Action and Energy of the Gravitational Field

We present a detailed examination of the variational principle for metric general relativity as applied to a ``quasilocal'' spacetime region \M (that is, a region that is both spatially and temporally bounded). Our analysis relies on the Hamiltonian formulation of general relativity, and thereby assumes a foliation of \M into spacelike hypersurfaces $\Sigma$. We allow for near complete generality in the choice of foliation. Using a field--theoretic generalization of Hamilton--Jacobi theory, we define the quasilocal stress-energy-momentum of the gravitational field by varying the action with respect to the metric on the boundary \partial\M. The gravitational stress-energy-momentum is defined for a two--surface $B$ spanned by a spacelike hypersurface in spacetime. We examine the behavior of the gravitational stress-energy-momentum under boosts of the spanning hypersurface. The boost relations are derived from the geometrical and invariance properties of the gravitational action and Hamiltonian. Finally, we present several new examples of quasilocal energy--momentum, including a novel discussion of quasilocal energy--momentum in the large-sphere limit towards spatial infinity.Comment: To be published in Annals of Physics. This final version includes two new sections, one giving examples of quasilocal energy and the other containing a discussion of energy at spatial infinity. References have been added to papers by Bose and Dadhich, Anco and Tun

Canonical Quasilocal Energy and Small Spheres

Consider the definition E of quasilocal energy stemming from the Hamilton-Jacobi method as applied to the canonical form of the gravitational action. We examine E in the standard "small-sphere limit," first considered by Horowitz and Schmidt in their examination of Hawking's quasilocal mass. By the term "small sphere" we mean a cut S(r), level in an affine radius r, of the lightcone belonging to a generic spacetime point. As a power series in r, we compute the energy E of the gravitational and matter fields on a spacelike hypersurface spanning S(r). Much of our analysis concerns conceptual and technical issues associated with assigning the zero-point of the energy. For the small-sphere limit, we argue that the correct zero-point is obtained via a "lightcone reference," which stems from a certain isometric embedding of S(r) into a genuine lightcone of Minkowski spacetime. Choosing this zero-point, we find agreement with Hawking's quasilocal mass expression, up to and including the first non-trivial order in the affine radius. The vacuum limit relates the quasilocal energy directly to the Bel-Robinson tensor.Comment: revtex, 22 p, uses amssymb option (can be removed

Parallel matrix inversion techniques

In this paper, we present techniques for inverting sparse, symmetric and positive definite matrices on parallel and distributed computers. We propose two algorithms, one for SIMD implementation and the other for MIMD implementation. These algorithms are modified versions of Gaussian elimination and they take into account the sparseness of the matrix. Our algorithms perform better than the general parallel Gaussian elimination algorithm. In order to demonstrate the usefulness of our technique, we implemented the snake problem using our sparse matrix algorithm. Our studies reveal that the proposed sparse matrix inversion algorithm significantly reduces the time taken for obtaining the solution of the snake problem. In this paper, we present the results of our experimental work

New variables, the gravitational action, and boosted quasilocal stress-energy-momentum

This paper presents a complete set of quasilocal densities which describe the stress-energy-momentum content of the gravitational field and which are built with Ashtekar variables. The densities are defined on a two-surface $B$ which bounds a generic spacelike hypersurface $\Sigma$ of spacetime. The method used to derive the set of quasilocal densities is a Hamilton-Jacobi analysis of a suitable covariant action principle for the Ashtekar variables. As such, the theory presented here is an Ashtekar-variable reformulation of the metric theory of quasilocal stress-energy-momentum originally due to Brown and York. This work also investigates how the quasilocal densities behave under generalized boosts, i. e. switches of the $\Sigma$ slice spanning $B$. It is shown that under such boosts the densities behave in a manner which is similar to the simple boost law for energy-momentum four-vectors in special relativity. The developed formalism is used to obtain a collection of two-surface or boost invariants. With these invariants, one may ``build" several different mass definitions in general relativity, such as the Hawking expression. Also discussed in detail in this paper is the canonical action principle as applied to bounded spacetime regions with ``sharp corners."Comment: Revtex, 41 Pages, 4 figures added. Final version has been revised and improved quite a bit. To appear in Classical and Quantum Gravit

