Model-independent characterisation of strong gravitational lenses

We develop a new approach to extracting model-independent information from observations of strong gravitational lenses. The approach is based on the generic properties of images near the fold and cusp catastrophes in caustics and critical curves. Observables used are the relative image positions, the magnification ratios and ellipticities of extended images, and time delays between images with temporally varying intensity. We show how these observables constrain derivatives and ratios of derivatives of the lensing potential near a critical curve. Based on these measured properties of the lensing potential, classes of parametric lens models can then easily be restricted to such parameter values compatible with the measurements, thus allowing fast scans of large varieties of models. Applying our approach to a representative galaxy (JVAS B1422+231) and a galaxy-cluster lens (MACS J1149.5+2223), we show which model-independent information can be extracted in those cases and demonstrate that the parameters obtained by our approach for known parametric lens models agree well with those found by detailed model fitting.Comment: 8 pages, 3 figures, submitted for publication to Astronomy & Astrophysic

Analysis of Turbulent Free Convection in a Rectangular Rayleigh-Benard Cell

The present study compares results of direct numerical simulations of thermal convection within a rectangular geometry with Rayleigh-Benard convection in thin fluid layers and cylindrical geometries. It is shown that boundary layer thicknesses show similar tendencies in the rectangular geometry and a thin fluid layer, but the quasi two-dimensional geometry of the container delays the onset of convection significantly. Analysis of the thermal dissipation rates indicates that there are three distinct regimes, of the small scale contribution grows rap-idly as Rayleigh number is increasing, whereas the large scale contribution remains almost constant

Transitions in the Stock Markets of the US, UK, and Germany

In an analysis of the US, the UK, and the German stock market we find a change in the behavior based on the stock's beta values. Before 2006 risky trades were concentrated on stocks in the IT and technology sector. Afterwards risky trading takes place for stocks from the financial sector. We show that an agent-based model can reproduce these changes. We further show that the initial impulse for the transition might stem from the increase of high frequency trading at that time

The Dynamics of Nutrition and Child Health Stocks

Height-for-age (HA) and weight-for-age (WA) of children are standard measures to study the determinants of stunting and short-term underweight. Rather than studying these indicators separately, this paper looks at their interaction and therefore at the dynamics of height and weight. Considering HA a child's health stock and WA nutritional investment, we develop an overlapping generations model. The main features of the model are self-productivity of health stocks and the dynamic complementarity between past health stocks and contemporaneous nutrition. We test the model's predictions on a Senegalese panel of 305 children between 0 and 5 years over three periods. To control for endogeneity and serial correlation we employ different GMM methods. We find evidence of self-productive health stocks and that child health produced at one stage raises the productivity of nutritional inputs at subsequent stages. Our results indicate that child health is quickly depleted and needs constant updating. Simulations based on our estimates show that a positive nutritional shock during the first six months of life is essentially depleted at the age of 2. Consequently, sustainable development and nutrition programs have to be long-term and yield higher returns if they reach babies in the early months of infancy.Child health, Health production, Height-for-Age, Weight-for-Age, Dynamic Panel Regression, GMM

[μ-3,3′-Bis(tri­hydro­bor­yl)[3]ferroceno­phane]bis­(chlorido­zirconocene)

The title compound, [FeZr2(C5H5)4Cl2(C13H18B2)], is a heteronuclear complex that consists of a [3]ferrocenophane moiety substituted at each cyclo­penta­dienyl (Cp) ring by a BH3 group; the BH3 group is bonded via two H atoms to the Zr atom of the zirconocene chloride moiety in a bidentate fashion. The two Cp rings of the [3]ferrocenophane moiety are aligned at a dihedral angle of 8.9 (4)° arising from the strain of the propane-1,3-diyl bridge linking the two Cp rings. [One methyl­ene group is disordered over two positions with a site-occupation factor of 0.552 (18) for the major occupied site.] The dihedral angles between the Cp rings at the two Zr atoms are 50.0 (3) and 51.7 (3)°. The bonding Zr(...)H distances are in the range 1.89 (7)–2.14 (7) Å. As the two Cp rings of the ferrocene unit are connected by an ansa bridge, the two Zr atoms approach each other at 6.485 (1) Å. The crystal packing features C—H(...)Cl inter­actions

Multivariate GARCH for a large number of stocks

The problems related to the application of multivariate GARCH models to a market with a large number of stocks are solved by restricting the form of the conditional covariance matrix. It contains one component describing the market and a second simple component to account for the remaining contribution to the volatility. This allows the analytical calculation of the inverse covariance matrix. We compare our model with the results of other GARCH models for the daily returns from the S&P500 market. The description of the covariance matrix turns out to be similar to the DCC model but has fewer free parameters and requires less computing time. As applications we use the daily values of beta coefficients available from the market component to confirm a transition of the market in 2006. Further we discuss properties of the leverage effect

Kurt Cobains Lithium-Song : Kurioses und Wissenswertes über die chemischen Elemente

Rezension zu: Ulf von Rauchhaupt: Die Ordnung der Stoffe: Ein Streifzug durch die Welt der chemischen Elemente. Frankfurt, Fischer Taschenbuch Verlag 2009, ISBN 3596185904 250 Seiten, 9,95 Eur