Comment on "Relativistic Effects of Light in Moving Media with Extremely Low Group Velocity"

In [cond-mat/9906332; Phys. Rev. Lett. 84, 822 (2000)] and [physics/9906038; Phys. Rev. A 60, 4301 (1999)] Leonhardt and Piwnicki have presented an interesting analysis of how to use a flowing dielectric fluid to generate a so-called "optical black hole". Qualitatively similar phenomena using acoustical processes have also been much investigated. Unfortunately there is a subtle misinterpretation in the Leonhardt-Piwnicki analysis regarding these "optical black holes": While it is clear that "optical black holes" can certainly exist as theoretical constructs, and while the experimental prospects for actually building them in the laboratory are excellent, the particular model geometries that Leonhardt and Piwnicki write down as alleged examples of "optical black holes" are in fact not black holes at all.Comment: one page comment, uses ReV_TeX 3; discussion clarified; basic physical results unaltere

Hexagon functions and the three-loop remainder function

We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar N=4 super-Yang-Mills theory, as a function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of "hexagon functions" which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined previously. The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematics limits, including the near-collinear and multi-Regge limits. These limits allow us to impose constraints from the operator product expansion and multi-Regge factorization directly at the function level, and thereby to fix uniquely a set of Riemann-zeta-valued constants that could not be fixed at the level of the symbol. The near-collinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability. The multi-Regge limits agree with the factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one. For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to -7.Comment: 103 pages, 12 figures, 9 ancillary files. v2: typos corrected, references adde

Regulating Systemic Risk: Towards an Analytical Framework

The global financial crisis demonstrated the inability and unwillingness of financial market participants to safeguard the stability of the financial system. It also highlighted the enormous direct and indirect costs of addressing systemic crises after they have occurred, as opposed to attempting to prevent them from arising. Governments and international organizations are responding with measures intended to make the financial system more resilient to economic shocks, many of which will be implemented by regulatory bodies over time. These measures suffer, however, from the lack of a theoretical account of how systemic risk propagates within the financial system and why regulatory intervention is needed to disrupt it. In this Article, we address this deficiency by examining how systemic risk is transmitted. We then proceed to explain why, in the absence of regulation, market participants cannot be relied upon to disrupt or otherwise limit the transmission of systemic risk. Finally, we advance an analytical framework to inform systemic risk regulation

An extended scheme for fitting X-ray data with accretion disk spectra in the strong gravity regime

Accreting black holes are believed to emit X-rays which then mediate information about strong gravity in the vicinity of the emission region. We report on a set of new routines for the Xspec package for analysing X-ray spectra of black-hole accretion disks. The new computational tool significantly extends the capabilities of the currently available fitting procedures that include the effects of strong gravity, and allows one to systematically explore the constraints on more model parameters than previously possible (for example black-hole angular momentum). Moreover, axial symmetry of the disk intrinsic emissivity is not assumed, although it can be imposed to speed up the computations. The new routines can be used also as a stand-alone and flexible code with the capability of handling time-resolved spectra in the regime of strong gravity. We have used the new code to analyse the mean X-ray spectrum from the long XMM--Newton 2001 campaign of the Seyfert 1 galaxy MCG--6-30-15. Consistent with previous findings, we obtained a good fit to the broad Fe K line profile for a radial line intrinsic emissivity law in the disk which is not a simple power law, and for near maximal value of black hole angular momentum. However, equally good fits can be obtained also for small values of the black hole angular momentum. The code has been developed with the aim of allowing precise modelling of relativistic effects. Although we find that current data cannot constrain the parameters of black-hole/accretion disk system well, the approach allows, for a given source or situation, detailed investigations of what features of the data future studies should be focused on in order to achieve the goal of uniquely isolating the parameters of such systems.Comment: Accepted for publication in ApJ S

