Thus, OGSR might remain longer on other skin surfaces, hair and clothing than on the hands of a suspect. As a consequence, sampling should also include clothing, hair and face

Diluted and Undiluted Mercox Severely Destroy Unfixed Endothelial Cells. A Light and Electron Microscopic Study Using Cultured Endothelial Cells and Tadpole Tail Fin Vessels

Mercox is a methylmethacrylate-based resin which is widely used for vascular corrosion casting with subsequent scanning electron microscopic analysis. In the present study the effect of undiluted and diluted Mercox (4+1; volume + volume; Mercox: monomeric methylmethacrylate (MMA); 0.02 g catalyst MA/ml Mercox) and methylmethacrylate with and without catalyst MA (0.625 g/10 ml MMA) on fixed and unfixed endothelial cells was studied. Light microscopy (LM) of cultured capillary endothelial cells (ECs), which were replicated with diluted or undiluted Mercox shows degranulation and membrane perturbation of ECs, while no morphological changes occur in glutaraldehyde-prefixed ECs. Scanning electron microscopy (SEM) of replicas ( = resin blocks) polymerized on prefixed ECs reveals unchanged ECs and replicas show many details. Unfixed ECs are destroyed and replicas reveal aberrant features. Transmission electron microscopy (TEM) of prefixed and unfixed ECs (cultured endothelial cells, endothelial cells of perfusion prefixed and of unfixed tadpole tail fin vessels) substantiates LM and SEM findings. Prefixed ECs resist Mercox without fine structural changes, while unfixed cells undergo destruction. It is recommended to fix vessels prior to casting. Extravasations in microvessels are considered to be caused by focal chemical destruction of endothelial cells

Radiation And Annealing Characteristics Of Neutron Bombarded Silicon Transistors

Operating a silicon planar epitaxial transistor in the inverse configuration allows one to demonstrate clearly the importance of the neutron-induced base current component and its degradation of the emitter efficiency, and, because of the much larger depletion layer, to compute a volume dependent damage constant applicable to all silicon p-n junctions. The importance of minimizing the absolute change versus relative change in radiation hardening studies is clearly illustrated. Surface effects were found to be significant for transistors mounted in gas-filled cans. The diffusion potential was predicted, on theoretical grounds, to vary with neutron fluence, and the theory was experimentally confirmed. Isochronal and isothermal annealing data were obtained for the inverse configuration and from these data, it is concluded that the neutron-induced defect centers are field dependent. Copyright © 1968 by The Institute of Electrical and Electronics Engineers, Inc