Generalized Galilean Algebras and Newtonian Gravity

The non-relativistic versions of the generalized Poincar\'{e} algebras and generalized $AdS$-Lorentz algebras are obtained. This non-relativistic algebras are called, generalized Galilean algebras type I and type II and denoted by $\mathcal{G}\mathfrak{B}_{n}$ and $\mathcal{G}\mathfrak{L}_{_{n}}$ respectively. Using a generalized In\"{o}n\"{u}--Wigner contraction procedure we find that the generalized Galilean algebras type I can be obtained from the generalized Galilean algebras type II. The $S$-expansion procedure allows us to find the $\mathcal{G}\mathfrak{B}_{_{5}}$ algebra from the Newton--Hooke algebra with central extension. The procedure developed in Ref. \cite{newton} allow us to show that the non-relativistic limit of the five dimensional Einstein--Chern--Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.Comment: 16 pages, no figures in 755 (2016) 433-43

Non-adiabatic effects in long-pulse mixed-field orientation of a linear polar molecule

We present a theoretical study of the impact of an electrostatic field combined with non-resonant linearly polarized laser pulses on the rotational dynamics of linear molecules. Within the rigid rotor approximation, we solve the time-dependent Schr\"odinger equation for several field configurations. Using the OCS molecule as prototype, the field-dressed dynamics is analyzed in detail for experimentally accessible static field strengths and laser pulses. Results for directional cosines are presented and compared to the predictions of the adiabatic theory. We demonstrate that for prototypical field configuration used in current mixed-field orientation experiments, the molecular field dynamics is, in general, non-adiabatic, being mandatory a time-dependent description of these systems. We investigate several field regimes identifying the sources of non-adiabatic effects, and provide the field parameters under which the adiabatic dynamics would be achieved.Comment: 16 pages, 16 figures. Submitted to Physical Review

Strongly driven quantum pendulum of the OCS molecule

We demonstrate and analyze a strongly driven quantum pendulum in the angular motion of stateselected and laser aligned OCS molecules. Raman-couplings during the rising edge of a 50-picosecond laser pulse create a wave packet of pendular states, which propagates in the confining potential formed by the polarizability interaction between the molecule and the laser field. This wave-packet dynamics manifests itself as pronounced oscillations in the degree of alignment with a laser-intensity dependent period.Comment: 6 pages, 4 figure

Accretion and photodesorption of CO ice as a function of the incident angle of deposition

Non-thermal desorption of inter- and circum-stellar ice mantles on dust grains, in particular ultraviolet photon-induced desorption, has gained importance in recent years. These processes may account for the observed gas phase abundances of molecules like CO toward cold interstellar clouds. Ice mantle growth results from gas molecules impinging on the dust from all directions and incidence angles. Nevertheless, the effect of the incident angle for deposition on ice photo-desorption rate has not been studied. This work explores the impact on the accretion and photodesorption rates of the incidence angle of CO gas molecules with the cold surface during deposition of a CO ice layer. Infrared spectroscopy monitored CO ice upon deposition at different angles, ultraviolet-irradiation, and subsequent warm-up. Vacuum-ultraviolet spectroscopy and a Ni-mesh measured the emission of the ultraviolet lamp. Molecules ejected from the ice to the gas during irradiation or warm-up were characterized by a quadrupole mass spectrometer. The photodesorption rate of CO ice deposited at 11 K and different incident angles was rather stable between 0 and 45$^{\circ}$. A maximum in the CO photodesorption rate appeared around 70$^{\circ}$-incidence deposition angle. The same deposition angle leads to the maximum surface area of water ice. Although this study of the surface area could not be performed for CO ice, the similar angle dependence in the photodesorption and the ice surface area suggests that they are closely related. Further evidence for a dependence of CO ice morphology on deposition angle is provided by thermal desorption of CO ice experiments

A comparative study of root system architecture in seedlings of Brachypodium spp. using three plant growth supports

