Orbit and altimetric corrections for the ERS satellites through analysis of single and dual satellite crossovers

Due to the failure of PRARE the orbital accuracy of ERS-1 is typically 10-15 cm radially as compared to 3-4cm for TOPEX/Poseidon. To gain the most from these simultaneous datasets it is necessary to improve the orbital accuracy of ERS-1 so that it is commensurate with that of TOPEX/Poseidon. For the integration of these two datasets it is also necessary to determine the altimeter and sea state biases for each of the satellites. Several models for the sea state bias of ERS-1 are considered by analysis of the ERS-1 single satellite crossovers. The model adopted consists of the sea state bias as a percentage of the significant wave height, namely 5.95%. The removal of ERS-1 orbit error and recovery of an ERS-1 - TOPEX/Poseidon relative bias are both achieved by analysis of dual crossover residuals. The gravitational field based radial orbit error is modelled by a finite Fourier expansion series with the dominant frequencies determined by analysis of the JGM-2 co-variance matrix. Periodic and secular terms to model the errors due to atmospheric density, solar radiation pressure and initial state vector mis-modelling are also solved for. Validation of the dataset unification consists of comparing the mean sea surface topographies and annual variabilities derived from both the corrected and uncorrected ERS-1 orbits with those derived from TOPEX/Poseidon. The global and regional geographically fixed/variable orbit errors are also analysed pre and post correction, and a significant reduction is noted. Finally the use of dual/single satellite crossovers and repeat pass data, for the calibration of ERS-2 with respect to ERS-1 and TOPEX/Poseidon is shown by calculating the ERS-1/2 sea state and relative biases.

An investigation of the pressaccidic spike potential

A large negative spike potential, which is closely related to the onset of saccadic eyemovements, can be recorded from electrodes adjacent to the orbits. This potential, thepresaccadic spike potential, has often been regarded as an artefact related to eyemovement recordings and little work has been performed to establish its normal waveformand parameters. A positive spike potential, exactly coincident with the frontal negativespike, has also been recorded from electrodes positioned over the posterior scalp andthere has been some debate regarding any possible relationship between the twopotentials. The frontal spike potential has been associated with motor unit activity in theextraocular muscles prior to the saccade. This thesis investigates both the large anteriorand smaller posterior spike potentials and relates these recordings to the saccadic eyemovements associated with them. The anterior spike potential has been recorded from normal subjects to ascertain its normallatency and amplitude parameters for both horizontal and vertical saccades. A relationshipbetween saccade size and spike potential amplitude is described, the spike potentialamplitude reducing with smaller saccades. The potential amplitude also reduces withadvancing age. Studying the topographical distribution of the spike potential across thescalp shows the posterior spike activity may arise from potential spread of the larger frontalspike potential. Spike potential recordings from subjects with anomalous eye movements further implicate the extraocular muscles and their innervation in the generation of the spike potential. These recordings indicate that the spike potential may have some use as a clinical recording from patients with disease conditions affecting either their extraocular muscles or the innervational pathways to these muscles. Further recordings of the potential are necessary, however, to determine the exact nature of the changes which may occur with such conditions.

Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.

On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem

Pólya’s fundamental enumeration theorem and some results from Williamson’s generalized setup of it are proved in terms of Schur- Macdonald’s theory (S-MT) of “invariant matrices”. Given a permutation group W ≤ Sd and a one-dimensional character χ of W , the polynomial functor Fχ corresponding via S-MT to the induced monomial representation Uχ = ind|Sdv/W (χ) of Sd , is studied. It turns out that the characteristic ch(Fχ ) is the weighted inventory of some set J(χ) of W -orbits in the integer-valued hypercube [0, ∞)d . The elements of J(χ) can be distinguished among all W -orbits by a maximum property. The identity ch(Fχ ) = ch(Uχ ) of both characteristics is a consequence of S-MT, and is equivalent to a result of Williamson. Pólya’s theorem can be obtained from the above identity by the specialization χ = 1W , where 1W is the unit character of W.

Neural Control of Chaos and Aplications

Signal processing is an important topic in technological research today. In the areas of nonlinear dynamics search, the endeavor to control or order chaos is an issue that has received increasing attention over the last few years. Increasing interest in neural networks composed of simple processing elements (neurons) has led to widespread use of such networks to control dynamic systems learning. This paper presents backpropagation-based neural network architecture that can be used as a controller to stabilize unsteady periodic orbits. It also presents a neural network-based method for transferring the dynamics among attractors, leading to more efficient system control. The procedure can be applied to every point of the basin, no matter how far away from the attractor they are. Finally, this paper shows how two mixed chaotic signals can be controlled using a backpropagation neural network as a filter to separate and control both signals at the same time. The neural network provides more effective control, overcoming the problems that arise with control feedback methods. Control is more effective because it can be applied to the system at any point, even if it is moving away from the target state, which prevents waiting times. Also control can be applied even if there is little information about the system and remains stable longer even in the presence of random dynamic noise.

