Symmetries of the Einstein Equations

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, \ie at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions and find that the only generalized symmetry transformations consist of: (i) constant scalings of the metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms. Our results rule out a large class of possible ``observables'' for the gravitational field, and suggest that the vacuum Einstein equations are not integrable.Comment: 15 pages, FTG-114-USU, Plain Te

Evaluation of a bulk calorimeter and heat balance for determination of supersonic combustor efficiency

Results are presented from the shakedown and evaluation test of a bulk calorimeter. The calorimeter is designed to quench the combustion at the exit of a direct-connect, hydrogen fueled, scramjet combustor model, and to provide the measurements necessary to perform an analysis of combustion efficiency. Results indicate that the calorimeter quenches reaction, that reasonable response times are obtained, and that the calculated combustion efficiency is repeatable within + or -3 percent and varies in a regular way with combustor model parameters such as injected fuel equivalence ratio

Parametric analysis of diffuser requirements for high expansion ratio space engine

A supersonic diffuser ejector design computer program was developed. Using empirically modified one dimensional flow methods the diffuser ejector geometry is specified by the code. The design code results for calculations up to the end of the diffuser second throat were verified. Diffuser requirements for sea level testing of high expansion ratio space engines were defined. The feasibility of an ejector system using two commonly available turbojet engines feeding two variable area ratio ejectors was demonstrated

Calculation of flow about posts and powerhead model

A three dimensional analysis of the non-uniform flow around the liquid oxygen (LOX) posts in the Space Shuttle Main Engine (SSME) powerhead was performed to determine possible factors contributing to the failure of the posts. Also performed was three dimensional numerical fluid flow analysis of the high pressure fuel turbopump (HPFTP) exhaust system, consisting of the turnaround duct (TAD), two-duct hot gas manifold (HGM), and the Version B transfer ducts. The analysis was conducted in the following manner: (1) modeling the flow around a single and small clusters (2 to 10) of posts; (2) modeling the velocity field in the cross plane; and (3) modeling the entire flow region with a three dimensional network type model. Shear stress functions which will permit viscous analysis without requiring excessive numbers of computational grid points were developed. These wall functions, laminar and turbulent, have been compared to standard Blasius solutions and are directly applicable to the cylinder in cross flow class of problems to which the LOX post problem belongs

New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory

DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors and other tensorial invariants, algebraic classification of curvature, and symmetry reduction of field equations.Comment: 42 page

Factors affecting environmental attitudes and volunteering in England and Wales

This paper investigates the demographic, social, political and religious factors that affect people’s attitudes to the environment and their involvement in environmental volunteering in England and Wales, using data from four waves of the Home Office Citizenship Survey between 2003 and 2009. Approximately 14,000 people were included in each wave of the survey, with around 85%-90% of people having a positive attitude to the environment, while 7%-8% were involved in volunteering. The data were analysed using logistic regression models. Covariates included sex, ethnicity, age, income, education, religion and region. We found that positive attitude and volunteering increased up to the age of 65 before decreasing sharply. People on middling incomes between £20k and £60k were the most likely to have positive environmental attitude and activity. We found no evidence of behavioural change—the results on both environmental attitudes and volunteering remained stable across all four waves of the survey