A collocation finite element method for potential problems in irregular domains

A potentially powerful numerical method for solving certain boundary value problems is developed. The method combines the simplicity of orthogonal collocation with the versatility of deformable finite elements. Bicubic Hermite elements with four degrees-of-freedom per node are used. A subparametric transformation permits the precise positioning of the collocation points for maximum accuracy as well as a unique representation of irregular boundaries. It is shown that by taking advantage of the boundary conditions, a minimum number of collocation points can be used. The method is particularly suitable for potential and mass transport problems where a C¹ continuous solution is required. In contrast to the Galerkin approach, it does not require the evaluation of basis function products and numerical integration, also the coefficient matrix contains only about half as many non-zero terms as the corresponding Galerkin coefficient matrix. This results in approximately a 90 per cent reduction in formulation and a 50 per cent reduction in solution operation, as compared with the Galerkin finite element method, for this type of problem. Examples show that the accuracy of the collocation solution is as good as or better than that of the Galerkin solution.     

Learning About 3d Melting With Solid Helium

Theories of bulk melting rely on a sudden proliferation of crystalline defects in order to destabilize the lattice. However, these scenarios were never confirmed experimentally, as it is impossible to approach the transition sufficiently to see critical behaviour. In experiments investigating plastic flow of solid ⁴He, we observed such critical behaviour involving a dramatic decrease of the resistance to shear near the first order bcc-hcp transition at 1.772K on the melting curve. By measuring the plastic flow over a wide range of shear stress, we were able to differentiate between the contribution of vacancies and of dislocations to this process. We argue that the mechanism by which the crystal loses its shear resistance involves coupling of vacancy diffusion with a transverse phonon which softens as the transition is approached. Dislocations seem to play no fundamental role in this process. These results suggest a refinement of the Lindemann picture, as the phonon mode which plays a dominant role in this process is near the edge of the Brillouin zone.     

Copper converter refractory practices

The articles appearing in the following section are condensations of papers presented at a round table discussion on the subject of “Copper Converter Refractory Practices”, sponsored by the Extractive Metallurgy Division of The Metallurgical Society. The discussion was held during the AIME Annual Meeting in New York City, February 1968. All deletions, and the omission of references, have been made solely because of space limitations, and should not be construed as reflections upon the individual authors or their papers.     

Shrinkage-Free Sintering of Low-Temperature Cofired Ceramics by Loading Dilatometry

Sintering with zero radial shrinkage of low-temperature cofired ceramics (LTCC) was investigated by means of loading dilatometry. The results indicate that constant compressive loads tend to produce either decreased or increased radial shrinkages, and this can vary as a function of density, depending on the magnitude of the applied stresses. Coupling the real-time applied uniaxial load to the radial strain of cylindrical samples afforded a sintering scheme where the radial strain was precisely kept near zero (±0.02%). This approach possibly perfects an existing hot-pressing technique for zero-shrinkage sintering technology of LTCC materials.     

Production of CO during burnup of (Th,U)O2 kerneled HTR fuel particles

The CO content of irradiated (Th, U)O₂ kerneled HTR fuel particles has been measured by mass spectrometry. An evaluation of all the data thus obtained showed that the oxygen release, O/f (atoms per fission), during irradiation is governed by thermodynamic equilibrium; O/f is a function of the irradiation temperature $\text{T}$(K), the initial Th/U-235 ratio $\text{N}$, and the burnup $\text{F}$ (fissions per initial heavy metal atom). Within the limits of $\text{1073 < T < 2273}$, $\text{4 < N <50}$, and $\text{0.04 < F < 0.17}$, the oxygen release can be represented by the expression $\text{log}{}_{10}\text{O/f = 0.96 ? 4420/T + 0.4 log}{}_{10}\text{N + 0.3 log}{}_{10}\text{F}$.The attainment of equilibrium proceeds rather slowly; at 1473 K it takes about 130 h to reach 99% of the equilibrium value.Coated particles which had undergone large fission-product losses showed significantly increased oxygen release values.     

Some regional costs of a synthetic fuel industry: The case of illinois

The Federal Government's efforts to induce development of a coal-based synthetic fuel industry include direct subsidies, tax concessions, and assurances that it will purchase the industry's output, even if above the market price. In this note it is argued that these subsidies will enable this industry to secure a region's largest and lowest-cost coal deposits and that the costs imposed on other coal users will be substantial. Moreover, because the lowest-cost coal deposits will be committed to synthetic fuels production regardless of the industry's commercial viability, distortions in regional coal markets will develop. If economic efficiency requires that the price of the resource reflect its replacement value, then a State government is justified in imposing a tax on coal destined for subsidized synthetic fuel plants. Amounts of such a tax, based on the higher costs of coal that must be accepted by other users as the result of the subsidized synthetic fuel plants' preempting the largest and lowest-cost deposits, are estimated for the case of Illinois strippable coal.     

Risk Governance of Emerging Technologies Demonstrated in Terms of its Applicability to Nanomaterials

Nanotechnologies have reached maturity and market penetration that require nano‐specific changes in legislation and harmonization among legislation domains, such as the amendments to REACH for nanomaterials (NMs) which came into force in 2020. Thus, an assessment of the components and regulatory boundaries of NMs risk governance is timely, alongside related methods and tools, as part of the global efforts to optimise nanosafety and integrate it into product design processes, via Safe(r)‐by‐Design (SbD) concepts. This paper provides an overview of the state‐of‐the‐art regarding risk governance of NMs and lays out the theoretical basis for the development and implementation of an effective, trustworthy and transparent risk governance framework for NMs. The proposed framework enables continuous integration of the evolving state of the science, leverages best practice from contiguous disciplines and facilitates responsive re‐thinking of nanosafety governance to meet future needs. To achieve and operationalise such framework, a science‐based Risk Governance Council (RGC) for NMs is being developed. The framework will provide a toolkit for independent NMs' risk governance and integrates needs and views of stakeholders. An extension of this framework to relevant advanced materials and emerging technologies is also envisaged, in view of future foundations of risk research in Europe and globally.     

Exploring Tabular Verification and Refinement

Tabular representations have been proposed for structuring complex mathematical expressions as they appear in the specification of programs. We argue that tables not only help in writing and checking complex expressions, but also in their formal manipulation. More specifically, we explore the use of tabular predicates and tabular relations in program verification and refinement.     

Single Shot Dual-Wavelength Digital Holography: Calibration Based on Speckle Displacements

We present a calibration method which allows single shot dual wavelength online shape measurement in a disturbed environment. Effects of uncontrolled carrier frequency filtering are discussed as well. We demonstrate that phase maps and speckle displacements can be recovered free of chromatic aberrations. To our knowledge, this is the first time that a single shot dual wavelength calibration is reported by defining a criteria to make the spatial filtering automatic avoiding the problems of manual methods. The procedure is shown to give shape accuracy of 35 µm with negligible systematic errors using a synthetic wavelength of 1.1 mm.