The Effects of Stress Tensor Fluctuations upon Focusing

We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources. We give explicit results for the case of a scalar field on a flat background in a thermal state.Comment: 26 pages, 1 figure, new material added in Sect. III and in Appendices B and

On certain quasi-local spin-angular momentum expressions for small spheres

The Ludvigsen-Vickers and two recently suggested quasi-local spin-angular momentum expressions, based on holomorphic and anti-holomorphic spinor fields, are calculated for small spheres of radius $r$ about a point $o$. It is shown that, apart from the sign in the case of anti-holomorphic spinors in non-vacuum, the leading terms of all these expressions coincide. In non-vacuum spacetimes this common leading term is of order $r^4$, and it is the product of the contraction of the energy-momentum tensor and an average of the approximate boost-rotation Killing vector that vanishes at $o$ and of the 3-volume of the ball of radius $r$. In vacuum spacetimes the leading term is of order $r^6$, and the factor of proportionality is the contraction of the Bel-Robinson tensor and an other average of the same approximate boost-rotation Killing vector.Comment: 16 pages, Plain Te

Classroom dialogue and digital technologies: A scoping review

AbstractThis article presents a systematic scoping review of the literature focusing on interactions between classroom dialogue and digital technology. The first review of its type in this area, it both maps extant research and, through a process of thematic synthesis, investigates the role of technology in supporting classroom dialogue. In total, 72 studies (published 2000–2016) are analysed to establish the characteristics of existing evidence and to identify themes. The central intention is to enable researchers and others to access an extensive base of studies, thematically analysed, when developing insights and interpretations in a rapidly changing field of study. The discussion illustrates the interconnectedness of key themes, placing the studies in a methodological and theoretical context and examining challenges for the future.</jats:p

Two dimensional Sen connections and quasi-local energy-momentum

The recently constructed two dimensional Sen connection is applied in the problem of quasi-local energy-momentum in general relativity. First it is shown that, because of one of the two 2 dimensional Sen--Witten identities, Penrose's quasi-local charge integral can be expressed as a Nester--Witten integral.Then, to find the appropriate spinor propagation laws to the Nester--Witten integral, all the possible first order linear differential operators that can be constructed only from the irreducible chiral parts of the Sen operator alone are determined and examined. It is only the holomorphy or anti-holomorphy operator that can define acceptable propagation laws. The 2 dimensional Sen connection thus naturally defines a quasi-local energy-momentum, which is precisely that of Dougan and Mason. Then provided the dominant energy condition holds and the 2-sphere S is convex we show that the next statements are equivalent: i. the quasi-local mass (energy-momentum) associated with S is zero; ii.the Cauchy development $D(\Sigma)$ is a pp-wave geometry with pure radiation ($D(\Sigma)$ is flat), where $\Sigma$ is a spacelike hypersurface whose boundary is S; iii. there exist a Sen--constant spinor field (two spinor fields) on S. Thus the pp-wave Cauchy developments can be characterized by the geometry of a two rather than a three dimensional submanifold.Comment: 20 pages, Plain Tex, I

Positive Mass Theorem for Black Holes in Einstein-Maxwell Axion-dilaton Gravity

We presented the proof of the positive mass theorem for black holes in Einstein-Maxwell axion-dilaton gravity being the low-energy limit of the heterotic string theory. We show that the total mass of a spacetime containing a black hole is greater or equal to the square root of the sum of squares of the adequate dilaton-electric and dilaton-axion charges.Comment: latex file, to appear in Classical Quantum Gravit

Two dimensional Sen connections in general relativity

The two dimensional version of the Sen connection for spinors and tensors on spacelike 2-surfaces is constructed. A complex metric $\gamma_{AB}$ on the spin spaces is found which characterizes both the algebraic and extrinsic geometrical properties of the 2-surface $\$$. The curvature of the two dimensional Sen operator $\Delta_e$ is the pull back to $\$$ of the anti-self-dual part of the spacetime curvature while its `torsion' is a boost gauge invariant expression of the extrinsic curvatures of $\$$. The difference of the 2 dimensional Sen and the induced spin connections is the anti-self-dual part of the `torsion'. The irreducible parts of $\Delta_e$ are shown to be the familiar 2-surface twistor and the Weyl--Sen--Witten operators. Two Sen--Witten type identities are derived, the first is an identity between the 2 dimensional twistor and the Weyl--Sen--Witten operators and the integrand of Penrose's charge integral, while the second contains the `torsion' as well. For spinor fields satisfying the 2-surface twistor equation the first reduces to Tod's formula for the kinematical twistor.Comment: 14 pages, Plain Tex, no report numbe

Quasi-local energy-momentum and two-surface characterization of the pp-wave spacetimes