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Spectroscopy of Electroproduced Light to Medium Mass Lambda Hypernuclei

The E01-011 experiment at Jefferson Laboratory (JLab) studied light-to-medium mass Λ hypernuclei via the AZ + e → [special characters omitted] + e' + K+ electroproduction reaction. Precise measurement of hypernuclear ground state masses and excitation energies provides information about the nature of hyperon-nucleon interactions. Until recently, hypernuclei were studied at accelerator facilities with intense π+ and K- meson beams. The poor quality of these beams limited the resolution of the hypernuclear excitation energy spectra to about 1.5 MeV (FWHM). This resolution is not sufficient for resolving the rich structure observed in the excitation spectra. By using a high quality electron beam and employing a new high resolution spectrometer system, this study aims to improve the resolution to a few hundred keV with an absolute precision of about 100 keV for excitation energies. In this work the high-resolution excitation spectra of [special characters omitted], and [special characters omitted] hypernuclei are presented. In an attempt to emphasize the presence of the core-excited states we introduced a novel likelihood approach to particle identification (PID) to serve as an alternative to the commonly used standard hard-cut PID. The new method resulted in almost identical missing mass spectra as obtained by the standard approach. An energy resolution of approximately 400–500 keV (FWHM) has been achieved, an unprecedented value in hypernuclear reaction spectroscopy. For [special characters omitted] the core-excited configuration has been clearly observed with significant statistics. The embedded Λ hyperon increases the excitation energies of the 11B nuclear core by 0.5–1 MeV. The [special characters omitted] spectrum has been observed with significant statistics for the first time. The ground state is bound deeper by roughly 400 keV than currently predicted by theory. Indication for the core-excited doublet, which is unbound in the core itself, is observed. The measurement of [special characters omitted] provides the first study of a d-shell hypernucleus with sub-MeV resolution. Discrepancies of up to 2 MeV between measured and theoretically predicted binding energies are found. Similar disagreement exists when comparing to the [special characters omitted] mirror hypernucleus. Also the core-excited structure observed between the major s-, p- and d-shell Λ orbits is not consistent with the available theoretical calculations. In conclusion, the discrepancies found in this study will provide valuable input for the further development of theoretical models.

Estabilização de órbitas periódicas instáveis utilizando controle por modos deslizantes com compensação adaptativa

The chaotic behavior has been widely observed in nature, from physical and chemical phenomena to biological systems, present in many engineering applications and found in both simple mechanical oscillators and advanced communication systems. With regard to mechanical systems, the effects of nonlinearities on the dynamic behavior of the system are often of undesirable character, which has motivated the development of compensation strategies. However, it has been recently found that there are situations in which the richness of nonlinear dynamics becomes attractive. Due to their parametric sensitivity, chaotic systems can suffer considerable changes by small variations on the value of their parameters, which is extremely favorable when we want to give greater flexibility to the controlled system. Hence, we analyze in this work the parametric sensitivity of Duffing oscillator, in particular its unstable periodic orbits and Poincar´e section due to changes in nominal value of the parameter that multiplies the cubic term. Since the amount of energy needed to stabilize Unstable Periodic Orbits is minimum, we analyze the control action needed to control and stabilize such orbits which belong to different versions of the Duffing oscillator. For that we will use a smoothed sliding mode controller with an adaptive compensation term based on Fourier series.

Uma proposta para o ensino das estações do ano com base em um referencial topocêntrico

Studies carried out in several countries have confirmed the students’ difficulty in explaining the causes of the seasons of the year, and most of times their learning takes place incorrectly. The seasons of the year have been generally treated in didactic books apart from people´s routine, based on the heliocentric system, what demands abstraction to understand the phenomenon. Before this difficulty, it is necessary to think about a teaching proposal which allows the students to realize the environmental characteristics and its changes over time, as well as the seasons themselves. Thus, our goal was to work from the perspective of the observer on the terrestrial surface, therefore using the topocentric system. For that, we constructed a didactic sequence, grounded in Ausubel´s meaningful learning theory (2003) and in Moreira´s critical meaningful learning theory (2010), which was applied to students in 9th grade of elementary school and in 2th grade of high school at Escola Estadual Jerônimo Arantes, in Uberlândia, Minas Gerais, owing to their previous knowledge and alternative conceptions, which were collected via interviews. Afterwards, to evaluate the applied methodology, we made new interviews, by which we realized improvement in learning in relation to the characteristics of the seasons based on Sun´s apparent path, which we attribute to reference the change of observation and the means to obtain data on the volume of rainfall and average temperature in the city throughout the year. On the other hand, there are points that were not highlighted in learning, such as the link between winter and rainy season and the causes of the seasons, points left to be discussed in future investigations.

