The local dayside reconnection rate for oblique interplanetary magnetic fields

We present an analysis of local properties of magnetic reconnection at the dayside magnetopause for various interplanetary magnetic field (IMF) orientations in global magnetospheric simulations. This has heretofore not been practical because it is difficult to locate where reconnection occurs for oblique IMF, but new techniques make this possible. The approach is to identify magnetic separators, the curves separating four regions of differing magnetic topology, which map the reconnection X-line. The electric field parallel to the X-line is the local reconnection rate. We compare results to a simple model of local two-dimensional asymmetric reconnection. To do so, we find the plasma parameters that locally drive reconnection in the magnetosheath and magnetosphere in planes perpendicular to the X-line at a large number of points along the X-line. The global magnetohydrodynamic simulations are from the three-dimensional Block-Adaptive, Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) code with a uniform resistivity, although the techniques described here are extensible to any global magnetospheric simulation model. We find that the predicted local reconnection rates scale well with the measured values for all simulations, being nearly exact for due southward IMF. However, the absolute predictions differ by an undetermined constant of proportionality, whose magnitude increases as the IMF clock angle changes from southward to northward. We also show similar scaling agreement in a simulation with oblique southward IMF and a dipole tilt. The present results will be an important component of a full understanding of the local and global properties of dayside reconnection.Comment: 12 pages, 7 figures, 1 table, Submitted to Journal Geophysical Research Space Physics February 12, 2016; Revised April 28, 201

An Analogue of the Kac-Wakimoto Formula and Black Hole Conditional Entropy

A local formula for the dimension of a superselection sector in Quantum Field Theory is obtained as vacuum expectation value of the exponential of the proper Hamiltonian. In the particular case of a chiral conformal theory, this provides a local analogue of a global formula obtained by Kac and Wakimoto within the context of representations of certain affine Lie algebras. Our formula is model independent and its version in general Quantum Field Theory applies to black hole thermodynamics. The relative free energy between two thermal equilibrium states associated with a black hole turns out to be proportional to the variation of the conditional entropy in different superselection sectors, where the conditional entropy is defined as the Connes-Stoermer entropy associated with the DHR localized endomorphism representing the sector. The constant of proportionality is half of the Hawking temperature. As a consequence the relative free energy is quantized proportionally to the logarithm of a rational number, in particular it is equal to a linear function the logarithm of an integer once the initial state or the final state is taken fixed.Comment: AMS-TeX v1.1c, minor grammatical correction

The Global Star Formation Rate from the 1.4 GHz Luminosity Function

The decimetric luminosity of many galaxies appears to be dominated by synchrotron emission excited by supernova explosions. Simple models suggest that the luminosity is directly proportional to the rate of supernova explosions of massive stars averaged over the past 30 Myr. The proportionality may be used together with models of the evolving 1.4 GHz luminosity function to estimate the global star formation rate density in the era z < 1. The local value is estimated to be 0.026 solar masses per year per cubic megaparsec, some 50% larger than the value inferred from the Halpha luminosity density. The value at z ~ 1 is found to be 0.30 solar masses per year per cubic megaparsec. The 10-fold increase in star formation rate density is consistent with the increase inferred from mm-wave, far-infrared, ultra-violet and Halpha observations.Comment: 10 pages, 2 figures, Astrophysical Journal Letters (in press); new PS version has improved figure placemen

Subsidiarity and Proportionality in the Single Market: An EU fit for inclusive growth

This report offers a fresh perspective on the principles of subsidiarity and proportionality in the European Union based on a thorough-going economic analysis. Specifically, the report uses the EU Single Market as a case to discuss shortcomings and potential improvements in five key policy areas. It reviews how the principles of subsid- iarity and proportionality can help boost growth in the EU at the aggregate country level – while at the same time allowing EU regions to benefit from growth. The report focuses on the regional level as economic growth has been uneven across the EU’s regions over the last decade and, consequently, growing disparities between re- gions have emerged. This alone merits a review on how we can reconcile the twin objectives in the future

Local meanings of proportionality : judicial review in France, England and Greece

