Investigation on reference frames and time systems in Multi-GNSS

Receivers able to track satellites belonging to different GNSSs (Global Navigation Satellite Systems) are available on the market. To compute coordinates and velocities it is necessary to identify all the elements that contribute to interoperability of the different GNSSs. For example the timescales kept by different GNSSs have to be aligned. Receiver-specific biases, or firmware-dependent biases, need to be calibrated. The reference frame used in the representation of the orbits must be unique. In this paper we address the interoperability issues from the standpoint of a Single Point Positioning (SPP) user, i.e., using pseudoranges and broadcast ephemeris. The biases between GNSSs timescales and receiver-dependent biases are analyzed for a set of 31 MGEX (Multi-GNSS Experiment) stations over a time span of more than three years. Time series of biases between timescales of GPS (Global Positioning System), GLONASS (Global Navigation Satellite System), Galileo, BeiDou, QZSS (Quasi-Zenith Satellite System), SBAS (Satellite Based Augmentation System) and NAVIC (Navigation with Indian Constellation) are investigated, in addition to the identification of events like discontinuity of receiver-dependent biases due to firmware updating. The GPS broadcast reference frame is shown to be aligned to the one (IGS14) realized by the precise ephemeris of CODE (Center for Orbit Determination in Europe) to within 0.1 m and 2 milliarcsec, with values dependent on whether IIR-A, IIR-B/M or IIF satellite blocks are considered. Larger offsets are observed for GLONASS, up to 1 m for GLONASS K satellites. For Galileo the alignment of the broadcast orbit to IGS14/CODE is again at the 0.1 m and several milliarcsec level, with the FOC (Full Operational Capability) satellites slightly better than IOV (In Orbit Validation). For BeiDou an alignment of the broadcast frame to IGS14/CODE comparable to GLONASS is observed, regardless of whether IGSO (Inclined Geosynchronous Orbit) or MEO (Medium Earth Orbit) satellites are considered. For all satellites, position differences according to the broadcast ephemeris relative to IGS14/CODE orbits are projected to the radial, along-track and crosstrack triad, with the largest periodic differences affecting mostly the along track component. Sudden discontinuities at the level of up to 1 m and 2–3 ns are observed for the along-track component and the satellite clock, respectively. The time scales of GLONASS, Galileo, QZSS, SBAS and NAVIC are very closely aligned to GPS, with constant offsets depending on receiver type. The offset of the BeiDou time scale to GPS has an oscillatory pattern with peak-to-peak values up to 100 ns. To characterize receiver-dependent biases the average of six Septentrio receivers is taken as reference, and relative offsets of the other receiver types are investigated. These receiver-dependent biases may depend on the individual station, or for the same station on the update of the firmware. A detailed calibration history is presented for each multiGNSS station studied

The Hawking-Page crossover in noncommutative anti-deSitter space

We study the problem of a Schwarzschild-anti-deSitter black hole in a noncommutative geometry framework, thought to be an effective description of quantum-gravitational spacetime. As a first step we derive the noncommutative geometry inspired Schwarzschild-anti-deSitter solution. After studying the horizon structure, we find that the curvature singularity is smeared out by the noncommutative fluctuations. On the thermodynamics side, we show that the black hole temperature, instead of a divergent behavior at small scales, admits a maximum value. This fact implies an extension of the Hawking-Page transition into a van der Waals-like phase diagram, with a critical point at a critical cosmological constant size in Plank units and a smooth crossover thereafter. We speculate that, in the gauge-string dictionary, this corresponds to the confinement "critical point" in number of colors at finite number of flavors, a highly non-trivial parameter that can be determined through lattice simulations.Comment: 24 pages, 6 figure, 1 table, version matching that published on JHE

Spinning Loop Black Holes

In this paper we construct four Kerr-like spacetimes starting from the loop black hole Schwarzschild solutions (LBH) and applying the Newman-Janis transformation. In previous papers the Schwarzschild LBH was obtained replacing the Ashtekar connection with holonomies on a particular graph in a minisuperspace approximation which describes the black hole interior. Starting from this solution, we use a Newman-Janis transformation and we specialize to two different and natural complexifications inspired from the complexifications of the Schwarzschild and Reissner-Nordstrom metrics. We show explicitly that the space-times obtained in this way are singularity free and thus there are no naked singularities. We show that the transformation move, if any, the causality violating regions of the Kerr metric far from r=0. We study the space-time structure with particular attention to the horizons shape. We conclude the paper with a discussion on a regular Reissner-Nordstrom black hole derived from the Schwarzschild LBH and then applying again the Newmann-Janis transformation.Comment: 18 pages, 18 figure

