Effects of Quantized Scalar Fields in Cosmological Spacetimes with Big Rip Singularities

Effects of quantized free scalar fields in cosmological spacetimes with Big Rip singularities are investigated. The energy densities for these fields are computed at late times when the expansion is very rapid. For the massless minimally coupled field it is shown that an attractor state exists in the sense that, for a large class of states, the energy density of the field asymptotically approaches the energy density it would have if it was in the attractor state. Results of numerical computations of the energy density for the massless minimally coupled field and for massive fields with minimal and conformal coupling to the scalar curvature are presented. For the massive fields the energy density is seen to always asymptotically approach that of the corresponding massless field. The question of whether the energy densities of quantized fields can be large enough for backreaction effects to remove the Big Rip singularity is addressed.Comment: PRD version. References added. Several minor corrections and changes. 22 pages, 3 figure

The Pseudo-continuum Bound-free Opacity of Hydrogen and its Importance in Cool White Dwarf Atmospheres

We investigate the importance of the pseudo-continuum bound-free opacity from hydrogen atoms in the atmospheres of cool white dwarfs. This source of absorption, when calculated by the occupation probability formalism applied in the modeling of white dwarf atmospheres with $T_{\rm eff}\rm <17000 K$, dominates all other sources of opacity at optical wavelengths. This is unrealistic and not observed. On the other hand, a significant flux suppression in the blue part of the spectra of cool white dwarfs has been reported, and mainly interpreted as a result of the pseudo-continuum absorption from atomic hydrogen. We investigate this problem by proposing a new, more realistic approach to calculating this source of opacity. We show that this absorption is orders of magnitude smaller than that predicted by current methods. Therefore, we rule out the pseudo-continuum opacity as a source of the flux deficiency observed in the spectra of cool white dwarfs.Comment: 11 pages, 5 gigures, accepted for publication in the Astrophysical Journa

A note on commuting graphs for symmetric groups

The commuting graph C(G;X) , where G is a group and X a subset of G, has X as its vertex set with two distinct elements of X joined by an edge when they commute in G. Here the diameter and disc structure of C(G;X) is investigated when G is the symmetric group and X a conjugacy class of G

Low cost solar array project 1: Silicon material

The low cost production of silicon by deposition of silicon from a hydrogen/chlorosilane mixture is described. Reactor design, reaction vessel support systems (physical support, power control and heaters, and temperature monitoring systems) and operation of the system are reviewed. Testing of four silicon deposition reactors is described, and test data and consequently derived data are given. An 18% conversion of trichlorosilane to silicon was achieved, but average conversion rates were lower than predicted due to incomplete removal of byproduct gases for recycling and silicon oxide/silicon polymer plugging of the gas outlet. Increasing the number of baffles inside the reaction vessel improved the conversion rate. Plans for further design and process improvements to correct the problems encountered are outlined

Resistive Magnetohydrodynamic Equilibria in a Torus

It was recently demonstrated that static, resistive, magnetohydrodynamic equilibria, in the presence of spatially-uniform electrical conductivity, do not exist in a torus under a standard set of assumed symmetries and boundary conditions. The difficulty, which goes away in the ``periodic straight cylinder approximation,'' is associated with the necessarily non-vanishing character of the curl of the Lorentz force, j x B. Here, we ask if there exists a spatial profile of electrical conductivity that permits the existence of zero-flow, axisymmetric r esistive equilibria in a torus, and answer the question in the affirmative. However, the physical properties of the conductivity profile are unusual (the conductivity cannot be constant on a magnetic surface, for example) and whether such equilibria are to be considered physically possible remains an open question.Comment: 17 pages, 4 figure