Random Aharonov-Bohm vortices and some funny families of integrals

A review of the random magnetic impurity model, introduced in the context of the integer Quantum Hall effect, is presented. It models an electron moving in a plane and coupled to random Aharonov-Bohm vortices carrying a fraction of the quantum of flux. Recent results on its perturbative expansion are given. In particular, some funny families of integrals show up to be related to the Riemann $\zeta(3)$ and $\zeta(2)$.Comment: 10 page

Witnessing the Growth of the Nearest Galaxy Cluster: Thermodynamics of the Virgo Cluster Outskirts

We present results from Suzaku Key Project observations of the Virgo Cluster, the nearest galaxy cluster to us, mapping its X-ray properties along four long `arms' extending beyond the virial radius. The entropy profiles along all four azimuths increase with radius, then level out beyond $0.5r_{200}$, while the average pressure at large radii exceeds Planck Sunyaev-Zel'dovich measurements. These results can be explained by enhanced gas density fluctuations (clumping) in the cluster's outskirts. Using a standard Navarro, Frenk and White (1997) model, we estimate a virial mass, radius, and concentration parameter of $M_{200}=1.05\pm0.02\times10^{14}$ M$_\odot$, $r_{200}=974.1\pm5.7$ kpc, and $c = 8.8 \pm0.2$, respectively. The inferred cumulative baryon fraction exceeds the cosmic mean at $r\sim r_{200}$ along the major axis, suggesting enhanced gas clumping possibly sourced by a candidate large-scale structure filament along the north-south direction. The Suzaku data reveal a large-scale sloshing pattern, with two new cold fronts detected at radii of 233 kpc and 280 kpc along the western and southern arms, respectively. Two high-temperature regions are also identified 1 Mpc towards the south and 605 kpc towards the west of M87, likely representing shocks associated with the ongoing cluster growth. Although systematic uncertainties in measuring the metallicity for low temperature plasma remain, the data at large radii appear consistent with a uniform metal distribution on scales of $\sim 90\times180$ kpc and larger, providing additional support for the early chemical enrichment scenario driven by galactic winds at redshifts of 2-3.Comment: submitted to MNRA

A uniform metallicity in the outskirts of massive, nearby galaxy clusters

Suzaku measurements of a homogeneous metal distribution of $Z\sim0.3$ Solar in the outskirts of the nearby Perseus cluster suggest that chemical elements were deposited and mixed into the intergalactic medium before clusters formed, likely over 10 billion years ago. A key prediction of this early enrichment scenario is that the intracluster medium in all massive clusters should be uniformly enriched to a similar level. Here, we confirm this prediction by determining the iron abundances in the outskirts ($r>0.25r_{200}$) of a sample of ten other nearby galaxy clusters observed with Suzaku for which robust measurements based on the Fe-K lines can be made. Across our sample the iron abundances are consistent with a constant value, $Z_{\rm Fe}=0.316\pm0.012$ Solar ($\chi^2=28.85$ for 25 degrees of freedom). This is remarkably similar to the measurements for the Perseus cluster of $Z_{\rm Fe}=0.314\pm0.012$ Solar, using the Solar abundance scale of Asplund et al. (2009).Comment: accepted for publication in MNRA

On separability of quantum states and the violation of Bell-type inequalities

In contrast to the wide-spread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where a separable quantum state does not satisfy the original Bell inequality although the latter inequality, in its perfect correlation form, is valid for all joint classical measurements. In a very general setting, we discuss inequalities for joint experiments upon a bipartite quantum system in a separable state. We derive quantum analogues of the original Bell inequality and specify the conditions sufficient for a separable state to satisfy the original Bell inequality. We introduce the extended CHSH inequality and prove that, for any separable quantum state, this inequality holds for a variety of linear combinations.Comment: 13 pages, extended versio

Chemical Treatment Methods Pilot (CTMP) System for Treatment of Urban Runoff – Phase I. Feasibility and Design

(pdf contains 418 pages

The X-ray coronae of the two brightest galaxies in the Coma cluster

We use deep Chandra X-ray Observatory observations to examine the coronae of the two brightest cluster galaxies in the Coma cluster of galaxies, NGC 4874 and NGC 4889. We find that NGC 4889 hosts a central depression in X-ray surface brightness consistent with a cavity or pair of cavities of radius 0.6 kpc. If the central cavity is associated with an AGN outburst and contains relativistic material, its enthalpy should be around 5x10^55 erg. The implied heating power of this cavity would be around an order of magnitude larger than the energy lost by X-ray emission. It would be the smallest and youngest known cavity in a brightest cluster galaxy and the lack of over pressuring implies heating is still gentle. In contrast, NGC 4874 does not show any evidence for cavities, although it hosts a well-known wide-angle-tail radio source which is visible outside the region occupied by the X-ray corona. These two galaxies show that AGN feedback can behave in varied ways in the same cluster environment.Comment: 11 pages, 11 figures, accepted by MNRA

Best practice in license allocation in the oil and gas industry: a review of five countries

The implementation of good practice in the natural resource management processes is crucial to the economic development of many countries. Well managed resources can bring high financial rewards and benefit the entire country, while poor resource management can lead to severe social and economic consequences. The allocation of licenses for the exploration and development of the natural resources is of particular importance in establishing good management and ensuring the accrual of benefits to the country. In this paper we identify an analytic framework for establishing the most suitable license allocation approach in any context, and apply this to five case studies. From this application we draw conclusions regarding best practice and identify the policy implications of this discussion