Zonal shear and super-rotation in a magnetized spherical Couette flow experiment

We present measurements performed in a spherical shell filled with liquid sodium, where a 74 mm-radius inner sphere is rotated while a 210 mm-radius outer sphere is at rest. The inner sphere holds a dipolar magnetic field and acts as a magnetic propeller when rotated. In this experimental set-up called DTS, direct measurements of the velocity are performed by ultrasonic Doppler velocimetry. Differences in electric potential and the induced magnetic field are also measured to characterize the magnetohydrodynamic flow. Rotation frequencies of the inner sphere are varied between -30 Hz and +30 Hz, the magnetic Reynolds number based on measured sodium velocities and on the shell radius reaching to about 33. We have investigated the mean axisymmetric part of the flow, which consists of differential rotation. Strong super-rotation of the fluid with respect to the rotating inner sphere is directly measured. It is found that the organization of the mean flow does not change much throughout the entire range of parameters covered by our experiment. The direct measurements of zonal velocity give a nice illustration of Ferraro's law of isorotation in the vicinity of the inner sphere where magnetic forces dominate inertial ones. The transition from a Ferraro regime in the interior to a geostrophic regime, where inertial forces predominate, in the outer regions has been well documented. It takes place where the local Elsasser number is about 1. A quantitative agreement with non-linear numerical simulations is obtained when keeping the same Elsasser number. The experiments also reveal a region that violates Ferraro's law just above the inner sphere.Comment: Phys Rev E, in pres

X-ray and Radio Interactions in the Cores of Cooling Flow Clusters

We present high resolution ROSAT x-ray and radio observations of three cooling flow clusters containing steep spectrum radio sources at their cores. All three systems exhibit strong signs of interaction between the radio plasma and the hot intracluster medium. Two clusters, A133 and A2626, show enhanced x-ray emission spatially coincident with the radio source whereas the third cluster, A2052, exhibits a large region of x-ray excess surrounding much of the radio source. Using 3-D numerical simulations, we show that a perturbed jet propagating through a cooling flow atmosphere can give rise to amorphous radio morphologies, particularly in the case where the jet was ``turned off'' and allowed to age passively. In addition, the simulated x-ray surface brightness produced both excesses and deficits as seen observationally.Comment: 25 pages, 10 figures, accepted for publication in A

Divergent mathematical treatments in utility theory

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper

Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem for the natural diagonal (almost) para-K\"ahlerian structures on the total spaces of the cotangent bundle.Comment: 10 pages, will appear in Czechoslovak Mathematical Journa

An ISOCAM survey through gravitationally lensing galaxy clusters. III. New results from mid-infrared observations of th e cluster Abell 2219

The massive cluster of galaxies Abell 2219 (z = 0.228) was observed at 14.3 $\mu$m with the Infrared Space Observatory and results were published by Barvainis et al. (1999). These observations have been reanalyzed using a method specifically designed for the detection of faint sources that had been applied to other clusters. Five new sources were detected and the resulting cumulative total of ten sources all have optical counterparts. The mid-infrared sources are identified with three cluster members, three foreground galaxies, an Extremely Red Object, a star and two galaxies of unknown redshift. The spectral energy distributions (SEDs) of the galaxies are fit with models from a selection, using the program GRASIL. Best-fits are obtained, in general, with models of galaxies with ongoing star formation. For three cluster members the infrared luminosities derived from the model SEDs are between ~5.7x10^10 Lsun and 1.4x10^11 Lsun, corresponding to infrared star formation rates between 10 and 24 Msun yr^-1. The two cluster galaxies that have optical classifications are in the Butcher-Oemler region of the color-magnitude diagramme. The three foreground galaxies have infrared luminosities between 1.5x10^10 Lsun and 9.4x10^10 Lsun yielding infrared star formation rates between 3 and 16 Msun yr^-1. Two of the foreground galaxies are located in two foreground galaxy enhancements (Boschin et al. 2004). Including Abell 2219, six distant clusters of galaxies have been mapped with ISOCAM and luminous infrared galaxies (LIRGs) have been found in three of them. The presence of LIRGs in Abell 2219 strengthens the association between luminous infrared galaxies in clusters and recent or ongoing cluster merger activity.Comment: 8 pages, 4 figures, A&A accepted, full paper with high-resolution figures available at http://bermuda.ucd.ie/~dcoia/papers/. Reference adde

Radio loud AGN and the L_X - \sigma relation of galaxy groups and clusters

We use the ROSAT All-Sky Survey to study the X-ray properties of a sample of 625 groups and clusters of galaxies selected from the Sloan Digital Sky Survey. We stack clusters with similar velocity dispersions and investigate whether their average X-ray luminosities and surface brightness profiles vary with the radio activity level of their central galaxies. We find that at a given value of $\sigma$, clusters with a central radio AGN have more concentrated X-ray surface brightness profiles, larger central galaxy masses, and higher X-ray luminosities than clusters with radio-quiet central galaxies. The enhancement in X-ray luminosity is more than a factor of two, is detected with better than 6$\sigma$ significance, and cannot be explained by X-ray emission from the radio AGN itself. This difference is largely due to a subpopulation of radio-quiet, high velocity dispersion clusters with low mass central galaxies. These clusters are underluminous at X-ray wavelengths when compared to otherwise similar clusters where the central galaxy is radio-loud, more massive, or both.Comment: Section 5.2 is updated, more discussion on the dependence of L_X - \sigma relation on the stellar mass of BCG

Introduction to special issue: Aesthetics in mathematics

Mathematicians often appreciate the beauty and elegance of particular theorems, proofs, and definitions, attaching importance not only to the truth but also to the aesthetic merit of their work. As Henri Poincaré [1930, p. 59] put it, mathematical beauty is a ‘real aesthetic feeling that all true mathematicians recognise’. Others went further, regarding mathematical beauty as a key motivation driving the formulation of mathematical proofs and even as a criterion for choosing one proof over another. As Hermann Weyl famously and provocatively declared, ‘My work always tried to unite the true with the beautiful, but when I had to choose one or the other, I usually chose the beautiful’ (cited [Chandrasekhar, 1987, p. 52])....Talk of the beauty of mathematical theorems, proofs, and definitions may thus be commonplace