Report of activities of the advanced coal extraction systems definition project, 1979 - 1980

During this period effort was devoted to: formulation of system performance goals in the areas of production cost, miner safety, miner health, environmental impact, and coal conservation, survey and in depth assessment of promising technology, and characterization of potential resource targets. Primary system performance goals are to achieve a return on incremental investment of 150% of the value required for a low risk capital improvement project and to reduce deaths and disability injuries per million man-hour by 50%. Although these performance goals were developed to be immediately applicable to the Central Appalachian coal resources, they were also designed to be readily adaptable to other coals by appending a geological description of the new resource. The work done on technology assessment was concerned with the performance of the slurry haulage system

Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics

We show that sets of conformal data on closed manifolds with the metric in the positive or zero Yamabe class, and with the gradient of the mean curvature function sufficiently small, are mapped to solutions of the Einstein constraint equations. This result extends previous work which required the conformal metric to be in the negative Yamabe class, and required the mean curvature function to be nonzero.Comment: 15 page

Oscillatory approach to the singularity in vacuum T2T^2 symmetric spacetimes

A combination of qualitative analysis and numerical study indicates that vacuum $T^2$ symmetric spacetimes are, generically, oscillatory.Comment: 2 pages submitted to the Ninth Marcel Grossmann Proceedings; v2, "all known cases" changed to "various known cases" in the first paragrap

Development of integrated programs for Aerospace-vehicle Design (IPAD): Product program management systems

The Integrated Programs for Aerospace Vehicle Design (IPAD) is a computing system to support company-wide design information processing. This document presents a brief description of the management system used to direct and control a product-oriented program. This document, together with the reference design process (CR 2981) and the manufacture interactions with the design process (CR 2982), comprises the reference information that forms the basis for specifying IPAD system requirements

A model problem for conformal parameterizations of the Einstein constraint equations

We investigate the possibility that the conformal and conformal thin sandwich (CTS) methods can be used to parameterize the set of solutions of the vacuum Einstein constraint equations. To this end we develop a model problem obtained by taking the quotient of certain symmetric data on conformally flat tori. Specializing the model problem to a three-parameter family of conformal data we observe a number of new phenomena for the conformal and CTS methods. Within this family, we obtain a general existence theorem so long as the mean curvature does not change sign. When the mean curvature changes sign, we find that for certain data solutions exist if and only if the transverse-traceless tensor is sufficiently small. When such solutions exist, there are generically more than one. Moreover, the theory for mean curvatures changing sign is shown to be extremely sensitive with respect to the value of a coupling constant in the Einstein constraint equations.Comment: 40 pages, 4 figure

Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations

We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of large sets of asymptotically hyperbolic non constant mean curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure

A rigidity theorem for nonvacuum initial data

In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a ``rigidity phenomenon'' for the extrinsic curvature, caused by the non-positive scalar curvature. More precisely, we state that in the case of asymptotically flat non-vacuum initial data if the metric has everywhere non-positive scalar curvature then the extrinsic curvature cannot be compactly supported.Comment: This is an extended and published version: LaTex, 10 pages, no figure

The constraint equations for the Einstein-scalar field system on compact manifolds

We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed scalar curvature problem as special cases.Comment: Minor changes, final version. To appear: Classical and Quantum Gravit