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

Accommodation and vergence response gains to different near cues characterize specific esotropias

Aim. To describe preliminary findings of how the profile of the use of blur, disparity and proximal cues varies between non-strabismic groups and those with different types of esotropia. Design. Case control study Methodology. A remote haploscopic photorefractor measured simultaneous convergence and accommodation to a range of targets containing all combinations of binocular disparity, blur and proximal (looming) cues. 13 constant esotropes, 16 fully accommodative esotropes, and 8 convergence excess esotropes were compared with age and refractive error matched controls, and 27 young adult emmetropic controls. All wore full refractive correction if not emmetropic. Response AC/A and CA/C ratios were also assessed. Results. Cue use differed between the groups. Even esotropes with constant suppression and no binocular vision (BV) responded to disparity in cues. The constant esotropes with weak BV showed trends for more stable responses and better vergence and accommodation than those without any BV. The accommodative esotropes made less use of disparity cues to drive accommodation (p=0.04) and more use of blur to drive vergence (p=0.008) than controls. All esotropic groups failed to show the strong bias for better responses to disparity cues found in the controls, with convergence excess esotropes favoring blur cues. AC/A and CA/C ratios existed in an inverse relationship in the different groups. Accommodative lag of >1.0D at 33cm was common (46%) in the pooled esotropia groups compared with 11% in typical children (p=0.05). Conclusion. Esotropic children use near cues differently from matched non-esotropic children in ways characteristic to their deviations. Relatively higher weighting for blur cues was found in accommodative esotropia compared to matched controls

Future asymptotic expansions of Bianchi VIII vacuum metrics

Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in an article by Wainwright and Hsu, and in a previous article we analyzed the asymptotic behaviour of solutions in these variables. One objective of this paper is to give an asymptotic expansion for the metric. Furthermore, we relate this expansion to the topology of the compactified spatial hypersurfaces of homogeneity. The compactified spatial hypersurfaces have the topology of Seifert fibred spaces and we prove that in the case of NUT Bianchi VIII spacetimes, the length of a circle fibre converges to a positive constant but that in the case of general Bianchi VIII solutions, the length tends to infinity at a rate we determine.Comment: 50 pages, no figures. Erronous definition of Seifert fibred spaces correcte

The effects of passing speed distribution on rail corrugation growth rate

The transportation phenomenon known as wear-type rail corrugation is a significant problem in railway engineering, which manifests as a periodic wear pattern developing on the surface of the wheel and rail with use. Some field studies and recent theoretical results by the current authors have suggested that uniformity in pass speed causes an increase in corrugation growth rate. This paper presents the predicted change in corrugation growth rate and dominant wavelengths with change in passing speed distribution, based on state of the art cornering growth modelling techniques