Closed Expressions for Lie Algebra Invariants and Finite Transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.Comment: 34 pages, ps file, no figure

Influence of disordered porous media in the anomalous properties of a simple water model

The thermodynamic, dynamic and structural behavior of a water-like system confined in a matrix is analyzed for increasing confining geometries. The liquid is modeled by a two dimensional associating lattice gas model that exhibits density and diffusion anomalies, in similarity to the anomalies present in liquid water. The matrix is a triangular lattice in which fixed obstacles impose restrictions to the occupation of the particles. We show that obstacules shortens all lines, including the phase coexistence, the critical and the anomalous lines. The inclusion of a very dense matrix not only suppress the anomalies but also the liquid-liquid critical point

Properties of magnetic nanodots with perpendicular anisotropy

Nanodots with magnetic vortices have many potential applications, such as magnetic memories (VRAMs) and spin transfer nano-oscillators (STNOs). Adding a perpendicular anisotropy term to the magnetic energy of the nanodot it becomes possible to tune the vortex core properties. This can be obtained, e.g., in Co nanodots by varying the thickness of the Co layer in a Co/Pt stack. Here we discuss the spin configuration of circular and elliptical nanodots for different perpendicular anisotropies; we show for nanodisks that micromagnetic simulations and analytical results agree. Increasing the perpendicular anisotropy, the vortex core radii increase, the phase diagrams are modified and new configurations appear; the knowledge of these phase diagrams is relevant for the choice of optimum nanodot dimensions for applications. MFM measurements on Co/Pt multilayers confirm the trend of the vortex core diameters with varying Co layer thicknesses.Comment: 7 pages, 8 figure

Network conduciveness with application to the graph-coloring and independent-set optimization transitions

We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another. We exemplify its use through an application to the two problems in combinatorial optimization that, given an undirected graph, ask that its so-called chromatic and independence numbers be found. Though NP-hard, when solved on sequences of expanding random graphs there appear marked transitions at which optimal solutions can be obtained substantially more easily than right before them. We demonstrate that these phenomena can be understood by resorting to the network that represents the solution space of the problems for each graph and examining its conduciveness between the non-optimal solutions and the optimal ones. At the said transitions, this network becomes strikingly more conducive in the direction of the optimal solutions than it was just before them, while at the same time becoming less conducive in the opposite direction. We believe that, besides becoming useful also in other areas in which network theory has a role to play, network conduciveness may become instrumental in helping clarify further issues related to NP-hardness that remain poorly understood

Searching for Very High Energy Emission from Pulsars Using the High Altitude Water Cherenkov (HAWC) Observatory

There are currently over 160 known gamma-ray pulsars. While most of them are detected only from space, at least two are now seen also from the ground. MAGIC and VERITAS have measured the gamma ray pulsed emission of the Crab pulsar up to hundreds of GeV and more recently MAGIC has reported emission at $\sim2$ TeV. Furthermore, in the Southern Hemisphere, H.E.S.S. has detected the Vela pulsar above 30 GeV. In addition, non-pulsed TeV emission coincident with pulsars has been detected by many groups, including the Milagro Collaboration. These GeV-TeV observations open the possibility of searching for very-high-energy (VHE, > 100GeV) pulsations from gamma-rays pulsars in the HAWC field of view.Comment: Presented at the 34th International Cosmic Ray Conference (ICRC2015), The Hague, The Netherlands. See arXiv:1508.03327 for all HAWC contribution

The Stellar Content of Obscured Galactic Giant HII Regions. VI: W51A

We present K-band spectra of newly born OB stars in the obscured Galactic giant H II region W51A and ~ 0.8'' angular resolution images in the J, H and K_S-bands. Four objects have been spectroscopically classified as O-type stars. The mean spectroscopic parallax of the four stars gives a distance of 2.0 \pm 0.3 kpc (error in the mean), significantly smaller than the radio recombination line kinematic value of 5.5 kpc or the values derived from maser propermotion observations (6--8 kpc). The number of Lyman continuum photons from the contribution of all massive stars (NLyc ~ 1.5 x 10^{50} s^{-1}) is in good agreement with that inferred from radio recombination lines (NLyc = 1.3 x 10^{50} s^{-1}) after accounting for the smaller distance derived here. We present analysis of archival high angular resolution images (NAOS CONICA at VLT and T-ReCS at Gemini) of the compact region W51 IRS2. The K_S--band images resolve the infrared source IRS~2 indicating that it is a very young compact HII region. Sources IRS2E was resolved into compact cluster (within 660 AU of projected distance) of 3 objects, but one of them is just bright extended emission. W51d1 and W51d2 were identified with compact clusters of 3 objects (maybe 4 in the case of W51d1) each one. Although IRS~2E is the brightest source in the K-band and at 12.6 \micron, it is not clearly associated with a radio continuum source. Our spectrum of IRS~2E shows, similar to previous work, strong emission in Br$\gamma$ and HeI, as well as three forbidden emission lines of FeIII and emission lines of molecular hydrogen (H_2) marking it as a massive young stellar object.Comment: 31 pages and 9 figures, submitted to A