Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity which offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: 54 pages, submitted to Living Reviews in Relativit

The Einstein-Vlasov System/Kinetic Theory

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein--Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov system. Since then many theorems on global properties of solutions to this system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-

Triple Task method: systemic, reflective action research

This brief article introduces a new methodology for systemic action research – Triple Task (TT) – and sets out its rationale and initial progress in becoming an embedded method for group working. Arising from the authors previous work with soft systems approaches, the Imagine method for sustainable development assessment and action research in a variety of global locations, TT provides a means for groups to engage together in purposive work and, at the same time, for facilitators to understand how the dynamic of the group influences the groups output. TT is based on an ambitious concept and at the time of writing the results of TT applied in the context of an EU Framework 7 funded project are in their early stages but importantly, significant insights are already arising including the answers to some puzzling questions: -Do purposeful groups always produce the most insightful outcomes? -Do conflictual groups produce incoherent results? -What makes a 'good' group?

The role of tear physiology in ocular surface temperature

PURPOSE: To determine whether the more rapid cooling of the tear film in dry eyes is related to other tear film parameters, a battery of tear physiology tests was performed on dry eye patients and control subjects. METHODS: Tear evaporation rate was measured with a modified Servomed (vapour pressure) evaporimeter and ocular temperature with an NEC San-ei 6T62 Thermo Tracer in 9 patients diagnosed as having dry eye and in 13 healthy control subjects. Variability in temperature across the ocular surface was described by the temperature variation factor (TVF). Lipid layer structure and tear film stability were assessed with the Keeler Tearscope and tear osmolality was measured by freezing point depression nanolitre osmometry. RESULTS: The data were explored by principal component analysis. The subjects with and without dry eye could be separated into two distinct groups entirely on the basis of their tear physiology. Dry eye patients exhibited higher tear evaporation rates, osmolalities and TVF, lower tear film stabilities and poorer-quality lipid layers than the control subjects. A significant linear relationship was found to exist between tear evaporation rate and TVF for all subjects (R2 = 0.242, p = 0.024). CONCLUSIONS: Rapid cooling of the tear film in dry eyes appears to be related to the reduced stability of the tears and the increased rate of evaporation. The higher latent heat of vaporisation, associated with the increased evaporation in dry eyes, may account for the increased rate of cooling of the tear film in this condition