Two-dimensional approach to relativistic positioning systems

A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allows to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out.Comment: 11 pages, 5 figures. v2: a brief description of the principal bibliography has been adde

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

Neutrinos from supernovae: experimental status and perspectives

I discuss the state of the art in the search for neutrinos from galactic stellar collapses and the future perspectives of this field. The implications for the neutrino physics of a high statistics supernova neutrino burst detection by the network of detectors operating around the world are also reviewed.Comment: 19 pages, 12 figures. Extended version of talk given at IInd International Workshop on Matter, Anti-Matter and Dark Matter, Trento (Italy), 29-30 October 2001. A reduced version will appear in Int. J. of Mod. Phys.

Positioning systems in Minkowski space-time: from emission to inertial coordinates

The coordinate transformation between emission coordinates and inertial coordinates in Minkowski space-time is obtained for arbitrary configurations of the emitters. It appears that a positioning system always generates two different coordinate domains, namely, the front and the back emission coordinate domains. For both domains, the corresponding covariant expression of the transformation is explicitly given in terms of the emitter world-lines. This task requires the notion of orientation of an emitter configuration. The orientation is shown to be computable from the emission coordinates for the users of a `central' region of the front emission coordinate domain. Other space-time regions associated with the emission coordinates are also outlined.Comment: 20 pages; 1 figur

DAMA detection claim is still compatible with all other DM searches

We show that the annual modulation signal observed by DAMA can be reconciled with all other negative results from dark matter searches with a conventional halo model for particle masses around 5 to 9 GeV. We also show which particular dark matter stream could produce the DAMA signal.Comment: Talk given at TAUP2005, Sept. 10-14 2005, Zaragoza (Spain). 3 pages, 4 figure

Bioactive flavanones from Luma chequen

A bioassay-guided chemical study of a methanolic extract of fresh leaves of Luma chequen led to the isolation of lumaflavanones A (1), B (2) and C (3) whose structures are proposed on the basis of NMR spectroscopic data. The structure of lumaflavanone A was confirmed by X-ray analysis. Antifeedant (Spodoptera littoralis), brine shrimp (Artemia salina) and fungistatic (Botrytis cinerea) bioassays showed that while 3 was the most active in the first two assays the mixture of 1 and 2 was more effective as a fungistatic

Universal deformation formulas and breaking symmetry

AbstractWe show that an algebra with a non-nilpotent Lie group of automorphisms or “symmetries” (e.g., smooth functions on a manifold with such a group of diffeomorphisms) may generally be deformed (in the function case, “quantized”) in such a way that only a proper subgroup of the original group acts. This symmetry breaking is a consequence of the existence of certain “universal deformation formulas” which are elements, independent of the original algebra, in the tensor algebra of the enveloping algebra of the Lie algebra of the group

Navigation-Assisted Posterior Open Reduction and Internal Fixation in a C-CLAMP Fashion for an Isolated C1 Fracture.

C1 fractures with an intact transverse ligament are usually treated conservatively. Patients who present with a progressive diastasis of bone fragments and a progressive articular subluxation mainly attributed to progressive lengthening of the transverse ligament (TAL) fibers can be treated with a C1 "C-clamp" fusion. A 75-year-old male who sustained a motor vehicle accident was neurologically intact. A computed tomography (CT) imaging demonstrated a Jefferson's type-C1 fracture with a slight lateral displacement of the C1 left lateral mass (LM) and a rotatory subluxation on the right. MRI showed an intact TAL and demonstrated an isolated rupture of the left alar ligament. Conservative treatment was chosen. Radiographic follow-up showed, at 3 months, progressive lateral mass displacement, most likely due to elongation of the TAL fibers; this was also associated with a persistent mechanical neck pain. For this reason, we performed a posterior reduction and internal fixation in a C-clamp fashion by placement of C1 lateral mass screws and posterior compression sparing the C1-2 joint. Using navigation, a 3.5-mm screw was inserted into the LM bilaterally. The screw heads were then connected with a rod and compression was applied before tightening. Postoperative CT scan demonstrated a satisfying reduction and further imaging will be made during the follow-up. The patient had a considerable relief of neck pain. Simple lateral mass fixation with C-clamp technique is a reasonable option in case of isolated C1 fractures in patients who have failed conservative management while preserving the range of motion (ROM) at the atlanto-axial joint. The link to the video can be found at: https://youtu.be/x8bsVwzCt_M