Some Spinor-Curvature Identities

We describe a class of spinor-curvature identities which exist for Riemannian or Riemann-Cartan geometries. Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the curvature plus an exact differential. Certain special cases in 3 and 4 dimensions which have been or could be used in applications to General Relativity are noted.Comment: 5 pages Plain TeX, NCU-GR-93-SSC

A Quadratic Spinor Lagrangian for General Relativity

We present a new finite action for Einstein gravity in which the Lagrangian is quadratic in the covariant derivative of a spinor field. Via a new spinor-curvature identity, it is related to the standard Einstein-Hilbert Lagrangian by a total differential term. The corresponding Hamiltonian, like the one associated with the Witten positive energy proof is fully four-covariant. It defines quasi-local energy-momentum and can be reduced to the one in our recent positive energy proof. (Fourth Prize, 1994 Gravity Research Foundation Essay.)Comment: 5 pages (Plain TeX), NCU-GR-94-QSL

Ashtekar's New Variables and Positive Energy

We discuss earlier unsuccessful attempts to formulate a positive gravitational energy proof in terms of the New Variables of Ashtekar. We also point out the difficulties of a Witten spinor type proof. We then use the special orthonormal frame gauge conditions to obtain a locally positive expression for the New Variables Hamiltonian and thereby a ``localization'' of gravitational energy as well as a positive energy proof.Comment: 12 pages Plain Te

Symptomatic pes planus in children : a synthesis of allied health professional practices

This study sought to explore professional perspectives on the assessment and management of symptomatic pes planus in children. Data was collected from three professional groups (podiatrists, physiotherapists, and orthotists) with experience of managing foot problems in children. The survey was undertaken in the United Kingdom via a self-administered, online survey. Data was captured over a four-month period in 2018. Fifty-five health professionals completed the survey and the results highlighted that assessment techniques varied between professions, with standing tip-toe and joint range of motion being the most common. Treatment options for children were diverse and professionals were adopting different strategies as their first line intervention. All professions used orthoses. There were inconsistencies in how the health professionals assessed children presenting with foot symptoms, variation in how the condition was managed and differences in outcome measurement. These findings might be explained by the lack of robust evidence and suggests that more effort is needed to harmonise assessment and treatment approaches between professions. Addressing discrepancies in practice could help prioritise professional roles in this area, and better support the management of children with foot pain. [Abstract copyright: © The Author(s). 2020.

Influence of variation of the contact area upon the slip resistance of a bolted joint

If the plates in a joint are not initially flat it may not be possible to bring the plates together over the entire faying area when the bolts are tightened. To ascertain whether or not it is necessary to have full contact over the entire faying area to develop the slip resistance of a joint, fifteen butt joints were tested

Quasi-local Energy for Spherically Symmetric Spacetimes

We present two complementary approaches for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test them on spherically symmetric spacetimes. On the one hand, we isometrically match the 2-surface and extremize the energy. This can be done in two ways, which we call programs I (without constraint) and II (with additional constraints). On the other hand, we match the orthonormal 4-frames of the dynamic and the reference spacetimes. Then, if we further specify the observer by requiring the reference displacement to be the timelike Killing vector of the reference, the result is the same as program I, and the energy can be positive, zero, or even negative. If, instead, we require that the Lie derivatives of the two-area along the displacement vector in both the dynamic and reference spacetimes to be the same, the result is the same as program II, and it satisfies the usual criteria: the energies are non-negative and vanish only for Minkowski (or anti-de Sitter) spacetime.Comment: 16 pages, no figure