On measuring the Galactic dark matter halo with hypervelocity stars

Hypervelocity stars (HVSs) travel from the Galactic Centre across the dark matter halo of the Milky Way, where they are observed with velocities in excess of the Galactic escape speed. Because of their quasi-radial trajectories, they represent a unique probe of the still poorly constrained dark matter component of the Galactic potential. In this paper, we present a new method to produce such constraints. Our likelihood is based on the local HVS density obtained by back-propagating the observed phase space position and quantifies the ejection probability along the orbit. To showcase our method, we apply it to simulated Gaia samples of $\sim200$ stars in three realistic Galactic potentials with dark matter components parametrized by spheroidal NFW profiles. We find that individual HVSs exhibit a degeneracy in the scale mass-scale radius plane ($M_s-r_s$) and are able to measure only the combination $\alpha = M_s/r_s^2$. Likewise, a degeneracy is also present between $\alpha$ and the spheroidal axis-ratio $q$. In the absence of observational errors, we show the whole sample can nail down both parameters with {\it sub-per cent} precision (about $1\%$ and $0.1\%$ for $\alpha$ and $q$ respectively) with no systematic bias. This remarkable power to constrain deviations from a symmetric halo is a consequence of the Galactocentric origin of HVSs. To compare our results with other probes, we break the degeneracy in the scale parameters and impose a mass-concentration relation. The result is a competitive precision on the virial mass $M_{200}$ of about $10\%$.Comment: See Fig. 8 for a summar

Shape maps for second order partial differential equations

We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate evolution equation, akin to Raychaudhuri's equation. We develop the necessary geometric framework on a suitable jet space in which the shape maps appear naturally associated with certain linear connections. Explicit computations are given, along with a nontrivial example

Experimental and numerical studies of ferritic stainless steel tubular cross sections under combined compression and bending

An experimental and numerical study of ferritic stainless steel tubular cross sections under combined loading is presented in this paper. Two square hollow section (SHS) sizes—SHS 40×40×240×40×2 and SHS 50×50×250×50×2 made of Grade EN 1.4509 (AISI 441) stainless steel—were considered in the experimental program, which included 2 concentrically loaded stub column tests, 2 four-point bending tests, and 14 eccentrically loaded stub column tests. In parallel with the experimental investigation, a finite-element (FE) study was also conducted. Following validation of the FE models against the test results, parametric analyses were carried out to generate further structural performance data. The experimental and numerical results were analyzed and compared with the design strengths predicted by the current European stainless steel design code EN 1993-1-4 and American stainless steel design specification SEI/ASCE-8. The comparisons revealed that the codified capacity predictions for ferritic stainless steel cross sections under combined loading are unduly conservative. The deformation-based continuous strength method (CSM) has been extended to cover the case of combined loading. The applicability of CSM to the design of ferritic stainless steel cross sections under combined loading was also evaluated. The CSM was shown to offer substantial improvements in design efficiency over existing codified methods. Finally, the reliability of the proposals was confirmed by means of statistical analyses according to both the SEI/ASCE-8 requirements and those of EN 1990

Elucidating the NuclearQuantum Dynamics of Intramolecular Double Hydrogen Transfer in Porphycene

We address the double hydrogen transfer (DHT) dynamics of the porphycene molecule: A complex paradigmatic system where the making and breaking of H-bonds in a highly anharmonic potential energy surface requires a quantum mechanical treatment not only of the electrons, but also of the nuclei. We combine density-functional theory calculations, employing hybrid functionals and van der Waals corrections, with recently proposed and optimized path-integral ring-polymer methods for the approximation of quantum vibrational spectra and reaction rates. Our full-dimensional ring-polymer instanton simulations show that below 100 K the concerted DHT tunneling pathway dominates, but between 100 K and 300 K there is a competition between concerted and stepwise pathways when nuclear quantum effects are included. We obtain ground-state reaction rates of $2.19 \times 10^{11} \mathrm{s}^{-1}$ at 150 K and $0.63 \times 10^{11} \mathrm{s}^{-1}$ at 100 K, in good agreement with experiment. We also reproduce the puzzling N-H stretching band of porphycene with very good accuracy from thermostatted ring-polymer molecular dynamics simulations. The position and lineshape of this peak, centered at around 2600 cm$^{-1}$ and spanning 750 cm$^{-1}$, stems from a combination of very strong H-bonds, the coupling to low-frequency modes, and the access to $cis$-like isomeric conformations, which cannot be appropriately captured with classical-nuclei dynamics. These results verify the appropriateness of our general theoretical approach and provide a framework for a deeper physical understanding of hydrogen transfer dynamics in complex systems