Hard X-ray emission from the galaxy cluster A2256

After the positive detection by BeppoSAX of hard X-ray radiation up to ~80 keV in the Coma cluster spectrum, we present evidence for nonthermal emission from A2256 in excess of thermal emission at a 4.6sigma confidence level. In addition to this power law component, a second nonthermal component already detected by ASCA could be present in the X-ray spectrum of the cluster, not surprisingly given the complex radio morphology of the cluster central region. The spectral index of the hard tail detected by the PDS onboard BeppoSAX is marginally consistent with that expected by the inverse Compton model. A value of ~0.05 microG is derived for the intracluster magnetic field of the extended radio emission in the northern regions of the cluster, while a higher value of \~0.5 microG could be present in the central radio halo, likely related to the hard tail detected by ASCA.Comment: 10 pages, 2 figures. To appear in ApJ

The profile of an emission line from relativistic outflows around a black hole

Recent observations show strong evidence for the presence of Doppler-shifted emission lines in the spectrum of both black hole candidates and active galactic nuclei. These lines are likely to originate from relativistic outflows (or jets) in the vicinity of the central black hole. Consequently, the profile of such a line should be distorted by strong gravitational effects near the black hole, as well as special relativistic effects. In this paper, we present results from a detailed study on how each process affects the observed line profile. We found that the profile is sensitive to the intrinsic properties of the jets (Lorentz factor, velocity profile, and emissivity law), as well as to the spin of the black hole and the viewing angle (with respect to the axis of the jets). More specifically, in the case of approaching jets, an intrisically narrow line (blue-shifted) is seen as simply broadened at small viewing angles, but it shows a doubly peaked profile at large viewing angles for extreme Kerr black holes (due to the combination of gravitational focusing and Doppler effects); the profile is always singly peaked for Schwarzschild black holes. For receding jets, however, the line profile becomes quite complicated owing to complicated photon trajectories. To facilitate comparison with observations, we searched a large parameter space to derive representative line profiles. We show the results and discuss how to use emission lines as a potential tool for probing the inner region of a black hole jet system.Comment: 16 pages in emulateapj style, 11 figure

Analysis of Dialogical Argumentation via Finite State Machines

Dialogical argumentation is an important cognitive activity by which agents exchange arguments and counterarguments as part of some process such as discussion, debate, persuasion and negotiation. Whilst numerous formal systems have been proposed, there is a lack of frameworks for implementing and evaluating these proposals. First-order executable logic has been proposed as a general framework for specifying and analysing dialogical argumentation. In this paper, we investigate how we can implement systems for dialogical argumentation using propositional executable logic. Our approach is to present and evaluate an algorithm that generates a finite state machine that reflects a propositional executable logic specification for a dialogical argumentation together with an initial state. We also consider how the finite state machines can be analysed, with the minimax strategy being used as an illustration of the kinds of empirical analysis that can be undertaken.Comment: 10 page

Component-based records: a novel method to record transaction design work

The growing pressures from global competitive markets signal the inevitable challenge for companies to rapidly design and develop new successful products. To continually improve design quality and efficiency, companies must consider how to speed design processes, minimise human-errors, avoid unnecessary iterations, and sustain knowledge embedded in the design process. All of these issues strongly concern one topic: how to make and exploit records of design activities. Using process modelling ideas, this paper introduces a new method called component-based records, in place of traditional design reports. The proposed method records transaction elements of the actual design processes undertaken in a design episode, which aims to continually improve design quality and efficiency, reduce designers’ workload for routine tasks, and sustain competitiveness of companies

Gravitational vacuum polarization III: Energy conditions in the (1+1) Schwarzschild spacetime

Building on a pair of earlier papers, I investigate the various point-wise and averaged energy conditions for the quantum stress-energy tensor corresponding to a conformally-coupled massless scalar field in the in the (1+1)-dimensional Schwarzschild spacetime. Because the stress-energy tensors are analytically known, I can get exact results for the Hartle--Hawking, Boulware, and Unruh vacua. This exactly solvable model serves as a useful sanity check on my (3+1)-dimensional investigations wherein I had to resort to a mixture of analytic approximations and numerical techniques. Key results in (1+1) dimensions are: (1) NEC is satisfied outside the event horizon for the Hartle--Hawking vacuum, and violated for the Boulware and Unruh vacua. (2) DEC is violated everywhere in the spacetime (for any quantum state, not just the standard vacuum states).Comment: 7 pages, ReV_Te