Uma proposta para o ensino das estações do ano com base em um referencial topocêntrico

Studies carried out in several countries have confirmed the students’ difficulty in explaining the causes of the seasons of the year, and most of times their learning takes place incorrectly. The seasons of the year have been generally treated in didactic books apart from people´s routine, based on the heliocentric system, what demands abstraction to understand the phenomenon. Before this difficulty, it is necessary to think about a teaching proposal which allows the students to realize the environmental characteristics and its changes over time, as well as the seasons themselves. Thus, our goal was to work from the perspective of the observer on the terrestrial surface, therefore using the topocentric system. For that, we constructed a didactic sequence, grounded in Ausubel´s meaningful learning theory (2003) and in Moreira´s critical meaningful learning theory (2010), which was applied to students in 9th grade of elementary school and in 2th grade of high school at Escola Estadual Jerônimo Arantes, in Uberlândia, Minas Gerais, owing to their previous knowledge and alternative conceptions, which were collected via interviews. Afterwards, to evaluate the applied methodology, we made new interviews, by which we realized improvement in learning in relation to the characteristics of the seasons based on Sun´s apparent path, which we attribute to reference the change of observation and the means to obtain data on the volume of rainfall and average temperature in the city throughout the year. On the other hand, there are points that were not highlighted in learning, such as the link between winter and rainy season and the causes of the seasons, points left to be discussed in future investigations.

The crowded magnetosphere of the post-common-envelope binary QS Virginis

We present high-speed photometry and high-resolution spectroscopy of the eclipsing post-common-envelope binary QS Virginis (QS Vir). Our Ultraviolet and Visual Echelle Spectrograph (UVES) spectra span multiple orbits over more than a year and reveal the presence of several large prominences passing in front of both the M star and its white dwarf companion, allowing us to triangulate their positions. Despite showing small variations on a time-scale of days, they persist for more than a year and may last decades. One large prominence extends almost three stellar radii from the M star. Roche tomography reveals that the M star is heavily spotted and that these spots are long-lived and in relatively fixed locations, preferentially found on the hemisphere facing the white dwarf. We also determine precise binary and physical parameters for the system. We find that the 14 220 ± 350 K white dwarf is relatively massive, 0.782 ± 0.013 M⊙, and has a radius of 0.010 68 ± 0.000 07 R⊙, consistent with evolutionary models. The tidally distorted M star has a mass of 0.382 ± 0.006 M⊙ and a radius of 0.381 ± 0.003 R⊙, also consistent with evolutionary models. We find that the magnesium absorption line from the white dwarf is broader than expected. This could be due to rotation (implying a spin period of only ˜700 s), or due to a weak (˜100 kG) magnetic field, we favour the latter interpretation. Since the M star's radius is still within its Roche lobe and there is no evidence that it is overinflated, we conclude that QS Vir is most likely a pre-cataclysmic binary just about to become semidetached.

The HARPS-N Rocky Planet Search. I. HD 219134 b: A transiting rocky planet in a multi-planet system at 6.5 pc from the Sun

We know now from radial velocity surveys and transit space missions thatplanets only a few times more massive than our Earth are frequent aroundsolar-type stars. Fundamental questions about their formation history,physical properties, internal structure, and atmosphere composition are,however, still to be solved. We present here the detection of a systemof four low-mass planets around the bright (V = 5.5) and close-by (6.5pc) star HD 219134. This is the first result of the Rocky Planet Searchprogramme with HARPS-N on the Telescopio Nazionale Galileo in La Palma.The inner planet orbits the star in 3.0935 ± 0.0003 days, on aquasi-circular orbit with a semi-major axis of 0.0382 ± 0.0003AU. Spitzer observations allowed us to detect the transit of the planetin front of the star making HD 219134 b the nearest known transitingplanet to date. From the amplitude of the radial velocity variation(2.25 ± 0.22 ms-1) and observed depth of the transit(359 ± 38 ppm), the planet mass and radius are estimated to be4.36 ± 0.44 M⊕ and 1.606 ± 0.086R⊕, leading to a mean density of 5.76 ± 1.09 gcm-3, suggesting a rocky composition. One additional planetwith minimum-mass of 2.78 ± 0.65 M⊕ moves on aclose-in, quasi-circular orbit with a period of 6.767 ± 0.004days. The third planet in the system has a period of 46.66 ± 0.08days and a minimum-mass of 8.94 ± 1.13 M⊕, at0.233 ± 0.002 AU from the star. Its eccentricity is 0.46 ±0.11. The period of this planet is close to the rotational period of thestar estimated from variations of activity indicators (42.3 ± 0.1days). The planetary origin of the signal is, however, thepreferredsolution as no indication of variation at the corresponding frequency isobserved for activity-sensitive parameters. Finally, a fourth additionallonger-period planet of mass of 71 M⊕ orbits the starin 1842 days, on an eccentric orbit (e = 0.34 ± 0.17) at adistance of 2.56 AU.The photometric time series and radial velocities used in this work areavailable in electronic form at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr(ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/584/A72

