Affine Wa(A4), Quaternions, and Decagonal Quasicrystals

We introduce a technique of projection onto the Coxeter plane of an arbitrary higher dimensional lattice described by the affine Coxeter group. The Coxeter plane is determined by the simple roots of the Coxeter graph I2 (h) where h is the Coxeter number of the Coxeter group W(G) which embeds the dihedral group Dh of order 2h as a maximal subgroup. As a simple application we demonstrate projections of the root and weight lattices of A4 onto the Coxeter plane using the strip (canonical) projection method. We show that the crystal spaces of the affine Wa(A4) can be decomposed into two orthogonal spaces whose point groups is the dihedral group D5 which acts in both spaces faithfully. The strip projections of the root and weight lattices can be taken as models for the decagonal quasicrystals. The paper also revises the quaternionic descriptions of the root and weight lattices, described by the affine Coxeter group Wa(A3), which correspond to the face centered cubic (fcc) lattice and body centered cubic (bcc) lattice respectively. Extensions of these lattices to higher dimensions lead to the root and weight lattices of the group Wa(An), n>=4 . We also note that the projection of the Voronoi cell of the root lattice of Wa(A4) describes a framework of nested decagram growing with the power of the golden ratio recently discovered in the Islamic arts.Comment: 26 pages, 17 figure

Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics

Using the NU method [A.F.Nikiforov, V.B.Uvarov, Special Functions of Mathematical Physics, Birkhauser,Basel,1988], we investigated the real eigenvalues of the complex and/or $PT$- symmetric, non-Hermitian and the exponential type systems, such as Poschl-Teller and Morse potentials.Comment: 14 pages, Late

Spectrum of the Relativistic Particles in Various Potentials

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a Schr\"{o}dinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics

New lattice action for heavy quarks

We extend the Fermilab method for heavy quarks to include interactions of dimensions 6 and 7 in the action. There are, in general, many new interactions, but we carry out the calculations needed to match the lattice action to continuum QCD at the tree level, finding six non-zero couplings. Using the heavy-quark theory of cutoff effects, we estimate how large the remaining discretization errors are. We find that our tree-level matching, augmented with one-loop matching of the dimension-five interactions, can bring these errors below 1%, at currently available lattice spacings.Comment: 43 pp; v2 conforms with PRD version, improving plots and many minor thing

Use of polyethylene glycol coatings for optical fibre humidity sensing

Humidity induced change in the refractive index and thickness of the polyethylene glycol (PEG) coatings are in situ investigated for a range from 10 to 95%, using an optical waveguide spectroscopic technique. It is experimentally demonstrated that, upon humidity change, the optical and swelling characteristics of the PEG coatings can be employed to build a plastic fibre optic humidity sensor. The sensing mechanism is based on the humidity induced change in the refractive index of the PEG film, which is directly coated onto a polished segment of a plastic optical fibre with dip-coating method. It is observed that PEG, which is a highly hydrophilic material, shows no monotonic linear response to humidity but gives different characteristics for various ranges of humidity levels both in index of refraction and in thickness. It undergoes a physical phase change from a semi-crystal line structure to a gel one at around 80% relative humidity. At this phase change point, a drastic decrease occurs in the index of refraction as well as a drastic increase in the swelling of the PEG film. In addition, PEG coatings are hydrogenated in a vacuum chamber. It is observed that the hydrogen has a preventing effect on the humidity induced phase change in PEG coatings. Finally, the possibility of using PEG coatings in construction of a real plastic fibre optic humidity sensor is discussed. (C) 2008 The Optical Society of Japan

Gravitational Waves From Known Pulsars: Results From The Initial Detector Era

We present the results of searches for gravitational waves from a large selection of pulsars using data from the most recent science runs (S6, VSR2 and VSR4) of the initial generation of interferometric gravitational wave detectors LIGO (Laser Interferometric Gravitational-wave Observatory) and Virgo. We do not see evidence for gravitational wave emission from any of the targeted sources but produce upper limits on the emission amplitude. We highlight the results from seven young pulsars with large spin-down luminosities. We reach within a factor of five of the canonical spin-down limit for all seven of these, whilst for the Crab and Vela pulsars we further surpass their spin-down limits. We present new or updated limits for 172 other pulsars (including both young and millisecond pulsars). Now that the detectors are undergoing major upgrades, and, for completeness, we bring together all of the most up-to-date results from all pulsars searched for during the operations of the first-generation LIGO, Virgo and GEO600 detectors. This gives a total of 195 pulsars including the most recent results described in this paper.United States National Science FoundationScience and Technology Facilities Council of the United KingdomMax-Planck-SocietyState of Niedersachsen/GermanyAustralian Research CouncilInternational Science Linkages program of the Commonwealth of AustraliaCouncil of Scientific and Industrial Research of IndiaIstituto Nazionale di Fisica Nucleare of ItalySpanish Ministerio de Economia y CompetitividadConselleria d'Economia Hisenda i Innovacio of the Govern de les Illes BalearsNetherlands Organisation for Scientific ResearchPolish Ministry of Science and Higher EducationFOCUS Programme of Foundation for Polish ScienceRoyal SocietyScottish Funding CouncilScottish Universities Physics AllianceNational Aeronautics and Space AdministrationOTKA of HungaryLyon Institute of Origins (LIO)National Research Foundation of KoreaIndustry CanadaProvince of Ontario through the Ministry of Economic Development and InnovationNational Science and Engineering Research Council CanadaCarnegie TrustLeverhulme TrustDavid and Lucile Packard FoundationResearch CorporationAlfred P. Sloan FoundationAstronom

