1,528 research outputs found

    Corrections to the Central Limit Theorem for Heavy-Tailed Probability Densities

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    Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given by a standard Edgeworth expansion in the general case of regularly varying distributions with diverging moments (beyond the second). The subsequent terms can be expressed in a simple closed form in terms of certain special functions (Dawson's integral and parabolic cylinder functions), and there are qualitative differences depending on whether the number of moments available is even, odd or not an integer, and whether the distributions are symmetric or not. If the increments have an even number of moments, then additional logarithmic corrections must also be incorporated in the expansion parameter. An interesting feature of our correction terms for the CLT is that they become dominant outside the central region and blend naturally with known large-deviation asymptotics when these are applied formally to the spatial scales of the CLT

    Crackling Noise, Power Spectra and Disorder Induced Critical Scaling

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    Crackling noise is observed in many disordered non-equilibrium systems in response to slowly changing external conditions. Examples range from Barkhausen noise in magnets to acoustic emission in martensites to earthquakes. Using the non-equilibrium random field Ising model, we derive universal scaling predictions for the dependence of the associated power spectra on the disorder and field sweep rate, near an underlying disorder-induced non-equilibrium critical point. Our theory applies to certain systems in which the crackling noise results from avalanche-like response to a (slowly) increasing external driving force, and is characterized by a broad power law scaling regime of the power spectra. We compute the critical exponents and discuss the relevance of the results to experiments.Comment: 27 Latex Pages, 14 eps figure

    Who do we inform? The role of status and target in intergroup whistle-blowing

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    In two experiments (n = 87 and n = 90), we showed that strongly identifying members of a low status group are more likely to actively inform the ingroup rather than the outgroup about an outgroup transgression, and consider it as more loyal to the ingroup to do so. Moreover, strongly identifying members of a high status group are more likely to actively inform the outgroup rather than the ingroup about an outgroup transgression, and consider this to be more loyal to the ingroup. The results are in support of the notion that, depending on a group's existing status position, negative outgroup information can be used to enhance or confirm the ingroup's standing, affecting whether the ingroup or the outgroup will initially be informed about an outgroup transgression. Copyright © The Author(s), 2009

    Ion-beam-induced reconstruction of amorphous GaN

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    Wurtzite GaN can be rendered amorphous by high-dose heavy-ion bombardment. We show here that relatively low-dose reirradiation of such amorphous GaN (a-GaN) with MeV light ions can significantly change some of the physical properties of a-GaN. In particular, light-ion reirradiation of a-GaN results in (i) an increase in material density, (ii) the suppression of complete decomposition during postimplantation annealing, (iii) a significant increase in the values of hardness and Young's modulus, and (iv) an apparent decrease in the absorption of visible light. Transmission electronmicroscopy shows that a-GaN remains completely amorphous after light-ion reirradiation. Therefore, we attribute the above effects of light-ion reirradiation to an ion-beam-induced atomic-level reconstruction of the amorphous phase. Results indicate that electronic energy loss of light ions is responsible for the changes in the mechanical properties and for the suppression of thermally induced decomposition of a-GaN. However, the changes in the density of a-GaN appear to be controlled by the nuclear energy loss of light ions

    Interstellar MHD Turbulence and Star Formation

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    This chapter reviews the nature of turbulence in the Galactic interstellar medium (ISM) and its connections to the star formation (SF) process. The ISM is turbulent, magnetized, self-gravitating, and is subject to heating and cooling processes that control its thermodynamic behavior. The turbulence in the warm and hot ionized components of the ISM appears to be trans- or subsonic, and thus to behave nearly incompressibly. However, the neutral warm and cold components are highly compressible, as a consequence of both thermal instability in the atomic gas and of moderately-to-strongly supersonic motions in the roughly isothermal cold atomic and molecular components. Within this context, we discuss: i) the production and statistical distribution of turbulent density fluctuations in both isothermal and polytropic media; ii) the nature of the clumps produced by thermal instability, noting that, contrary to classical ideas, they in general accrete mass from their environment; iii) the density-magnetic field correlation (or lack thereof) in turbulent density fluctuations, as a consequence of the superposition of the different wave modes in the turbulent flow; iv) the evolution of the mass-to-magnetic flux ratio (MFR) in density fluctuations as they are built up by dynamic compressions; v) the formation of cold, dense clouds aided by thermal instability; vi) the expectation that star-forming molecular clouds are likely to be undergoing global gravitational contraction, rather than being near equilibrium, and vii) the regulation of the star formation rate (SFR) in such gravitationally contracting clouds by stellar feedback which, rather than keeping the clouds from collapsing, evaporates and diperses them while they collapse.Comment: 43 pages. Invited chapter for the book "Magnetic Fields in Diffuse Media", edited by Elisabete de Gouveia dal Pino and Alex Lazarian. Revised as per referee's recommendation

