Real time GPS precise positioning of LEO satellites

Report for the scientific sojourn at the German Aerospace Center (DLR) , Germany, during June and July 2006. The main objective of the two months stay has been to apply the techniques of LEO (Low Earth Orbiters) satellites GPS navigation which DLR currently uses in real time navigation. These techniques comprise the use of a dynamical model which takes into account the precise earth gravity field and models to account for the effects which perturb the LEO’s motion (such as drag forces due to earth’s atmosphere, solar pressure, due to the solar radiation impacting on the spacecraft, luni-solar gravity, due to the perturbation of the gravity field for the sun and moon attraction, and tidal forces, due to the ocean and solid tides). A high parameterized software was produced in the first part of work, which has been used to asses which accuracy could be reached exploring different models and complexities. The objective was to study the accuracy vs complexity, taking into account that LEOs at different heights have different behaviors. In this frame, several LEOs have been selected in a wide range of altitudes, and several approaches with different complexity have been chosen. Complexity is a very important issue, because processors onboard spacecrafts have very limited computing and memory resources, so it is mandatory to keep the algorithms simple enough to let the satellite process it by itself.

Ionospheric tomography using GNSS reflections

In this paper, we report a preliminary analysis of the impact of Global Navigation Satellite System Reflections (GNSS-R) data on ionospheric monitoring over the oceans. The focus will be on a single polar Low Earth Orbiter (LEO) mission exploiting GNSS-R as well as Navigation (GNSS-N) and Occultation (GNSS-O) total electron content (TEC) measurements. In order to assess impact of the data, we have simulated GNSS-R/O/N TEC data as would be measured from the LEO and from International Geodesic Service (IGS) ground stations, with an electron density (ED) field generated using a climatic ionospheric model. We have also developed a new tomographic approach inspired by the physics of the hydrogen atom and used it to effectively retrieve the ED field from the simulated TEC data near the orbital plane. The tomographic inversion results demonstrate the significant impact of GNSS-R: three-dimensional ionospheric ED fields are retrieved over the oceans quite accurately, even as, in the spirit of this initial study, the simulation and inversion approaches avoided intensive computation and sophisticated algorithmic elements (such as spatio-temporal smoothing). We conclude that GNSS-R data over the oceans can contribute significantly to a Global/GNSS Ionospheric Observation System (GIOS). Index Terms Global Navigation Satellite System (GNSS), Global Navigation Satellite System Reflections (GNSS-R), ionosphere, Low Earth Orbiter (LEO), tomography.

Automatic low baseline stereo in urban areas

In this work we propose a new automatic methodology for computing accurate digital elevation models (DEMs) in urban environments from low baseline stereo pairs that shall be available in the future from a new kind of earth observation satellite. This setting makes both views of the scene similarly, thus avoiding occlusions and illumination changes, which are the main disadvantages of the commonly accepted large-baseline configuration. There still remain two crucial technological challenges: (i) precisely estimating DEMs with strong discontinuities and (ii) providing a statistically proven result, automatically. The first one is solved here by a piecewise affine representation that is well adapted to man-made landscapes, whereas the application of computational Gestalt theory introduces reliability and automation. In fact this theory allows us to reduce the number of parameters to be adjusted, and tocontrol the number of false detections. This leads to the selection of a suitable segmentation into affine regions (whenever possible) by a novel and completely automatic perceptual grouping method. It also allows us to discriminate e.g. vegetation-dominated regions, where such an affine model does not apply anda more classical correlation technique should be preferred. In addition we propose here an extension of the classical ”quantized” Gestalt theory to continuous measurements, thus combining its reliability with the precision of variational robust estimation and fine interpolation methods that are necessary in the low baseline case. Such an extension is very general and will be useful for many other applications as well.

Second differential of the entropy as a criterion for the stability in low-dimensional climate models

The second differential of the entropy is used for analysing the stability of a thermodynamic climatic model. A delay time for the heat flux is introduced whereby it becomes an independent variable. Two different expressions for the second differential of the entropy are used: one follows classical irreversible thermodynamics theory; the second is related to the introduction of response time and is due to the extended irreversible thermodynamics theory. the second differential of the classical entropy leads to unstable solutions for high values of delay times. the extended expression always implies stable states for an ice-free earth. When the ice-albedo feedback is included, a discontinuous distribution of stable states is found for high response times. Following the thermodynamic analysis of the model, the maximum rates of entropy production at the steady state are obtained. A latitudinally isothermal earth produces the extremum in global entropy production. the material contribution to entropy production (by which we mean the production of entropy by material transport of heat) is a maximum when the latitudinal distribution of temperatures becomes less homogeneous than present values

Niobium and rare earth minerals from the Virulundo carbonatite, Namibe, Angola

The Virulundo carbonatite in Angola, one of the biggest in the world, contains pyrochlore as an accessory mineral in all of the carbonatite units (calciocarbonatites, ferrocarbonatites, carbonatite breccias, trachytoids). The composition of the primary pyrochlore crystals is very close to fluornatrocalciopyrochlore in all these units. High-temperature hydrothermal processes caused the pseudomorphic replacement of the above crystals by a second generation of pyrochlore, characterized by lower F and Na contents. Low-temperature hydrothermal replacement of the above pyrochlores, associated with production of quartz-carbonates-fluorite veins, controled the development of a third generation of pyrochlore, characterized by high Sr contents. Finally, supergene processes produced the development of a secondary paragenesis in the carbonatite, consisting in late carbonates, goethite, hollandite and REE minerals (mainly synchysite-(Ce), britholite-(Ce), britholite-(La), cerite-(Ce)). Separation of Ce from the other REE was allowed by oxidizing conditions. Therefore, Ce4+ was also incorporated into a late generation of pyrochlore, which is also strongly enriched in Ba and strongly depleted in Ca and Na

