Ariane 5 verification and associated test facilities

The philosophy of verification tests of the Ariane 5 launcher program is already established. It corresponds to the development and the ground and flight qualification phases for both unmanned and manned launches. The different types of test are outlined for the system, booster, main core and upper structures, allowing the identification of the associated test facilities which are described

Two and three electrons in a quantum dot: 1/|J| - expansion

We consider systems of two and three electrons in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the electron plane of motion. We show that the energy levels corresponding to states with high angular momentum, J, and a low number of vibrational quanta may be systematically computed as power series in 1/|J|. These states are relevant in the high-B limit.Comment: LaTeX, 15 pages,6 postscript figure

On the Jacobi-Metric Stability Criterion

We investigate the exact relation existing between the stability equation for the solutions of a mechanical system and the geodesic deviation equation of the associated geodesic problem in the Jacobi metric constructed via the Maupertuis-Jacobi Principle. We conclude that the dynamical and geometrical approaches to the stability/instability problem are not equivalent.Comment: 14 pages, no figure

Weighted random--geometric and random--rectangular graphs: Spectral and eigenfunction properties of the adjacency matrix

Within a random-matrix-theory approach, we use the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length $\ell$ to study spectral and eigenfunction properties (of adjacency matrices) of weighted random--geometric and random--rectangular graphs. A random--geometric graph (RGG) considers a set of vertices uniformly and independently distributed on the unit square, while for a random--rectangular graph (RRG) the embedding geometry is a rectangle. The RRG model depends on three parameters: The rectangle side lengths $a$ and $1/a$, the connection radius $r$, and the number of vertices $N$. We then study in detail the case $a=1$ which corresponds to weighted RGGs and explore weighted RRGs characterized by $a\sim 1$, i.e.~two-dimensional geometries, but also approach the limit of quasi-one-dimensional wires when $a\gg1$. In general we look for the scaling properties of $P(s)$ and $\ell$ as a function of $a$, $r$ and $N$. We find that the ratio $r/N^\gamma$, with $\gamma(a)\approx -1/2$, fixes the properties of both RGGs and RRGs. Moreover, when $a\ge 10$ we show that spectral and eigenfunction properties of weighted RRGs are universal for the fixed ratio $r/{\cal C}N^\gamma$, with ${\cal C}\approx a$.Comment: 8 pages, 6 figure

Advertising for attention in a consumer search model

We model the idea that when consumers search for products, they first visit the firm whose advertising is more salient. The gains a firm derives from being visited early increase in search costs, so equilibrium advertising increases as search costs rise. This may result in lower firm profits when search costs increase. We extend the basic model by allowing for firm heterogeneity in advertising costs. Firms whose advertising is more salient and therefore raise attention more easily charge lower prices in equilibrium and obtain higher profits. As advertising cost asymmetries increase, aggregate profits increase, advertising falls and welfare increases.Advertising; attention; consumer search; saliency;

Probing the geometry and motion of AGN coronae through accretion disc emissivity profiles

To gain a better understanding of the inner disc region that comprises active galactic nuclei it is necessary to understand the pattern in which the disc is illuminated (the emissivity profile) by X-rays emitted from the continuum source above the black hole (corona). The differences in the emissivity profiles produced by various corona geometries are explored via general relativistic ray tracing simulations. Through the analysis of various parameters of the geometries simulated it is found that emissivity profiles produced by point source and extended geometries such as cylindrical slabs and spheroidal coronae placed on the accretion disc are distinguishable. Profiles produced by point source and conical geometries are not significantly different, requiring an analysis of reflection fraction to differentiate the two geometries. Beamed point and beamed conical sources are also simulated in an effort to model jet-like coronae, though the differences here are most evident in the reflection fraction. For a point source we determine an approximation for the measured reflection fraction with the source height and velocity. Simulating spectra from the emissivity profiles produced by the various geometries produce distinguishable differences. Overall spectral differences between the geometries do not exceed 15 per cent in the most extreme cases. It is found that emissivity profiles can be useful in distinguishing point source and extended geometries given high quality spectral data of extreme, bright sources over long exposure times. In combination with reflection fraction, timing, and spectral analysis we may use emissivity profiles to discern the geometry of the X-ray source.Comment: 15 pages, 12 figures. Accepted for publication in MNRA