A simple model of metal-halide arcs

Abstract

Energy balance calculations have been made of a cylindrical high-pressure LTE discharge which contains small quantities of metal halides with a large excess of mercury. It is assumed that the partial pressures of emitting atoms remain at a constant value throughout the arc, and that the emission coefficient for atoms and ions can be calculated using the Corliss and Bozman (1962) transition probabilities. The model has been used to compare the effects of adding different elements (scandium and iron) and mixtures of elements on the temperature profile, and other properties of metal halide lamps. The self-absorbed radiation of the mercury atoms must be included in order to obtain realistic temperature profiles. It is assumed that for all lines emitted by the added elements, the arc is optically thin.

Numerical investigation of cosmological singularities

“…The approach to it asymptotically falls into two classes. The first, called asymptotically velocity term dominated (AVTD) [1,2], refers to a cosmology that approaches the Kasner (vacuum, Bianchi I) solution [3] as τ → ∞. (Spatially homogeneous universes can be described as a sequence of homogeneous spaces labeled by τ .…”

Numerical evidence that the singularity in polarized U(1) symmetric cosmologies onT3×Ris velocity dominated

“…The cosmological singularity in spatially homogeneous models is known to be either asymptotically velocity term dominated (AVTD) (Kasner-like) [1,2] or Mixmaster-like [3,4]. Analytic [2,5] and numerical studies [6,7] have shown that the singularity in the spatially inhomogeneous Gowdy models [8] is AVTD everywhere in polarized models and everywhere except, perhaps, at a set of measure zero in the generic, unpolarized case.…”

The Gowdy cosmologies revisited

“…Early studies due to Belinskii et al [1] suggested that the behaviour of the generic singularity resembles that of the spatially homogeneous Bianchi VIII and IX cosmological models, commonly called mixmaster dynamics. It is generally felt, however, that matters are not this simple, and attention has focused on the velocity-term-dominated behaviour (VTDB) hypothesis due to Eardley et al [5]. It is very hard to give a covariant definition but, loosely speaking, the hypothesis claims that near the singularity spatial derivatives play no part in the evolution; locally one has a spatially homogeneous cosmology, but with the parameters varying from point to point.…”