Relativistic positioning: four-dimensional numerical approach in Minkowski space-time

We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating Earth. The trajectories are then circumferences centered at the same point as Earth. Photon motions are described in Minkowski space-time, where there is a well known relation, Coll, Ferrando & Morales-Lladosa (2010), between the emission and inertial coordinates of any event. Here, this relation is implemented in a numerical code, which is tested and applied. The first application is a detailed numerical four-dimensional analysis of the so-called emission coordinate region and co-region. In a second application, a GPS (Galileo) satellite is considered as the receiver and its emission coordinates are given by four Galileo (GPS) satellites. The bifurcation problem (double localization) in the positioning of the receiver satellite is then pointed out and discussed in detail.Comment: 16 pages, 9 figures, published (online) in Astrophys. Space Sc

Relativistic Positioning Systems: The Emission Coordinates

This paper introduces some general properties of the gravitational metric and the natural basis of vectors and covectors in 4-dimensional emission coordinates. Emission coordinates are a class of space-time coordinates defined and generated by 4 emitters (satellites) broadcasting their proper time by means of electromagnetic signals. They are a constitutive ingredient of the simplest conceivable relativistic positioning systems. Their study is aimed to develop a theory of these positioning systems, based on the framework and concepts of general relativity, as opposed to introducing `relativistic effects' in a classical framework. In particular, we characterize the causal character of the coordinate vectors, covectors and 2-planes, which are of an unusual type. We obtain the inequality conditions for the contravariant metric to be Lorentzian, and the non-trivial and unexpected identities satisfied by the angles formed by each pair of natural vectors. We also prove that the metric can be naturally split in such a way that there appear 2 parameters (scalar functions) dependent exclusively on the trajectory of the emitters, hence independent of the time broadcast, and 4 parameters, one for each emitter, scaling linearly with the time broadcast by the corresponding satellite, hence independent of the others.Comment: 13 pages, 3 figures. Only format changed for a new submission. Submitted to Class. Quantum Gra

A physical application of Kerr-Schild groups

The present work deals with the search of useful physical applications of some generalized groups of metric transformations. We put forward different proposals and focus our attention on the implementation of one of them. Particularly, the results show how one can control very efficiently the kind of spacetimes related by a Generalized Kerr-Schild (GKS) Ansatz through Kerr-Schild groups. Finally a preliminar study regarding other generalized groups of metric transformations is undertaken which is aimed at giving some hints in new Ans\"atze to finding useful solutions to Einstein's equations.Comment: 18 page

Homogenisation and analysis of an expanded long-term monthly rainfall network for the Island of Ireland (1850-2010)

Long-term precipitation series are critical for understanding emerging changes to the hydrological cycle. To this end we construct a homogenised Island of Ireland Precipitation (IIP) network comprising 25 stations and a composite series covering the period 1850-2010, providing the second- longest regional precipitation archive in the British-Irish Isles. We expand the existing catalogue of long-term precipitation records for the island by recovering archived data for an additional eight stations. Following bridging and updating of stations HOMER homogenisation software is used to detect breaks using pairwise and joint detection. Twenty-five breakpoints are detected across 14 stations, and the majority (20) are corroborated by metadata. Assessment of variability and change in homogenised and extended precipitation records reveal positive (winter) and negative (summer) trends. Trends in records covering the typical period of digitisation (1941 onwards) are not always representative of longer records. Furthermore, trends in post-homogenisation series change magnitude and even direction at some stations. While cautionary flags are raised for some series, confidence in the derived network is high given attention paid to metadata, coherence of behaviour across the network and consistency of findings with other long-term climatic series such as England and Wales precipitation. As far as we are aware, this work represents the first application of HOMER to a long- term precipitation network and bodes well for use in other regions. It is expected that the homogenised IIP network will find wider utility in benchmarking and supporting climate services across the Island of Ireland, a sentinel location in the North Atlantic

On the Weyl transverse frames in type I spacetimes

We apply a covariant and generic procedure to obtain explicit expressions of the transverse frames that a type I spacetime admits in terms of an arbitrary initial frame. We also present a simple and general algorithm to obtain the Weyl scalars $\Psi_2^T$, $\Psi_0^T$ and $\Psi_4^T$ associated with these transverse frames. In both cases it is only necessary to choose a particular root of a cubic expression.Comment: 12 pages, submitted to Gen. Rel. Grav. (6-3-2004

Neutrino physics at accelerators

Present and future neutrino experiments at accelerators are mainly concerned with understanding the neutrino oscillation phenomenon and its implications. Here a brief account of neutrino oscillations is given together with a description of the supporting data. Some current and planned accelerator neutrino experiments are also explained.Comment: 23 pages, 24 figures. Talk given at the Corfu Summer Institute on Elementary Particle Physics 200

Radiosurgery for Benign Vertebral Body Hemangiomas of the Spine: A Systematic Review and Meta-Analysis.

Spinal vertebral hemangiomas (SVHs) are the most common benign tumors of the spine. We performed a systematic review and meta-analysis of radiosurgery (RS) for SVHs. We reviewed articles published between January 1990 and December 2020 on PubMed. Tumor control, pain relief, and damage to surrounding tissues were evaluated with separate meta-analyses. This study was performed in accordance with the published Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. A total of 23 patients with 24 SVHs were reported in 3 studies. Follow-up time was 7.3-84 months. The vast majority of lesions were located at dorsal level (n = 18; 75%). In 20 (83.3%) patients, pain was the initial clinical presentation. Complete, partial, and stable responses after radiation were reported in 45.7% (P < 0.001), 23.6% (P = 0.02), and 37.2% (P = 0.7) of cases. Overall response was reported in 94.1% (P = 0.7). No progressive disease was reported. Pain relief was achieved in 87.5% of patients (P = 0.2). Damage to surrounding tissue caused by irradiation was reported in 22.3% (P = 0.02) of cases in 1 study, in which higher doses of radiation were delivered. Radiosurgery is safe and effective for SVHs. Pain relief after RS in symptomatic patients was extremely high, while no progressive disease was reported. Damage to surrounding tissues was reported in only 1 series and included osteitis, osteonecrosis, or soft tissue injury after higher radiation doses

Spin-Charge Separation in Two Dimensions - A Numerical Study

The question of spin-charge separation in two-dimensional lattices has been addressed by numerical simulations of the motion of one hole in a half-filled band. The calculations have been performed on finite clusters with Hubbard and t-J models. By comparing the time evolution of spin and charge polarisation currents in one and two dimensions, evidence in favor of spin-charge separation in two dimensions is presented. In contrast with this, spin-charge separation is absent in a highly doped, metallic, system.Comment: RevTeX 3.0, 10 Pages, 6 PostScript Figures (on request

Kerr-Schild Symmetries

We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions.Comment: 15 pages, no figures, LaTe