Rethinking political violence, memory and law. Introduction

This article introduces the critical analysis of the links between political violence, law and memory that is discussed in the collection of articles that follows. The collection challenge common assumptions about political violence, unveil the processes, practices and discourses through which the Sovereign’s violence is legitimized and the demos’ violence is delegitimized, and let emerge the dynamic links between violence and law

Jet quenching and elliptic flow at RHIC and LHC within a pQCD-based partonic transport model

Fully dynamic simulations of heavy ion collisions at RHIC and at LHC energies within the perturbative QCD-based partonic transport model BAMPS (Boltzmann Approach to Multi-Parton Scatterings) are presented, focusing on the simultaneous investigation of jet quenching and elliptic flow. The model features inelastic 2 3 processes based on the Gunion-Bertsch matrix element and has recently been extended to include light quark degrees of freedom, allowing for direct comparison to hadronic data on the nuclear modification factor via a fragmentation scheme for high-pT partons. The nuclear modification factor of neutral pions in central Au+Au collisions at RHIC energy is compared to experimental data. Furthermore first results on the nuclear modification factor and the integrated elliptic flow of charged hadrons in Pb+Pb collisions at LHC are presented and compared to recent ALICE data. These investigations are complemented by a study on the suppression of D-mesons at LHC based on elastic interactions with the medium.Comment: To appear in the proceedings of Quark Matter 201

The Cost of Capital in Regulated Firms: The Argentine Experience

The sustainability of service is one of the fundamental aims of any regulatory system, and this tends to be reflected in the general principles within the legal framework of each public service. The necessity to cover economic costs of service then follows, in order to cover costs in such a way as to guarantee the maintaining and continuity of the system as well as its expansion. These economic costs should necessarily include sufficient retribution for the capital used by investors: the cost of capital. In the case of Argentine regulation, it is usual practice to use an adapted form of the CAPM (Capital Asset Pricing Model) to calculate the opportunity cost of equity, in such a way as to take the country risk into account. In this work we will analyse the components of the adapted formula for the cost of capital, discussing incentives which generate each of the possible outcomes for the regulated firms. Finally, we will present a model of dynamic optimisation for a regulated firm in a country such as Argentina.regulatory system; public service; CAPM; country risk

Predicting the hypervelocity star population in Gaia

Hypervelocity stars (HVSs) are amongst the fastest objects in our Milky Way. These stars are predicted to come from the Galactic center (GC) and travel along unbound orbits across the Galaxy. In the coming years, the ESA satellite Gaia will provide the most complete and accurate catalogue of the Milky Way, with full astrometric parameters for more than $1$ billion stars. In this paper, we present the expected sample size and properties (mass, magnitude, spatial, velocity distributions) of HVSs in the Gaia stellar catalogue. We build three Gaia mock catalogues of HVSs anchored to current observations, exploring different ejection mechanisms and GC stellar population properties. In all cases, we predict hundreds to thousands of HVSs with precise proper motion measurements within a few tens of kpc from us. For stars with a relative error in total proper motion below $10 \%$, the mass range extends to ~$10 M_{\odot}$ but peaks at ~$1$ $M_\odot$. The majority of Gaia HVSs will therefore probe a different mass and distance range compared to the current non-Gaia sample. In addition, a subset of a few hundreds to a few thousands of HVSs with $M$ ~ $3$ $M_\odot$ will be bright enough to have a precise measurement of the three-dimensional velocity from Gaia alone. Finally, we show that Gaia will provide more precise proper motion measurements for the current sample of HVS candidates. This will help identifying their birthplace narrowing down their ejection location, and confirming or rejecting their nature as HVSs. Overall, our forecasts are extremely encouraging in terms of quantity and quality of HVS data that can be exploited to constrain both the Milky Way potential and the GC properties.Comment: 17 pages, 18 figures, accepted for publication in MNRA