Asymptotic dynamics of the exceptional Bianchi cosmologies

In this paper we give, for the first time, a qualitative description of the asymptotic dynamics of a class of non-tilted spatially homogeneous (SH) cosmologies, the so-called exceptional Bianchi cosmologies, which are of Bianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly, it is generic within the class of non-tilted SH cosmologies, being of the same generality as the models of Bianchi types VIII and IX. Secondly, it is the SH limit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies. Using the orthonormal frame formalism and Hubble-normalized variables, we show that the exceptional Bianchi cosmologies differ from the non-exceptional Bianchi cosmologies of type VI$_{h}$ in two significant ways. Firstly, the models exhibit an oscillatory approach to the initial singularity and hence are not asymptotically self-similar. Secondly, at late times, although the models are asymptotically self-similar, the future attractor for the vacuum-dominated models is the so-called Robinson-Trautman SH model instead of the vacuum SH plane wave models.Comment: 15 pages, 6 figures, submitted to Class. Quantum Gra

Exhaust jet wake and thrust characteristics of several nozzles designed for VTOL DOWNWASH suppression. Tests in and out of ground effect with 70 deg F and 1200 deg F nozzle discharge temperatures

Jet wake degradation and thrust characteristics of exhaust nozzles designed for VTOL downwash suppression and fuselage and ground effect

A new proof of the Bianchi type IX attractor theorem

We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The `Bianchi type IX attractor theorem' states that the past asymptotic behavior of generic type IX solutions is governed by Bianchi type I and II vacuum states (Mixmaster attractor). We give a comparatively short and self-contained new proof of this theorem. The proof we give is interesting in itself, but more importantly it illustrates and emphasizes that type IX is special, and to some extent misleading when one considers the broader context of generic models without symmetries.Comment: 26 pages, 5 figure

Bianchi VIII Empty Futures

Using a qualitative analysis based on the Hamiltonian formalism and the orthonormal frame representation we investigate whether the chaotic behaviour which occurs close to the initial singularity is still present in the far future of Bianchi VIII models. We describe some features of the vacuum Bianchi VIII models at late times which might be relevant for studying the nature of the future asymptote of the general vacuum inhomogeneous solution to the Einstein field equations.Comment: 22 pages, no figures, Latex fil