In the present paper the determination of the {\it pp}-wave metric form the geometry of certain spacelike two-surfaces is considered. It has been shown that the vanishing of the Dougan--Mason quasi-local mass $m_{\$}$, associated with the smooth boundary $\$:=\partial\Sigma\approx S^2$ of a spacelike hypersurface $\Sigma$, is equivalent to the statement that the Cauchy development $D(\Sigma)$ is of a {\it pp}-wave type geometry with pure radiation, provided the ingoing null normals are not diverging on $\$$ and the dominant energy condition holds on $D(\Sigma)$. The metric on $D(\Sigma)$ itself, however, has not been determined. Here, assuming that the matter is a zero-rest-mass-field, it is shown that both the matter field and the {\it pp}-wave metric of $D(\Sigma)$ are completely determined by the value of the zero-rest-mass-field on $\$$ and the two dimensional Sen--geometry of $\$$ provided a convexity condition, slightly stronger than above, holds. Thus the {\it pp}-waves can be characterized not only by the usual Cauchy data on a {\it three} dimensional $\Sigma$ but by data on its {\it two} dimensional boundary $\$$ too. In addition, it is shown that the Ludvigsen--Vickers quasi-local angular momentum of axially symmetric {\it pp}-wave geometries has the familiar properties known for pure (matter) radiation.Comment: 15 pages, Plain Tex, no figure

Water Quality Management Studies for Water Resources Development in the Bear River Basin

Summary: The quality of water that develops in the proposed reservoirs of the Upper Bear River Storage Project will determine the possible uses of the water. Previous studies of water quality in the Bear River and its tributaries have reported water quality problems relating to nitrate ion, sanitary indicator bacteria, suspended solids, and phosphorus concentrations. Most point sources of water pollution inthe basin have been eliminated or improved in quality, but nonpoint sources of pollution continue to degrade the quality of the Bear River. Concentrations of phosphours have been sufficiently high to encourage dense algal growth and create eutrophic conditions in the proposed impoundments where other factors were not limiting. The present study intended to investigate these problems relative to the potential use of impounded water for municipal and industrial purposes. Past water quality information for the study area of the Bear River basin was reviewed including analysis of 208 areawide planning data and STORET data accumulated by the Utah Bureau of Water Pollution Control since 1977. Salinity components were found to be the major factors describing water quality in the Bear River, but nutrients and microbial pollution indicators were also very important. Nitrate concentrations were not found to have approached the 10 mg N*l^-1 standard in the historical data reviewed. Thirteen monthly water quality sampling and analyses were performed from 15 locations on the Bear River and its tributaries beginning above Oneida Reservoir, Idaho, and extending to the interstate highway bridge near Honeyville, Utah. These data indicate that the Cub River continues to be an important source of nutrients and microbiological pollution to the Bear River. The lower reaches of the Little Bear River occasionally accumulate undesirable concentrations of biochemical oxygen demand, nutrients, and fecal indicator bacteria. Increases in suspended solids and phosphorus loads in the Bear River and its tributaries were observed during spring snowmelt and runoff. Weston Creek, Fivemile Creek, and Deep Creek carried exceptionally high suspended solids and phosphorus loads during this time. A major increase in total phosphorus and orthophosphorus in the Bear River below the confluences of these streams was observed. Landsliding and erosion in the watersheds of these streams probably contribute substantially to their phosphorus and sediment loads. A water temperature model, empirical trophic state models, and a computerized reservoir eutrophical model (RESEN) were used to simulate the eutrophication potential of the proposed reservoirs. Since turbidity is expected to decrease over the length of the reservoirs allowing more light energy for photosynthesis, and since ample phosphorus will be available, the proposed Amalga Reservoir is likely to be eutrophic near the dam and in the Cub River branch. Similarly, the proposed Honeyville Reservoir is likely to be eutrophic near the dam and pools of anoxic water may develop below the thermocline. High populations of zooplankton could reduce summertime algal populations in the Honeyville Reservoir of mesotrophic to eutrophic conditions. Zooplankton grazing has been observed to substantially reduce algal populations in the existing Hyrum Reservoir on the Little Bear River. The proposed Lower Oneida Reservoir in Idaho will probably not thermally stratify, but will have a temperature regime similar to the existing Oneidea Reservoir and remain essentially completely mixed throughout the year. The depth of mixing of the water column is expected to limit algal grwoth and maintain this reservoir in an oligotrophic condition. The proposed Mill Creek and Avon Reservoirs on the Blacksmith Fork and Little Bear Rivers, respectively, will probably produce spring and fall algal blooms of mesotrophic to eutrophic proportions. Strong thermal stratification of these reservoirs in the late spring will isolate the epilimnion from phosphorus sources. Available phosphorus in the epilimnion will be exhausted through algal growth and settling, and phosphourus in the photic zone will not be replaced until destratification occurs in the fall. Reservoirs may remove phosphours from streams by trapping sediment and converting soluble phosphorus to algae or other plants that are retained in the reservoir. Lower phosphorus concentrations in the stream then result in less productive conditions in downstream reservoirs. The proposed upstream reservoirs on the Bear River or its tributaries are not expected to produce an appreciable improvement in downstream reservoirs, however. Phosphorus inputs from tributaries and nonpoint sources will probably negate phosphorus removal by these reservoirs. A study of chemical use by the Little Cottonwood water treatment plant revealed a general independence on raw water quality except for taste and odor. Assuming that water from the Honeyville Reservoir will receive conventional treatment and treatment with permanganate to control taste and odor in the same way as water is treated at the Little Cottonwood plant, treatment costs were estimated to be approximately $80 per acre ft. If trihalomethane compounds are formed from chlorination of the water, and concentrations exceed drinking water standards, treatment costs would increase by$6 to $190 per acre ft depending on the degree of removal required and the treatment method selected. If eutrophic cnoditions can be prevented from developing in the Honeyville Reservoir, concentrations of trihalomethane precursors produced by algal growth and decomposition would be expected to be low, and trihalomethane formation would not be expected to be a problem