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

Escape probability and transience for SLE

We give estimates for the probability that a chordal, radial or two-sided radial SLE$_\kappa$ curve retreats far from its terminal point after coming close to it, for $\kappa \leq 4$. The estimates are uniform over all initial segments of the curve, and are sharp up to a universal constant.Comment: 20 pages, 4 figure

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

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

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

The Victorian Naturalist

v.113 (1996

The Victorian Naturalist

v.116 (1999

The Victorian Naturalist

v.112 (1995