Ti and V layers retard interaction between Al films and polycrystalline Si

Fine-grained polycrystalline Si (poly Si) in contact with Al films recrystallizes at temperatures well below the Si-Al eutectic (577 °C). We show that this interaction can be deferred or suppressed by placing a buffer layer of Ti or V between the Al film and the poly Si. During annealing, Ti or V form TiAl3 or Val3 at the buffer-layer–Al-film interface, but do not react with the poly Si so that the integrity of the poly Si is preserved as long as some unreacted Ti or V remains. The reaction between the Ti or V layer and the Al film is transport limited ([proportional]t^1/2) and characterized by the diffusion constants 1.5×10^15 exp(–1.8eV/kT) Å^2/sec or 8.4×10^12 exp(–1.7eV/kT) Å^2/sec, respectively

Evaluation of present thermal barrier coatings for potential service in electric utility gas turbines

The resistance of present-day thermal barrier coatings to combustion gases found in electric utility turbines was assessed. The plasma sprayed coatings, both duplex and graded types, were primarily zirconia-based, although a calcium silicate was also evaluated. Both atmospheric burner rig tests and high pressure tests (135 psig) showed that several present-day thermal barrier coatings have a high potential for service in gas turbines burning the relatively clean GT No. 2 fuel. However, coating improvements are needed for use in turbines burning lower grade fuel such as residual oil. The duplex ZrO2.8Y2O3/NiCrA1Y coating was ranked highest and selected for near-term field testing, with Ca2SiO4/NiCrA1Y ranked second. Graded coatings show potential for corrosive turbine operating conditions and warrant further development. The coating degradation mechanisms for each coating system subjected to the various environmental conditions are also described

Sequence of phase formation in planar metal-Si reaction couples

A correlation is found between the sequence of phase formation in thin-film metal-Si interactions and the bulk equilibrium phase diagram. After formation of the first silicide phase, which generally follows the rule proposed by Walser and Bené, the next phase formed at the interface between the first phase and the remaining element (Si or metal) is the nearest congruently melting compound richer in the unreacted element. If the compounds between the first phase and the remaining element are all noncongruently melting compounds (such as peritectic or peritectoid phases), the next phase formed is that with the smallest temperature difference between the liquidus curve and the peritectic (or peritectoid) point

Heterostructure by solid‐phase epitaxy in the Si〈111〉/Pd/Si (amorphous) system

When a thin film of Pd reacts with a 〈111〉 Si substrate, a layer of epitaxial Pd_2Si is formed. It is shown that Si can grow epitaxially on such a layer by solid‐phase reaction

Hamiltonians for a general dilaton gravity theory on a spacetime with a non-orthogonal, timelike or spacelike outer boundary

A generalization of two recently proposed general relativity Hamiltonians, to the case of a general (d+1)-dimensional dilaton gravity theory in a manifold with a timelike or spacelike outer boundary, is presented.Comment: 17 pages, 3 figures. Typos correcte

Predictors of Therapists Use of Homework in Community Mental Health: Session and Therapist Characteristics

Assigning and reviewing homework as a strategy to help clients gain therapeutic skills is a common technique used across a variety of evidence-based practices (EBPs) and has been shown to improve therapy outcomes for children and youth. However, in studies characterizing routine psychotherapy delivered in community mental health settings, homework is rarely used in sessions. While some therapist and client level predictors of EBP strategy use have been identified in routine psychotherapy (e.g. client stressors, therapists’ attitudes towards EBPs) it is unknown what is associated with community mental health therapists using homework in the increasingly common context of system-driven implementation of multiple EBPs. To identify predictors of therapists’ use of homework, 680 videos of sessions with 274 clients were collected from 103 therapists (of which 55% were Hispanic) providing children’s mental health services through the Los Angeles County Department of Mental Health (LACDMH). The current study uses a multilevel logistic regression analysis model to identify which factors are associated with therapist use of homework in therapy sessions when there is system-driven implementation support for the use of multiple EBPs in community mental health settings. After controlling for the EBP delivered in session and the number of EBPs therapists were trained in, having a caregiver present in the therapy session, older child age, and being an unlicensed therapist were associated with a higher likelihood of therapists assigning and reviewing homework during a specific session. Therapist race/ethnicity, perceptions of the EBP being delivered, their report of emotional exhaustion, and direct hours with clients, as well as emergent unexpected stressful client life events within a session were not significantly associated with therapists’ delivery of homework. These findings underscore the need to provide explicit attention during therapist training on the use of homework with younger clients when caregivers are absent from sessions and the need to facilitate the use of homework among licensed therapists