Diagnosing numerical Cherenkov instabilities in relativistic plasma simulations based on general meshes

Numerical Cherenkov radiation (NCR) or instability is a detrimental effect frequently found in electromagnetic particle-in-cell (EM-PIC) simulations involving relativistic plasma beams. NCR is caused by spurious coupling between electromagnetic-field modes and multiple beam resonances. This coupling may result from the slow down of poorly-resolved waves due to numerical (grid) dispersion and from aliasing mechanisms. NCR has been studied in the past for finite-difference-based EM-PIC algorithms on regular (structured) meshes with rectangular elements. In this work, we extend the analysis of NCR to finite-element-based EM-PIC algorithms implemented on unstructured meshes. The influence of different mesh element shapes and mesh layouts on NCR is studied. Analytic predictions are compared against results from finite-element-based EM-PIC simulations of relativistic plasma beams on various mesh types.Comment: 31 pages, 20 figure

Minimal Scales from an Extended Hilbert Space

We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our commutators do not depend on positions and momenta and we provide an extension of the coordinate coherent state approach to Noncommutative Geometry. We explore, as toy model, the corresponding quantum field theory in a (2+1)-dimensional spacetime. Then we investigate the more realistic case of a (3+1)-dimensional spacetime, foliated into noncommutative planes. As a result, we obtain propagators, which are finite in the ultraviolet as well as the infrared regime.Comment: 16 pages, version which matches that published on CQ

Self-completeness and spontaneous dimensional reduction

A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity -- spontaneous dimensional reduction and self-completeness. The former suggests the spacetime background at the Planck scale may be effectively two-dimensional, while the latter implies a condition of maximal compression of matter by the formation of an event horizon for Planckian scattering. We generalize such a result to an arbitrary number of dimensions, and show that gravity in higher than four dimensions remains self-complete, but in lower dimensions it is not. In such a way we established an "exclusive disjunction" or "exclusive or" (XOR) between the occurrence of self-completeness and dimensional reduction, with the goal of actually reducing the unknowns for the scenario of the physics at the Planck scale. Potential phenomenological implications of this result are considered by studying the case of a two-dimensional dilaton gravity model resulting from dimensional reduction of Einstein gravity.Comment: 12 pages, 3 figures; v3: final version in press on Eur. Phys. J. Plu

Practice-Focused, Constructivist Grounded Theory Methodology In Higher Education Leadership Research

A growing body of education research considers practices, however there is less focus on a methodology that enables practical analysis of practices. Use of practice theory is growing, particularly in work and organisational studies, but practice focused studies more frequently address theoretical than methodological agenda. This chapter proposes a practice-focused, constructivist grounded theory methodology as one approach which can address this gap. After first considering the ways in which, separately and in combination, practice-theory and constructivist grounded theory can support higher education leadership and management research, the chapter considers implementation of this methodology by drawing on a study into the practice of authority in higher education leadership. It concludes by considering some implications for the ways in which practices can be understood and the affordances and limitations of this methodology.Peer reviewe

Sub-Planckian black holes and the Generalized Uncertainty Principle

The Black Hole Uncertainty Principle correspondence suggests that there could exist black holes with mass beneath the Planck scale but radius of order the Compton scale rather than Schwarzschild scale. We present a modified, self-dual Schwarzschild-like metric that reproduces desirable aspects of a variety of disparate models in the sub-Planckian limit, while remaining Schwarzschild in the large mass limit. The self-dual nature of this solution under $M \leftrightarrow M^{-1}$ naturally implies a Generalized Uncertainty Principle with the linear form $\Delta x \sim \frac{1}{\Delta p} + \Delta p$. We also demonstrate a natural dimensional reduction feature, in that the gravitational radius and thermodynamics of sub-Planckian objects resemble that of $(1+1)$-D gravity. The temperature of sub-Planckian black holes scales as $M$ rather than $M^{-1}$ but the evaporation of those smaller than $10^{-36}$g is suppressed by the cosmic background radiation. This suggests that relics of this mass could provide the dark matter.Comment: 12 pages, 9 figures, version published in J. High En. Phy