Spacetime perspective of Schwarzschild lensing

We propose a definition of an exact lens equation without reference to a background spacetime, and construct the exact lens equation explicitly in the case of Schwarzschild spacetime. For the Schwarzschild case, we give exact expressions for the angular-diameter distance to the sources as well as for the magnification factor and time of arrival of the images. We compare the exact lens equation with the standard lens equation, derived under the thin-lens-weak-field assumption (where the light rays are geodesics of the background with sharp bending in the lens plane, and the gravitational field is weak), and verify the fact that the standard weak-field thin-lens equation is inadequate at small impact parameter. We show that the second-order correction to the weak-field thin-lens equation is inaccurate as well. Finally, we compare the exact lens equation with the recently proposed strong-field thin-lens equation, obtained under the assumption of straight paths but without the small angle approximation, i.e., with allowed large bending angles. We show that the strong-field thin-lens equation is remarkably accurate, even for lightrays that take several turns around the lens before reaching the observer.Comment: 22 pages, 6 figures, to appear in Phys. Rev.

Thermodynamical Properties of a Rotating Ideal Bose Gas

In a recent experiment, a Bose-Einstein condensate was trapped in an anharmonic potential which is well approximated by a harmonic and a quartic part. The condensate was set into such a fast rotation that the centrifugal force in the corotating frame overcompensates the harmonic part in the plane perpendicular to the rotation axis. Thus, the resulting trap potential became Mexican-hat shaped. We present an analysis for an ideal Bose gas which is confined in such an anharmonic rotating trap within a semiclassical approximation where we calculate the critical temperature, the condensate fraction, and the heat capacity. In particular, we examine in detail how these thermodynamical quantities depend on the rotation frequency.Comment: Author Information under http://www.theo-phys.uni-essen.de/tp/ags/pelster_dir

Rossby waves in rapidly rotating Bose-Einstein condensates

We predict and describe a new collective mode in rotating Bose-Einstein condensates, which is very similar to the Rossby waves in geophysics. In the regime of fast rotation, the Coriolis force dominates the dynamics and acts as a restoring force for acoustic-drift waves along the condensate. We derive a nonlinear equation that includes the effects of both the zero-point pressure and the anharmonicity of the trap. It is shown that such waves have negative phase speed, propagating in the opposite sense of the rotation. We discuss different equilibrium configurations and compare with those resulting from the Thomas-Fermi approximation.Comment: 4 pages, 2 figures (submitted to PRL

Reduction of antimicrobial resistance as induced by Flavomycin

The demand for pork and poultry products is strongly influenced by the consumers concern for healthy and safe food The topic of food safety mainly concentrates on Salmonella contamination and is recently joined by the topic of antimicrobial resistance due to the use of antimicrobial growth promoters (AGP) in animal feed

Reducing effect of Flavomycin on Salmonella shedding and antibiotic resistance in pigs

The demand for food from pork origin is strongly influenced by consumers\u27 concern for healthy and safe food. The topic of food safety mainly concentrates on Salmonella contamination and is recently joined by the topic of antimicrobial resistance due to the use of antimicrobial growth promoters (AGMPs) in animal feed

Wide-field weak lensing by RXJ1347-1145

We present an analysis of weak lensing observations for RXJ1347-1145 over a 43' X 43' field taken in B and R filters on the Blanco 4m telescope at CTIO. RXJ1347-1145 is a massive cluster at redshift z=0.45. Using a population of galaxies with 20<R<26, we detect a weak lensing signal at the p<0.0005 level, finding best-fit parameters of \sigma_v=1400^{+130}_{-140} km s^{-1} for a singular isothermal sphere model and r_{200} = 3.5^{+0.8}_{-0.2} Mpc with c = 15^{+64}_{-10} for a NFW model in an \Omega_m = 0.3, \Omega_\Lambda = 0.7 cosmology. In addition, a mass to light ratio M/L_R =90 \pm 20 M_\odot / L_{R\odot} was determined. These values are consistent with the previous weak lensing study of RXJ1347--1145 by Fischer and Tyson, 1997, giving strong evidence that systemic bias was not introduced by the relatively small field of view in that study. Our best-fit parameter values are also consistent with recent X-ray studies by Allen et al, 2002 and Ettori et al, 2001, but are not consistent with recent optical velocity dispersion measurements by Cohen and Kneib, 2002.Comment: accepted to ApJ, tentative publication 10 May 2005, v624

Proof by analogy in mural

One of the most important advantages of using a formal method of developing software is that one can prove that development steps are correct with respect to their specification. Conducting proofs by hand, however,can be time consuming to the extent that designers have to judge whether a proof of a particular obligation is worth conducting. Even if hand proofs are worth conducting, how do we know that they are correct? One approach to overcoming this problem is to use an automatic theorem proving system to develop and check our proofs. However, in order to enable present day theorem provers to check proofs, one has to conduct them in much more detail than hand proofs. Carrying out more detailed proofs is of course more time consuming. This paper describes the use of proof by analogy in an attempt to reduce the time spent on proofs. We develop and implement a proof follower based on analogy and present two examples to illustrate its characteristics. One example illustrates the successful use of the proof follower. The other example illustrates that the follower's failure can provide a hint that enables the user to complete a proof

Attosecond control of electron dynamics in carbon monoxide

Laser pulses with stable electric field waveforms establish the opportunity to achieve coherent control on attosecond timescales. We present experimental and theoretical results on the steering of electronic motion in a multi-electron system. A very high degree of light-waveform control over the directional emission of C+ and O+ fragments from the dissociative ionization of CO was observed. Ab initio based model calculations reveal contributions to the control related to the ionization and laser-induced population transfer between excited electronic states of CO+ during dissociation

Null Cones in Schwarzschild Geometry

Light cones of Schwarzschild geometry are studied in connection to the Null Surface Formulation and gravitational lensing. The paper studies the light cone cut function's singularity structure, gives exact gravitational lensing equations, and shows that the "pseudo-Minkowski" coordinates are well defined within the model considered.Comment: 31 pages, 5 figure

Fermat Potentials for Non-Perturbative Gravitational Lensing

The images of many distant galaxies are displaced, distorted and often multiplied by the presence of foreground massive galaxies near the line of sight; the foreground galaxies act as gravitational lenses. Commonly, the lens equation, which relates the placement and distortion of the images to the real source position in the thin-lens scenario, is obtained by extremizing the time of arrival among all the null paths from the source to the observer (Fermat's principle). We show that the construction of envelopes of certain families of null surfaces consitutes an alternative variational principle or version of Fermat's principle that leads naturally to a lens equation in a generic spacetime with any given metric. We illustrate the construction by deriving the lens equation for static asymptotically flat thin lens spacetimes. As an application of the approach, we find the bending angle for moving thin lenses in terms of the bending angle for the same deflector at rest. Finally we apply this construction to cosmological spacetimes (FRW) by using the fact they are all conformally related to Minkowski space.Comment: accepted for publication in Phys. Rev.