A distortion measure to validate and generate curved high‐order meshes on CAD surfaces with independence of parameterization

A framework to validate and generate curved nodal high‐order meshes on Computer‐Aided Design (CAD) surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin‐shell and 3D finite element analysis with unstructured high‐order methods. First, we define a distortion (quality) measure for high‐order meshes on parameterized surfaces that we prove to be independent of the surface parameterization. Second, we derive a smoothing and untangling procedure based on the minimization of a regularization of the proposed distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes to enforce that the nodes slide on the surfaces. Moreover, the proposed algorithm repairs invalid curved meshes (untangling), deals with arbitrary polynomial degrees (high‐order), and handles with low‐quality CAD parameterizations (independence of parameterization). Third, we use the optimization procedure to generate curved nodal high‐order surface meshes by means of an a posteriori approach. Given a linear mesh, we increase the polynomial degree of the elements, curve them to match the geometry, and optimize the location of the nodes to ensure mesh validity. Finally, we present several examples to demonstrate the features of the optimization procedure, and to illustrate the surface mesh generation process. Copyright © 2015 John Wiley & Sons, Ltd.     

Study of Lanthanide Complexes with BTFA in Silica Gels by Photoacoustic Spectroscopy

In this work, lanthanide \(\beta \)-diketonate complexes Ln(btfa)\({}_{3} \cdot 2\hbox {H}_{2}\)O (Ln\(^{3+}\): Eu\(^{3+}\), Sm\(^{3+ }\), and Tb\(^{3+}\); btfa: 4,4,4-trifluoro-l-phenyl-1,3-butanedione) were incorporated into silica gels by a sol–gel method. Photoacoustic (PA) spectra of these complex-doped silica samples were measured and studied. The PA intensity of the \(\beta \)-diketonate ligand is nearly the same for lanthanide complexes in wet gels. After heat treatment at 150 \(^{\circ }\)C, however, the PA intensity of the ligand increases for Eu\(^{3+}\), Sm\(^{3+}\), and Tb\(^{3+}\) complexes in silica gels, respectively. Different PA intensities of the samples are interpreted by comparison with their luminescence spectra. The luminescence result is consistent with the PA spectra. The result indicates that lanthanide \(\beta \)-diketonate complexes cannot be formed in silica gels without a suitable heat treatment. Moreover, the relaxation process model is proposed based on the PA and luminescence results.     

Effects of Environmental Oxygen Content and Dissolved Oxygen on the Surface Tension and Viscosity of Liquid Nickel

The NASA Marshall Space Flight Center’s electrostatic levitation (ESL) laboratory has recently added an oxygen partial pressure controller. This system allows the oxygen partial pressure within the vacuum chamber to be measured and controlled in the range from approximately \(10^{-28}\,{\mathrm {to}}\,10^{-9}\) bar, while in a vacuum atmosphere. The oxygen control system installed in the ESL laboratory’s main chamber consists of an oxygen sensor, oxygen pump, and a control unit. The sensor is a potentiometric device that determines the difference in oxygen activity in two gas compartments (inside the chamber and the air outside of the chamber) separated by an electrolyte. The pump utilizes coulometric titration to either add or remove oxygen. The system is controlled by a desktop control unit, which can also be accessed via a computer. The controller performs temperature control for the sensor and pump, has a PID-based current loop and a control algorithm. Oxygen partial pressure has been shown to play a significant role in the surface tension of liquid metals. Oxide films or dissolved oxygen may lead to significant changes in surface tension. The effects on surface tension and viscosity by oxygen partial pressure in the surrounding environment and the melt dissolved oxygen content will be evaluated, and the results will be presented. The surface tension and viscosity will be measured at several different oxygen partial pressures while the sample is undercooled. Surface tension and viscosity will be measured using the oscillating droplet method.