Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes

Quantum inequality restrictions on the stress-energy tensor for negative energy are developed for three and four-dimensional static spacetimes. We derive a general inequality in terms of a sum of mode functions which constrains the magnitude and duration of negative energy seen by an observer at rest in a static spacetime. This inequality is evaluated explicitly for a minimally coupled scalar field in three and four-dimensional static Robertson-Walker universes. In the limit of vanishing curvature, the flat spacetime inequalities are recovered. More generally, these inequalities contain the effects of spacetime curvature. In the limit of short sampling times, they take the flat space form plus subdominant curvature-dependent corrections.Comment: 18 pages, plain LATEX, with 3 figures, uses eps

The design of an automated verification of redundant systems

Handbook describes design processes, presents design considerations and techniques, gives tutorial material on implementation and methodology, shows design aids, illustrates use of design aids and application samples, and identifies general practices to be adhered to or avoided

Mental Health of Children and Young People in England, 2017: Trends and characteristics

This survey series provides England’s best source of data on trends in child mental health. Emotional, behavioural, hyperactivity, and other types of mental disorder were assessed in 5 to 15 year olds in 1999, 5 to 16 year olds in 2004, and 5 to 19 year olds in 2017. One in eight (12.8%) 5 to 19 year olds had a mental disorder when assessed in 2017. Rates were similar in boys and girls. Data for 5 to 15 year olds show a slight upward trend over time in the prevalence of emotional disorders.Rates for behavioural, hyperactivity and other disorders have remained broadly stable

The Binary Boron Trifluoride-Hydroxylamine Molecular Complex: N-Bound or O-Bound?

Boron trifluoride acts as a classical Lewis acid in forming molecular complexes with a variety of electron donors. Recent computational results on a number of complexes with some oxygen and nitrogen bases have indicated relationships between the properties of the adducts, such as the interaction energies and the wavenumber shifts of some of the modes of the boron trifluoride sub-molecule, and some physical properties of the bases. Hydroxylamine represents an example of a base containing two potential sites of electron donation, the nitrogen and the oxygen atoms. Predictions based on our earlier investigations of systems of this type suggest that hydroxylamine would bind to boron trifluoride preferentially through its nitrogen atom. Whether such a complex adopts an equilibrium structure in which the NO bond of hydroxylamine lies cis or trans to one of the BF bonds of boron trifluoride is more difficult to predict. This paper investigates the relative binding properties of N-bound versus O-bound complexes of boron trifluoride with hydroxylamine, and explores the conformational preferences and vibrational spectra of both types of adduct.Keywords: Ab initio calculations, molecular complexes, boron trifluoride, hydroxylamin

Particle production in the outflow of a midlatitude storm

The concentrations of atmospheric gases and condensation nuclei (CN) or aerosol in the outflow of a storm were measured aboard a NASA DC-8 aircraft, as described in a companion paper [Twohy et al., 2002]. The data are used here to study the production of the aerosol. Major fluctuations in CN concentration are observed, in correlation with gas-phase species, but these are shown to arise as the result of the mixing of two distinct air masses. It is deduced that the CN originated in a storm outflow air mass and that its concentration before mixing was approximately uniform over a flight distance of about 200 km. The formation of the aerosol by nucleation followed by growth and coagulation is analyzed assuming that it consists of water and sulphuric acid produced locally by the oxidation of SO2. The analysis uses analytic models, and it is concluded that a 5 min burst of nucleation was followed by growth and coagulation over a period of about 5 hours. Both the mass and number concentrations of the observed aerosol can be reproduced by this analysis within a timescale consistent with that of the storm. The final number concentration is very insensitive to the initial SO2 concentration

Cosmological and Black Hole Horizon Fluctuations

The quantum fluctuations of horizons in Robertson-Walker universes and in the Schwarzschild spacetime are discussed. The source of the metric fluctuations is taken to be quantum linear perturbations of the gravitational field. Lightcone fluctuations arise when the retarded Green's function for a massless field is averaged over these metric fluctuations. This averaging replaces the delta-function on the classical lightcone with a Gaussian function, the width of which is a measure of the scale of the lightcone fluctuations. Horizon fluctuations are taken to be measured in the frame of a geodesic observer falling through the horizon. In the case of an expanding universe, this is a comoving observer either entering or leaving the horizon of another observer. In the black hole case, we take this observer to be one who falls freely from rest at infinity. We find that cosmological horizon fluctuations are typically characterized by the Planck length. However, black hole horizon fluctuations in this model are much smaller than Planck dimensions for black holes whose mass exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations which are sufficiently small as not to invalidate the semiclassical derivation of the Hawking process.Comment: 22 pages, Latex, 4 figures, uses eps

Optimization of controlled environments for hydroponic production of leaf lettuce for human life support in CELSS

A research project in the food production group of the Closed Ecological Life Support System (CELSS) program sought to define optimum conditions for photosynthetic productivity of a higher plant food crop. The effects of radiation and various atmospheric compositions were studied

Quantum Field Theory Constrains Traversable Wormhole Geometries

Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable.Comment: 26 pages, plain LaTe

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page