Convex regions in the plane and their domes

We make a detailed study of the relation of a euclidean convex region $\Omega \subset \mathbb C$ to $\mathrm{Dome} (\Omega)$. The dome is the relative boundary, in the upper halfspace model of hyperbolic space, of the hyperbolic convex hull of the complement of $\Omega$. The first result is to prove that the nearest point retraction $r: \Omega \to \mathrm{Dome} (\Omega)$ is 2-quasiconformal. The second is to establish precise estimates of the distortion of $r$ near $\partial \Omega$

Factors Affecting the Corporate Decision-Making Process of Air Transport Manufacturers

Fuel economy is a pivotal question influencing the future sale and utilization of commercial aircraft. The NASA Aircraft Energy Efficiency (ACEE) Program Office has a program intended to accelerate the readiness of advanced technologies for energy efficient aircraft. Because the decision to develop a new airframe or engine is a major financial hazard for manufacturers, it is important to know what factors influence the decision making process. A method is described for identifying and ranking individuals and organizations involved at each stage of commercial air transport development, and the barriers that must be overcome in adopting new technologies

School violence, school differences and school discourses

This article highlights one strand of a study which investigated the concept of the violenceresilient school. In six inner-city secondary schools, data on violent incidents in school and violent crime in the neighbourhood were gathered, and compared with school practices to minimise violence, accessed through interviews. Some degree of association between the patterns of behaviour and school practices was found: schools with a wider range of wellconnected practices seemed to have less difficult behaviour. Interviews also showed that the different schools had different organisational discourses for construing school violence, its possible causes and the possible solutions. Differences in practices are best understood in connection with differences in these discourses. Some of the features of school discourses are outlined, including their range, their core metaphor and their silences. We suggest that organisational discourse is an important concept in explaining school effects and school differences, and that improvement attempts could have clearer regard to this concept

Thin front propagation in random shear flows

Front propagation in time dependent laminar flows is investigated in the limit of very fast reaction and very thin fronts, i.e. the so-called geometrical optics limit. In particular, we consider fronts evolving in time correlated random shear flows, modeled in terms of Ornstein-Uhlembeck processes. We show that the ratio between the time correlation of the flow and an intrinsic time scale of the reaction dynamics (the wrinkling time $t_w$) is crucial in determining both the front propagation speed and the front spatial patterns. The relevance of time correlation in realistic flows is briefly discussed in the light of the bending phenomenon, i.e. the decrease of propagation speed observed at high flow intensities.Comment: 5 Revtex4 pages, 4 figures include

Energy Density-Flux Correlations in an Unusual Quantum State and in the Vacuum

In this paper we consider the question of the degree to which negative and positive energy are intertwined. We examine in more detail a previously studied quantum state of the massless minimally coupled scalar field, which we call a ``Helfer state''. This is a state in which the energy density can be made arbitrarily negative over an arbitrarily large region of space, but only at one instant in time. In the Helfer state, the negative energy density is accompanied by rapidly time-varying energy fluxes. It is the latter feature which allows the quantum inequalities, bounds which restrict the magnitude and duration of negative energy, to hold for this class of states. An observer who initially passes through the negative energy region will quickly encounter fluxes of positive energy which subsequently enter the region. We examine in detail the correlation between the energy density and flux in the Helfer state in terms of their expectation values. We then study the correlation function between energy density and flux in the Minkowski vacuum state, for a massless minimally coupled scalar field in both two and four dimensions. In this latter analysis we examine correlation functions rather than expectation values. Remarkably, we see qualitatively similar behavior to that in the Helfer state. More specifically, an initial negative energy vacuum fluctuation in some region of space is correlated with a subsequent flux fluctuation of positive energy into the region. We speculate that the mechanism which ensures that the quantum inequalities hold in the Helfer state, as well as in other quantum states associated with negative energy, is, at least in some sense, already ``encoded'' in the fluctuations of the vacuum.Comment: 21 pages, 7 figures; published version with typos corrected and one added referenc