    Atomic X-ray Spectroscopy of Accreting Black Holes

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    Current astrophysical research suggests that the most persistently luminous objects in the Universe are powered by the flow of matter through accretion disks onto black holes. Accretion disk systems are observed to emit copious radiation across the electromagnetic spectrum, each energy band providing access to rather distinct regimes of physical conditions and geometric scale. X-ray emission probes the innermost regions of the accretion disk, where relativistic effects prevail. While this has been known for decades, it also has been acknowledged that inferring physical conditions in the relativistic regime from the behavior of the X-ray continuum is problematic and not satisfactorily constraining. With the discovery in the 1990s of iron X-ray lines bearing signatures of relativistic distortion came the hope that such emission would more firmly constrain models of disk accretion near black holes, as well as provide observational criteria by which to test general relativity in the strong field limit. Here we provide an introduction to this phenomenon. While the presentation is intended to be primarily tutorial in nature, we aim also to acquaint the reader with trends in current research. To achieve these ends, we present the basic applications of general relativity that pertain to X-ray spectroscopic observations of black hole accretion disk systems, focusing on the Schwarzschild and Kerr solutions to the Einstein field equations. To this we add treatments of the fundamental concepts associated with the theoretical and modeling aspects of accretion disks, as well as relevant topics from observational and theoretical X-ray spectroscopy.Comment: 63 pages, 21 figures, Einstein Centennial Review Article, Canadian Journal of Physics, in pres

    Heavy quarkonium: progress, puzzles, and opportunities

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    A golden age for heavy quarkonium physics dawned a decade ago, initiated by the confluence of exciting advances in quantum chromodynamics (QCD) and an explosion of related experimental activity. The early years of this period were chronicled in the Quarkonium Working Group (QWG) CERN Yellow Report (YR) in 2004, which presented a comprehensive review of the status of the field at that time and provided specific recommendations for further progress. However, the broad spectrum of subsequent breakthroughs, surprises, and continuing puzzles could only be partially anticipated. Since the release of the YR, the BESII program concluded only to give birth to BESIII; the BB-factories and CLEO-c flourished; quarkonium production and polarization measurements at HERA and the Tevatron matured; and heavy-ion collisions at RHIC have opened a window on the deconfinement regime. All these experiments leave legacies of quality, precision, and unsolved mysteries for quarkonium physics, and therefore beg for continuing investigations. The plethora of newly-found quarkonium-like states unleashed a flood of theoretical investigations into new forms of matter such as quark-gluon hybrids, mesonic molecules, and tetraquarks. Measurements of the spectroscopy, decays, production, and in-medium behavior of c\bar{c}, b\bar{b}, and b\bar{c} bound states have been shown to validate some theoretical approaches to QCD and highlight lack of quantitative success for others. The intriguing details of quarkonium suppression in heavy-ion collisions that have emerged from RHIC have elevated the importance of separating hot- and cold-nuclear-matter effects in quark-gluon plasma studies. This review systematically addresses all these matters and concludes by prioritizing directions for ongoing and future efforts.Comment: 182 pages, 112 figures. Editors: N. Brambilla, S. Eidelman, B. K. Heltsley, R. Vogt. Section Coordinators: G. T. Bodwin, E. Eichten, A. D. Frawley, A. B. Meyer, R. E. Mitchell, V. Papadimitriou, P. Petreczky, A. A. Petrov, P. Robbe, A. Vair

    Time-integrated luminosity recorded by the BABAR detector at the PEP-II e+e- collider

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    This article is the Preprint version of the final published artcile which can be accessed at the link below.We describe a measurement of the time-integrated luminosity of the data collected by the BABAR experiment at the PEP-II asymmetric-energy e+e- collider at the ϒ(4S), ϒ(3S), and ϒ(2S) resonances and in a continuum region below each resonance. We measure the time-integrated luminosity by counting e+e-→e+e- and (for the ϒ(4S) only) e+e-→Ό+ÎŒ- candidate events, allowing additional photons in the final state. We use data-corrected simulation to determine the cross-sections and reconstruction efficiencies for these processes, as well as the major backgrounds. Due to the large cross-sections of e+e-→e+e- and e+e-→Ό+ÎŒ-, the statistical uncertainties of the measurement are substantially smaller than the systematic uncertainties. The dominant systematic uncertainties are due to observed differences between data and simulation, as well as uncertainties on the cross-sections. For data collected on the ϒ(3S) and ϒ(2S) resonances, an additional uncertainty arises due to ϒ→e+e-X background. For data collected off the ϒ resonances, we estimate an additional uncertainty due to time dependent efficiency variations, which can affect the short off-resonance runs. The relative uncertainties on the luminosities of the on-resonance (off-resonance) samples are 0.43% (0.43%) for the ϒ(4S), 0.58% (0.72%) for the ϒ(3S), and 0.68% (0.88%) for the ϒ(2S).This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat Ă  l’Energie Atomique and Institut National de Physique NuclĂ©aire et de Physiquedes Particules (France), the Bundesministerium fĂŒr Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Ciencia e InnovaciĂłn (Spain), and the Science and Technology Facilities Council (United Kingdom). Individuals have received support from the Marie-Curie IEF program (European Union) and the A.P. Sloan Foundation (USA)
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