Defence date: 19 September 2018Examining Board: Prof. Bruno De Witte, Maastricht University/EUI (Supervisor); Prof. Loïc Azoulai, Sciences Po Paris; Associate Prof. Jacco Bomhoff, LSE; Prof. Guillaume Tusseau, Science Po ParisThe author was awarded the Mauro Cappelletti Prize for the best doctoral thesis in the field of comparative law (June 2019)Proportionality increasingly dominates legal imagination. Initially conceived of as a principle that regulates police action, today it is progressively established as an advanced tool of liberal constitutional science. Its spread, accompanied by a global paradigm of constitutional rights, appears to be an irresistible natural development. This thesis was inspired by the intuition that even though courts and lawyers around the world reason more and more in proportionality terms, proportionality can mean very different things in different contexts, even within the same legal system. While the relevant literature has paid little attention to differences in the use of proportionality, identifying the local meanings of proportionality is crucial to making sense of its spread, to assessing its success, and to appraising the possibility of convergence between legal systems. Through an in-depth study and comparison of the use of proportionality by legal actors in France, England and Greece, this work shows that the local meanings of proportionality are not simply deviant applications of a global model. Instead, they reflect the legal cultures in which they evolve, local paths of cultural change and local patterns of Europeanisation. La proportionnalité a progressivement pris une place centrale dans l’imaginaire juridique. Initialement conçue comme un principe qui régit l’utilisation des pouvoirs de police, elle est aujourd’hui considérée comme un outil avancé de science constitutionnelle. Sa généralisation, accompagnée par le paradigme du droit constitutionnel global, est perçue comme irrésistible et naturelle. Cette recherche a été guidée par l’intuition que, même si les juristes à travers le monde raisonnent de plus en plus en termes de proportionnalité, celle-ci peut avoir des sens très différents, et ce, même au sein d’un seul système juridique. Les différentes utilisations du langage de la proportionnalité sont rarement étudiées en tant que tels. Pour autant, l’identification des sens locaux de la proportionnalité est cruciale si l’on veut comprendre sa propagation, apprécier son succès et évaluer les possibilités de convergence entre systèmes juridiques. Ce travail consiste en une étude approfondie et comparative de l’utilisation du langage de la proportionnalité parmi les acteurs juridiques en France, en Angleterre et en Grèce. Il cherche à montrer que les sens locaux de la proportionnalité ne sont pas simplement des applications imparfaites d’un modèle global. Au contraire, ils reflètent les cultures au sein desquelles ils évoluent, des chemins d’évolution culturelle propres à chaque système et des trajectoires locales d’européanisation

On Asymptotic Global Error Estimation and Control of Finite Difference Solutions for Semilinear Parabolic Equations

The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of semilinear parabolic partial differential equations. The approach presented there is combined with an estimation of the PDE spatial truncation error by Richardson extrapolation to estimate the overall error in the computed solution. Approximations of the error transport equations for spatial and temporal global errors are derived by using asymptotic estimates that neglect higher order error terms for sufficiently small step sizes in space and time. Asymptotic control in a discrete $L_2$-norm is achieved through tolerance proportionality and uniform or adaptive mesh refinement. Numerical examples are used to illustrate the reliability of the estimation and control strategies

American Equal Protection and Global Convergence

Commentators have noted that equal protection doctrine is in a state of transformation. The nature of that transformation, however, is poorly understood. This Article offers a clearer view of the change underway. This Article is the first to reveal and synthesize three major trajectories along which the U.S. Supreme Court has begun to move. First, the Court has begun to blur the line that it previously drew between facial discrimination and disparate impact. Second, the Court has begun to collapse its previously established tiered standards for reviewing discrimination. These two trajectories combine to produce a third trajectory of change: by blurring the distinction between facial discrimination and disparate impact, and by collapsing tiered review, the United States’ equal protection doctrine is converging with equality jurisprudence from peer jurisdictions abroad. After describing these changes, we argue that the collective wisdom of foreign jurisdictions should serve as persuasive authority encouraging the United States to continue along its current trajectories of doctrinal reform. We contend that foreign jurisdictions have served as laboratories of doctrinal innovation from which the United States could learn