The perihelion activity of comet 67P/Churyumov-Gerasimenko as seen by robotic telescopes

Around the time of its perihelion passage the observability of 67P/Churyumov-Gerasimenko from Earth was limited to very short windows each morning from any given site, due to the low solar elongation of the comet. The peak in the comet's activity was therefore difficult to observe with conventionally scheduled telescopes, but was possible where service/queue scheduled mode was possible, and with robotic telescopes. We describe the robotic observations that allowed us to measure the total activity of the comet around perihelion, via photometry (dust) and spectroscopy (gas), and compare these results with the measurements at this time by Rosetta's instruments. The peak of activity occurred approximately two weeks after perihelion. The total brightness (dust) largely followed the predictions from Snodgrass et al. 2013, with no significant change in total activity levels from previous apparitions. The CN gas production rate matched previous orbits near perihelion, but appeared to be relatively low later in the year.

Dynamics of coupled modes in two-section semiconductor lasers with saturable absorption

Semiconductor lasers have the potential to address a number of critical applications in advanced telecommunications and signal processing. These include applications that require pulsed output that can be obtained from self-pulsing and mode-locked states of two-section devices with saturable absorption. Many modern applications place stringent performance requirements on the laser source, and a thorough understanding of the physical mechanisms underlying these pulsed modes of operation is therefore highly desirable. In this thesis, we present experimental measurements and numerical simulations of a variety of self-pulsation phenomena in two-section semiconductor lasers with saturable absorption. Our theoretical and numerical results will be based on rate equations for the field intensities and the carrier densities in the two sections of the device, and we establish typical parameter ranges and assess the level of agreement with experiment that can be expected from our models. For each of the physical examples that we consider, our model parameters are consistent with the physical net gain and absorption of the studied devices. Following our introductory chapter, the first system that we consider is a two-section Fabry-Pérot laser. This example serves to introduce our method for obtaining model parameters from the measured material dispersion, and it also allows us to present a detailed discussion of the bifurcation structure that governs the appearance of selfpulsations in two-section devices. In the following two chapters, we present two distinct examples of experimental measurements from dual-mode two-section devices. In each case we have found that single mode self-pulsations evolve into complex coupled dualmode states following a characteristic series of bifurcations. We present optical and mode resolved power spectra as well as a series of characteristic intensity time traces illustrating this progression for each example. Using the results from our study of a twosection Fabry-Pérot device as a guide, we find physically appropriate model parameters that provide qualitative agreement with our experimental results. We highlight the role played by material dispersion and the underlying single mode self-pulsing orbits in determining the observed dynamics, and we use numerical continuation methods to provide a global picture of the governing bifurcation structure. In our concluding chapter we summarise our work, and we discuss how the presented results can inform the development of optimised mode-locked lasers for performance applications in integrated optics.

The SOPHIE search for northern extrasolar planets: X. Detection and characterization of giant planets by the dozen

We present new radial velocity measurements of eight stars that were secured with the spectrograph SOPHIE at the 193 cm telescope of the Haute-Provence Observatory. The measurements allow detecting and characterizing new giant extrasolar planets. The host stars are dwarfs of spectral types between F5 and K0 and magnitudes of between 6.7 and 9.6; the planets have minimum masses Mp sin i of between 0.4 to 3.8 MJup and orbitalperiods of several days to several months. The data allow only single planets to be discovered around the first six stars (HD 143105, HIP 109600, HD 35759, HIP 109384, HD 220842, and HD 12484), but one of them shows the signature of an additional substellar companion in the system. The seventh star, HIP 65407, allows the discovery of two giant planets that orbit just outside the 12:5 resonance in weak mutual interaction. The last star, HD 141399, was already known to host a four-planet system; our additional data and analyses allow new constraints to be set on it. We present Keplerian orbits of all systems, together with dynamical analyses of the two multi-planet systems. HD 143105 is one of the brightest stars known to host a hot Jupiter, which could allow numerous follow-up studies to be conducted even though this is not a transiting system. The giant planets HIP 109600b, HIP 109384b, and HD 141399c are located in the habitable zone of their host star.