Leibniz algebra deformations of a Lie algebra

In this note we compute Leibniz algebra deformations of the 3-dimensional nilpotent Lie algebra $\mathfrak{n}_3$ and compare it with its Lie deformations. It turns out that there are 3 extra Leibniz deformations. We also describe the versal Leibniz deformation of $\mathfrak{n}_3$ with the versal base.Comment: 15 page

Controlling the crystal polymorph by exploiting the time dependence of nucleation rates

Most substances can crystallise into two or more different crystal lattices, called polymorphs. Despite this, there are no systems in which we can quantitatively predict the probability of one competing polymorph forming, instead of the other. We address this problem using large scale (hundreds of events) studies of the competing nucleation of the alpha and gamma polymorphs of glycine. In situ Raman spectroscopy is used to identify the polymorph of each crystal. We find that the nucleation kinetics of the two polymorphs is very different. Nucleation of the alpha polymorph starts off slowly but accelerates, while nucleation of the gamma polymorph starts off fast but then slows. We exploit this difference to increase the purity with which we obtain the gamma polymorph by a factor of ten. The statistics of the nucleation of crystals is analogous to that of human mortality, and using a result from medical statistics we show that conventional nucleation data can say nothing about what, if any, are the correlations between competing nucleation processes. Thus we can show that, with data of our form, it is impossible to disentangle the competing nucleation processes. We also find that the growth rate and the shape of a crystal depends on when it nucleated. This is new evidence that nucleation and growth are linked.Comment: 8 pages, plus 17 pages of supplementary materia

Population Synthesis of Radio and Gamma-ray Pulsars in the Fermi Era

We present results of our pulsar population synthesis of normal pulsars from the Galactic disk using our previously developed computer code. On the same footing, we use slot gap and outer gap models for gamma-ray emission from normal pulsars to obtain statistics of radio-loud and radio-quiet gamma-ray pulsars. From recently improved understanding of HII and star forming regions in the Galaxy, we develop a new surface density model of the birth location of neutron stars. We explore models of neutron star evolution with magnetic field-decay, and with different initial period and magnetic field distributions. We present preliminary results including simulated population statistics that are compared with recent detections by Fermi of normal, isolated pulsars.Comment: 4 pages, 3 figures, to appear in the proceedings of the Pulsar 2010 Conference, Italy, 10 - 15 October 201

A Cone Jet-Finding Algorithm for Heavy-Ion Collisions at LHC Energies

Standard jet finding techniques used in elementary particle collisions have not been successful in the high track density of heavy-ion collisions. This paper describes a modified cone-type jet finding algorithm developed for the complex environment of heavy-ion collisions. The primary modification to the algorithm is the evaluation and subtraction of the large background energy, arising from uncorrelated soft hadrons, in each collision. A detailed analysis of the background energy and its event-by-event fluctuations has been performed on simulated data, and a method developed to estimate the background energy inside the jet cone from the measured energy outside the cone on an event-by-event basis. The algorithm has been tested using Monte-Carlo simulations of Pb+Pb collisions at $\sqrt{s}=5.5$ TeV for the ALICE detector at the LHC. The algorithm can reconstruct jets with a transverse energy of 50 GeV and above with an energy resolution of $\sim30$.Comment: 13 pages, 7 figure

Effects of Rotation and Relativistic Charge Flow on Pulsar Magnetospheric Structure

We propose an analytical 3-D model of the open field-line region of a neutron star (NS) magnetosphere. We construct an explicit analytic solution for arbitrary obliquity (angle between the rotation and magnetic axes) incorporating the effects of magnetospheric rotation, relativistic flow of charges (e.g. primary electron beam) along the open field lines, and E X B drift of these charges. Our solution employs the space-charge-limited longitudinal current calculated in the electrodynamic model of Muslimov & Tsygan (1992) and is valid up to very high altitudes nearly approaching the light cylinder. We assume that in the innermost magnetosphere, the NS magnetic field can be well represented by a static magnetic dipole configuration. At high altitudes the open magnetic field lines significantly deviate from those of a static dipole and tend to focus into a cylindrical bundle, swept back in the direction opposite to the rotation, and also bent towards the rotational equator. We briefly discuss some implications of our study to spin-powered pulsars.Comment: 24 pages, 3 figures, accepted for publication in Ap

Sports-related brain injury in the general population: An epidemiological study

Objectives To determine the incidence, nature and severity of all sports-related brain injuries in the general population. Design Population-based epidemiological incidence study. Methods Data on all traumatic brain injury events sustained during a sports-related activity were extracted from a dataset of all new traumatic brain injury cases (both fatal and non-fatal), identified over a one-year period in the Hamilton and Waikato districts of New Zealand. Prospective and retrospective case ascertainment methods from multiple sources were used. All age groups and levels of traumatic brain injury severity were included. Details of the registering injuries and recurrent injuries sustained over the subsequent year were obtained through medical/accident records and assessment interviews with participants. Results Of 1369 incident traumatic brain injury cases, 291 were identified as being sustained during a sports-related activity (21% of all traumatic brain injuries) equating to an incidence rate of 170 per 100,000 of the general population. Recurrent injuries occurred more frequently in adults (11%) than children (5%). Of the sports-related injuries 46% were classified as mild with a high risk of complications. Injuries were most frequently sustained during rugby, cycling and equestrian activities. It was revealed that up to 19% of traumatic brain injuries were not recorded in medical notes. Conclusions Given the high incidence of new and recurrent traumatic brain injury and the high risk of complications following injury, further sport specific injury prevention strategies are urgently needed to reduce the impact of traumatic brain injury and facilitate safer engagement in sports activities. The high levels of ‘missed’ traumatic brain injuries, highlights the importance in raising awareness of traumatic brain injury during sports-related activity in the general population

Rest-Frame Ultraviolet Spectra of z~3 Lyman Break Galaxies

We present the results of a systematic study of the rest-frame UV spectroscopic properties of Lyman Break Galaxies (LBGs). The database of almost 1000 LBG spectra proves useful for constructing high S/N composite spectra. The composite spectrum of the entire sample reveals a wealth of features attributable to hot stars, HII regions, dust, and outflowing neutral and ionized gas. By grouping the database according to galaxy parameters such as Lyman-alpha equivalent width, UV spectral slope, and interstellar kinematics, we isolate some of the major trends in LBG spectra which are least compromised by selection effects. We find that LBGs with stronger Lyman-alpha emission have bluer UV continua, weaker low-ionization interstellar absorption lines, smaller kinematic offsets between Lyman-alpha and the interstellar absorption lines, and lower star-formation rates. There is a decoupling between the dependence of low- and high-ionization outflow features on other spectral properties. Most of the above trends can be explained in terms of the properties of the large-scale outflows seen in LBGs. According to this scenario, the appearance of LBG spectra is determined by a combination of the covering fraction of outflowing neutral gas which contains dust, and the range of velocities over which this gas is absorbing. Higher sensitivity and spectral resolution observations are still required for a full understanding of the covering fraction and velocity dispersion of the outflowing neutral gas in LBGs, and its relationship to the escape fraction of Lyman continuum radiation in galaxies at z~3.Comment: 28 pages including 17 figures. Accepted for publication in Ap