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

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

Thermal hadron production in high energy collisions

It is shown that hadron abundances in high energy e+e-, pp and p{\bar p} collisions, calculated by assuming that particles originate in hadron gas fireballs at thermal and partial chemical equilibrium, are in very good agreement with the data. The freeze-out temperature of the hadron gas fireballs turns out to be nearly constant over a large center of mass energy range and not dependent on the initial colliding system. The only deviation from chemical equilibrium resides in the incomplete strangeness phase space saturation. Preliminary results of an analysis of hadron abundances in S+S and S+Ag heavy ion collisions are presented.Comment: 10 pages, 1 .eps figure, talk given at the Strangeness and Quark Matter 97 conferenc

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

Internal Migration and Regional Population Dynamics in Europe: Spain Case Study

Internal migration has been a key component in Spain’s sub-national population dynamics over the last century, particularly during the 1960s and 1970s, when the rural exodus was at its peak. Since then, as fertility levels have declined and the economy has been restructured, internal migration has continued to play an important, albeit different, role in shaping the distribution of the population across the country. This report, which is one of a series of studies of population dynamics and internal migration in different European countries, considers some of the more recent changes in the distribution of the population and in internal migration during each of the two calendar years, 1988 and 1994, at two spatial scales, provinces and municipalities. Whilst both the natural change and residual net migration components of population change are mapped at both geographical scales, the demographic dynamism of the ‘coastal’ provinces is evident when contrasted, in aggregate terms, with changes taking place in the ‘industrial’, ‘urban’ and ‘rural’ provinces. A Webb classification demonstrates the extent to which the number of municipalities with net migration gains increased between 1988 and 1994, and a size classification suggests a shift of population expansion down the urban hierarchy. Registration data for the two annual periods are used to examine the changes in the volume, geographical distribution and demographic structure of internal migration. Whilst it is clear that the volume of migration between municipalities in the same province has increased between 1988 and 1994 more rapidly than the migration taking place between municipalities in different provinces, the efficiency with which the latter redistributes population has declined. Spatial patterns of aggregate inter-provincial net migration, net migration rates, migration efficiencies and major flows are outlined but no evidence is found of a relationship between net migration and unemployment or density at the municipality scale. Age variations in migration propensities and net migration balances give some indications of the variety of determinants that influence directional migration flows at different stages in the life course. The report presents the profiles of national migration rate schedules in 1988 and 1994 and examines the spatial patterns of net migration for five-year age groups. Provinces are classified according to their migration efficiencies in the two annual periods and age-specific efficiencies are examined for selected provinces to demonstrate major changes in more detail. Migration of those of working age accounts for the large majority of inter-provincial movements and migration efficiencies of those in three broad working age groups (young, middle and older) provide a useful summary of the main patterns. Finally, the report makes use of the information available from the registration data on place of birth as well as on place of residence before and after the move. New insights are given on the proportion of inter-provincial migration that involves return to the province of birth, the age variations in return proportions and the major flows of return migrants between provinces

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: Bifurcation problem and observational data

In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know {\em independently} the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus solved by applying this observational rule, and consequently, {\em all} of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system.Comment: 10 pages, 7 figures. The version published in PRD contains a misprint in the caption of Figure 3, which is here amende