Three isoparametric solid elements for NASTRAN

Linear, quadratic, and cubic isoparametric hexahedral solid elements have been added to the element library of NASTRAN. These elements are available for static, dynamic, buckling, and heat-transfer analyses. Because the isoparametric element matrices are generated by direct numerical integration over the volume of the element, variations in material properties, temperatures, and stresses within the elements are represented in the computations. In order to compare the accuracy of the new elements, three similar models of a slender cantilever were developed, one for each element. All elements performed well. As expected, however, the linear element model yielded excellent results only when shear behavior predominated. In contrast, the results obtained from the quadratic and cubic element models were excellent in both shear and bending

On the zero set of G-equivariant maps

Let $G$ be a finite group acting on vector spaces $V$ and $W$ and consider a smooth $G$-equivariant mapping $f:V\to W$. This paper addresses the question of the zero set near a zero $x$ of $f$ with isotropy subgroup $G$. It is known from results of Bierstone and Field on $G$-transversality theory that the zero set in a neighborhood of $x$ is a stratified set. The purpose of this paper is to partially determine the structure of the stratified set near $x$ using only information from the representations $V$ and $W$. We define an index $s(\Sigma)$ for isotropy subgroups $\Sigma$ of $G$ which is the difference of the dimension of the fixed point subspace of $\Sigma$ in $V$ and $W$. Our main result states that if $V$ contains a subspace $G$-isomorphic to $W$, then for every maximal isotropy subgroup $\Sigma$ satisfying $s(\Sigma)>s(G)$, the zero set of $f$ near $x$ contains a smooth manifold of zeros with isotropy subgroup $\Sigma$ of dimension $s(\Sigma)$. We also present a systematic method to study the zero sets for group representations $V$ and $W$ which do not satisfy the conditions of our main theorem. The paper contains many examples and raises several questions concerning the computation of zero sets of equivariant maps. These results have application to the bifurcation theory of $G$-reversible equivariant vector fields

Identifying a pedagogy of initial teacher education (ITE): issues and ambiguities

The topic of this thesis is initial teacher education (ITE) pedagogy, exploring the nature of teaching and learning about teaching (or ‘meta-teaching’), and how teacher educators in English universities translate this into practice. Its purpose was to gain an appreciation of teacher educators’ pedagogical practice beyond their first three years in the role: not just how, but why they teach student teachers in a particular way, and to observe what this looks like in practice. A collective case study approach was taken, involving four participants working in four geographically distanced universities. The methods consisted of a semi-structured interview, videoed observation of a teaching session, and a stimulated recall interview which was led by the participant whilst co-viewing the video. Analysis of the data revealed that, whilst the meta-pedagogical practice appeared to have individual drivers for each of the participants, there could be potential inhibitors to developing a distinct pedagogy of ITE which are inherent in the teacher educators’ experience and practical wisdom accumulated as school teachers. These may hinder teacher educators’ engagement with a theoretically underpinned knowledge base for their pedagogical practice. The similarities and differences in meta-pedagogical practice were explored using Bourdieusian concepts of developing habitus in the new field, leading to expanding cultural capital. It is argued that distinct drivers for the participants’ respective practices impacted upon the development of first to second order habitus. A continued focus on (curriculum) subject knowledge or on passing on the craft knowledge of (school) teaching was shown to be located in first order practice, whereas a focus on developing meta-pedagogical understandings allowed for an expanding habitus, and thus to the potential for increased cultural capital – both for themselves as individuals, and for the occupational group of teacher educators. Whilst a deep-seated sense of teacher professional identity may help to bridge the two (sub-)fields, it appeared that an accepted body of knowledge based on theoretical underpinnings could distinguish this group and enhance their cultural capital. In light of this, the role of episteme and phronesis were explored as enablers of the development of a shared meta-pedagogy. By illuminating current meta-pedagogical understandings and practice, the study aims to feed into a wider debate on teaching and learning to teach, at a time when ITE in England is in a state of flux and the future of university-based programmes – as well as university involvement in school-based programmes – is under threat. It is argued that, not only would it be possible to accelerate the process of teacher educators developing their meta-pedagogical practice through exploration of the theoretical perspectives, but that this has the potential to underline and reinforce the distinction between university- and school-led ITE in uncertain times

Geology of the Snap Lake kimberlite intrusion, Northwest Territories, Canada: field observations and their interpretation

The Cambrian (523 Ma) Snap Lake hypabyssal kimberlite intrusion, Northwest Territories, Canada, is a complex segmented diamond-bearing ore-body. Detailed geological investigations suggest that the kimberlite is a multi-phase intrusion with at least four magmatic lithofacies. In particular, olivine-rich (ORK) and olivine-poor (OPK) varieties of hypabyssal kimberlite have been identified. Key observations are that the olivine-rich lithofacieshas a strong tendency to be located where the intrusion is thickest and that there is a good correlation between intrusion thickness, olivine crystal size and crystal content. Heterogeneities in the lithofacies are attributed to variations in intrusion thickness and structural complexities. The geometry and distribution of lithofacies points to magmaticco-intrusion, and flow segregation driven by fundamental rheological differences between the two phases. We envisage that the low-viscosity OPK magma acted as a lubricant for the highly viscous ORK magma. The presenceof such low-viscosity, crystal-poor magmas may explain how crystal-laden kimberlite magmas (>60 vol.%) are able to reach the surface during kimberlite eruptions. We also document the absence of crystal settling and the development of an unusual subvertical fabric of elongate olivine crystals, which are explained by rapid degassing-induced quench crystallization of the magmas during and after intrusio

The Indirect Limit on the Standard Model Higgs Boson Mass from the Precision FERMILAB, LEP and SLD Data

Standard Model fits are performed on the most recent leptonic and b quark Z decay data from LEP and SLD, and FERMILAB data on top quark production, to obtain $m_t$ and $m_H$. Poor fits are obtained, with confidence levels $\simeq$ 2%. Removing the b quark data improves markedly the quality of the fits and reduces the 95% CL upper limit on $m_H$ by $\simeq$ 50 GeV.Comment: 6 pages 3 tables i figur

Death of Stellar Baryonic Dark Matter

The nature of the dark matter in the haloes of galaxies is one of the outstanding questions in astrophysics. All stellar candidates, until recently thought to be likely baryonic contributions to the Halo of our Galaxy, are shown to be ruled out. Faint stars and brown dwarfs are found to constitute only a few percent of the mass of the Galaxy. Stellar remnants, including white dwarfs and neutron stars, are shown to be very constrained as well. High energy gamma-rays observed in HEGRA data place the strongest constraints, $\Omega_{WD} < 3 \times 10^{-3} h^{-1}$, where $h$ is the Hubble constant in units of 100 km s$^{-1}$ Mpc$^{-1}$. Hence one is left with several unanswered questions: 1) What are MACHOs seen in microlensing surveys? 2) What is the dark matter in our Galaxy? Indeed a nonbaryonic component in the Halo seems to be required.Comment: 6 pages ps fil

Addition of three-dimensional isoparametric elements to NASA structural analysis program (NASTRAN)

Implementation is made of the three-dimensional family of linear, quadratic and cubic isoparametric solid elements into the NASA Structural Analysis program, NASTRAN. This work included program development, installation, testing, and documentation. The addition of these elements to NASTRAN provides a significant increase in modeling capability particularly for structures requiring specification of temperatures, material properties, displacements, and stresses which vary throughout each individual element. Complete program documentation is presented in the form of new sections and updates for direct insertion to the three NASTRAN manuals. The results of demonstration test problems are summarized. Excellent results are obtained with the isoparametric elements for static, normal mode, and buckling analyses