A First Search for coincident Gravitational Waves and High Energy Neutrinos using LIGO, Virgo and ANTARES data from 2007

We present the results of the first search for gravitational wave bursts associated with high energy neutrinos. Together, these messengers could reveal new, hidden sources that are not observed by conventional photon astronomy, particularly at high energy. Our search uses neutrinos detected by the underwater neutrino telescope ANTARES in its 5 line configuration during the period January - September 2007, which coincided with the fifth and first science runs of LIGO and Virgo, respectively. The LIGO-Virgo data were analysed for candidate gravitational-wave signals coincident in time and direction with the neutrino events. No significant coincident events were observed. We place limits on the density of joint high energy neutrino - gravitational wave emission events in the local universe, and compare them with densities of merger and core-collapse events.Comment: 19 pages, 8 figures, science summary page at http://www.ligo.org/science/Publication-S5LV_ANTARES/index.php. Public access area to figures, tables at https://dcc.ligo.org/cgi-bin/DocDB/ShowDocument?docid=p120000

Swift follow-up observations of candidate gravitational-wave transient events

We present the first multi-wavelength follow-up observations of two candidate gravitational-wave (GW) transient events recorded by LIGO and Virgo in their 2009-2010 science run. The events were selected with low latency by the network of GW detectors and their candidate sky locations were observed by the Swift observatory. Image transient detection was used to analyze the collected electromagnetic data, which were found to be consistent with background. Off-line analysis of the GW data alone has also established that the selected GW events show no evidence of an astrophysical origin; one of them is consistent with background and the other one was a test, part of a "blind injection challenge". With this work we demonstrate the feasibility of rapid follow-ups of GW transients and establish the sensitivity improvement joint electromagnetic and GW observations could bring. This is a first step toward an electromagnetic follow-up program in the regime of routine detections with the advanced GW instruments expected within this decade. In that regime multi-wavelength observations will play a significant role in completing the astrophysical identification of GW sources. We present the methods and results from this first combined analysis and discuss its implications in terms of sensitivity for the present and future instruments.Comment: Submitted for publication 2012 May 25, accepted 2012 October 25, published 2012 November 21, in ApJS, 203, 28 ( http://stacks.iop.org/0067-0049/203/28 ); 14 pages, 3 figures, 6 tables; LIGO-P1100038; Science summary at http://www.ligo.org/science/Publication-S6LVSwift/index.php ; Public access area to figures, tables at https://dcc.ligo.org/cgi-bin/DocDB/ShowDocument?docid=p110003

Search for Gravitational Wave Bursts from Six Magnetars

Soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are thought to be magnetars: neutron stars powered by extreme magnetic fields. These rare objects are characterized by repeated and sometimes spectacular gamma-ray bursts. The burst mechanism might involve crustal fractures and excitation of non-radial modes which would emit gravitational waves (GWs). We present the results of a search for GW bursts from six galactic magnetars that is sensitive to neutron star f-modes, thought to be the most efficient GW emitting oscillatory modes in compact stars. One of them, SGR 0501+4516, is likely similar to 1 kpc from Earth, an order of magnitude closer than magnetars targeted in previous GW searches. A second, AXP 1E 1547.0-5408, gave a burst with an estimated isotropic energy >10(44) erg which is comparable to the giant flares. We find no evidence of GWs associated with a sample of 1279 electromagnetic triggers from six magnetars occurring between 2006 November and 2009 June, in GW data from the LIGO, Virgo, and GEO600 detectors. Our lowest model-dependent GW emission energy upper limits for band-and time-limited white noise bursts in the detector sensitive band, and for f-mode ringdowns (at 1090 Hz), are 3.0 x 10(44)d(1)(2) erg and 1.4 x 10(47)d(1)(2) erg, respectively, where d(1) = d(0501)/1 kpc and d(0501) is the distance to SGR 0501+4516. These limits on GW emission from f-modes are an order of magnitude lower than any previous, and approach the range of electromagnetic energies seen in SGR giant flares for the first time.United States National Science FoundationScience and Technology Facilities Council of the United KingdomMax-Planck-SocietyState of Niedersachsen/GermanyItalian Istituto Nazionale di Fisica NucleareFrench Centre National de la Recherche ScientifiqueAustralian Research CouncilCouncil of Scientific and Industrial Research of IndiaIstituto Nazionale di Fisica Nucleare of ItalySpanish Ministerio de Educacion y CienciaConselleria d'Economia Hisenda i Innovacio of the Govern de les Illes BalearsFoundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific ResearchPolish Ministry of Science and Higher EducationFoundation for Polish ScienceRoyal SocietyScottish Funding CouncilScottish Universities Physics AllianceNational Aeronautics and Space Administration NNH07ZDA001-GLASTCarnegie TrustLeverhulme TrustDavid and Lucile Packard FoundationResearch CorporationAlfred P. Sloan FoundationRussian Space AgencyRFBR 09-02-00166aIPN JPL Y503559 (Odyssey), NASA NNG06GH00G, NASA NNX07AM42G, NASA NNX08AC89G (INTEGRAL), NASA NNG06GI896, NASA NNX07AJ65G, NASA NNX08AN23G (Swift), NASA NNX07AR71G (MESSENGER), NASA NNX06AI36G, NASA NNX08AB84G, NASA NNX08AZ85G (Suzaku), NASA NNX09AU03G (Fermi)Astronom