Forecasting the Earth"s radiation belts and modeling solar energetic particle events: Recent results from SPACECAST

High-energy charged particles in the van Allen radiation belts and in solar energetic particle events can damage satellites on orbit leading to malfunctions and loss of satellite service. Here we describe some recent results from the SPACECAST project on modelling and forecasting the radiation belts, and modelling solar energetic particle events. We describe the SPACECAST forecasting system that uses physical models that include wave-particle interactions to forecast the electron radiation belts up to 3 h ahead. We show that the forecasts were able to reproduce the >2 MeV electron flux at GOES 13 during the moderate storm of 7-8 October 2012, and the period following a fast solar wind stream on 25-26 October 2012 to within a factor of 5 or so. At lower energies of 10- a few 100 keV we show that the electron flux at geostationary orbit depends sensitively on the high-energy tail of the source distribution near 10 RE on the nightside of the Earth, and that the source is best represented by a kappa distribution. We present a new model of whistler mode chorus determined from multiple satellite measurements which shows that the effects of wave-particle interactions beyond geostationary orbit are likely to be very significant. We also present radial diffusion coefficients calculated from satellite data at geostationary orbit which vary with Kp by over four orders of magnitude. We describe a new automated method to determine the position at the shock that is magnetically connected to the Earth for modelling solar energetic particle events and which takes into account entropy, and predict the form of the mean free path in the foreshock, and particle injection efficiency at the shock from analytical theory which can be tested in simulations.

Niobium and rare earth minerals from the Virulundo carbonatite, Namibe, Angola

The Virulundo carbonatite in Angola, one of the biggest in the world, contains pyrochlore as an accessory mineral in all of the carbonatite units (calciocarbonatites, ferrocarbonatites, carbonatite breccias, trachytoids). The composition of the primary pyrochlore crystals is very close to fluornatrocalciopyrochlore in all these units. High-temperature hydrothermal processes caused the pseudomorphic replacement of the above crystals by a second generation of pyrochlore, characterized by lower F and Na contents. Low-temperature hydrothermal replacement of the above pyrochlores, associated with production of quartz-carbonates-fluorite veins, controled the development of a third generation of pyrochlore, characterized by high Sr contents. Finally, supergene processes produced the development of a secondary paragenesis in the carbonatite, consisting in late carbonates, goethite, hollandite and REE minerals (mainly synchysite-(Ce), britholite-(Ce), britholite-(La), cerite-(Ce)). Separation of Ce from the other REE was allowed by oxidizing conditions. Therefore, Ce4+ was also incorporated into a late generation of pyrochlore, which is also strongly enriched in Ba and strongly depleted in Ca and Na

Forecasting the Earth"s radiation belts and modeling solar energetic particle events: Recent results from SPACECAST

High-energy charged particles in the van Allen radiation belts and in solar energetic particle events can damage satellites on orbit leading to malfunctions and loss of satellite service. Here we describe some recent results from the SPACECAST project on modelling and forecasting the radiation belts, and modelling solar energetic particle events. We describe the SPACECAST forecasting system that uses physical models that include wave-particle interactions to forecast the electron radiation belts up to 3 h ahead. We show that the forecasts were able to reproduce the >2 MeV electron flux at GOES 13 during the moderate storm of 7-8 October 2012, and the period following a fast solar wind stream on 25-26 October 2012 to within a factor of 5 or so. At lower energies of 10- a few 100 keV we show that the electron flux at geostationary orbit depends sensitively on the high-energy tail of the source distribution near 10 RE on the nightside of the Earth, and that the source is best represented by a kappa distribution. We present a new model of whistler mode chorus determined from multiple satellite measurements which shows that the effects of wave-particle interactions beyond geostationary orbit are likely to be very significant. We also present radial diffusion coefficients calculated from satellite data at geostationary orbit which vary with Kp by over four orders of magnitude. We describe a new automated method to determine the position at the shock that is magnetically connected to the Earth for modelling solar energetic particle events and which takes into account entropy, and predict the form of the mean free path in the foreshock, and particle injection efficiency at the shock from analytical theory which can be tested in simulations.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

The behavior of money velocity in low and high inflation countries

This paper presents a general equilibrium model of money demand where the velocity of money changes in response to endogenous fluctuations in the interest rate. The parameter space can be divided into two subsets: one where velocity is constant as in standard cash-in-advance models, and another one where velocity fluctuates as in Baumol (1952). The model provides an explanation of why, for a sample of 79 countries, the correlation between the velocity of money and the inflation rate appears to be low, unlike common wisdom would suggest. The reason is the diverse transaction technologies available in different economies.

Orbit decidability and the conjugacy problem for some extensions of groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

Formal deformations of Poisson structures in low dimensions

In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson cohomology space, we solve the deformation equations at each step and obtain a large family of formal deformations for each Poisson structure which we consider. With the help of an explicit formula, we show that this family contains, modulo equivalence, all possible formal eformations. We show moreover that, when the Poisson structure is generic, all members of the family are non-equivalent.