This work reports a rapid procedure of comparing root development among different genotypes of Brachypodium spp., using three plant growth supports: gel chamber, ‘Termita’ chamber and Whatman paper. Eight variables of the root system architecture (RSA) (number of seminal roots, number of lateral roots, total length of the roots, length of the primary root, mean diameter of the roots, mean diameter of the primary root, total surface area and total volume of the roots) were studied in seedling of four genotypes each of Brachypodium distachyon, B. stacei and B. hybridum. Correlations between pairs of growth supports in terms of the eight variables examined were highly significant. In all three supports, B. stacei showed the greatest root system development while B. distachyon showed the least; B. hybridum, an allotetraploid species derived from hybridization between B. distachyon and B. stacei, showed intermediate development. ANOVA and LSD tests showed that significant differences exist between the supports, species and genotypes with respect to all the variables analysed. A cluster analysis was conducted to determine if the RSA traits could be used to differentiate the species and genotypes of Brachypodium. This analysis allowed differentiated between the three species and twelve genotypes of Brachypodium spp., although a certain overlap between species was observed. The Whatman paper support was the easiest to use, and is recommended for the characterization of large collections of genotypes

Main-Sequence and sub-giant stars in the Globular Cluster NGC6397: The complex evolution of the lithium abundance

Thanks to the high multiplex and efficiency of Giraffe at the VLT we have been able for the first time to observe the Li I doublet in the Main Sequence (MS) stars of a Globular Cluster. At the same time we observed Li in a sample of Sub-Giant (SG) stars of the same B-V colour. Our final sample is composed of 84 SG stars and 79 MS stars. In spite of the fact that SG and MS span the same temperature range we find that the equivalent widths of the Li I doublet in SG stars are systematically larger than those in MS stars, suggesting a higher Li content among SG stars. This is confirmed by our quantitative analysis. We derived the effective temperatures, from H$\alpha$ fitting, and NLTE Li abundances of the stars in our the sample, using 3D and 1D models. We find that SG stars have a mean Li abundance higher by 0.1dex than MS stars, using both 1D and 3D models. We also detect a positive slope of Li abundance with effective temperature. These results provide an unambiguous evidence that the Li abundance changes with evolutionary status. The physical mechanisms responsible for this behaviour are not yet clear, and none of the existing models seems to describe accurately these observations. Based on these conclusions, we believe that the cosmological lithium problem still remains an open question.Comment: Proceedings of the contributed talk presented at the IAU Symposium 26

CNO behaviour in planet-harbouring stars. II. Carbon abundances in stars with and without planets using the CH band

Context. Carbon, oxygen and nitrogen (CNO) are key elements in stellar formation and evolution, and their abundances should also have a significant impact on planetary formation and evolution. Aims. We present a detailed spectroscopic analysis of 1110 solar-type stars, 143 of which are known to have planetary companions. We have determined the carbon abundances of these stars and investigate a possible connection between C and the presence of planetary companions. Methods. We used the HARPS spectrograph to obtain high-resolution optical spectra of our targets. Spectral synthesis of the CH band at 4300\AA was performed with the spectral synthesis codes MOOG and FITTING. Results. We have studied carbon in several reliable spectral windows and have obtained abundances and distributions that show that planet host stars are carbon rich when compared to single stars, a signature caused by the known metal-rich nature of stars with planets. We find no different behaviour when separating the stars by the mass of the planetary companion. Conclusions. We conclude that reliable carbon abundances can be derived for solar-type stars from the CH band at 4300\AA. We confirm two different slope trends for [C/Fe] with [Fe/H] because the behaviour is opposite for stars above and below solar values. We observe a flat distribution of the [C/Fe] ratio for all planetary masses, a finding that apparently excludes any clear connection between the [C/Fe] abundance ratio and planetary mass.Comment: 10 pages, 10 figures. Accepted to A&

From circular paths to elliptic orbits: A geometric approach to Kepler's motion

The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.Comment: 9 pages, 4 figure

C/O vs Mg/Si ratios in solar type stars: The HARPS sample

Aims. We present a detailed study of the Mg/Si and C/O ratios and their importance in determining the mineralogy of planetary companions. Methods. Using 499 solar-like stars from the HARPS sample, we determine C/O and Mg/Si elemental abundance ratios to study the nature of the possible planets formed. We separated the planetary population in low-mass planets ( < 30 $\rm M_{\odot}$) and high-mass planets ( > 30 $\rm M_{\odot}$) to test for possible relation with the mass. Results. We find a diversity of mineralogical ratios that reveal the different kinds of planetary systems that can be formed, most of them dissimilar to our solar system. The different values of the Mg/Si and C/O ratios can determine different composition of planets formed. We found that 100\% of our planetary sample present C/O < 0.8. 86\% of stars with high-mass companions present 0.8 > C/O > 0.4, while 14\% present C/O values lower than 0.4. Regarding Mg/Si, all stars with low-mass planetary companion showed values between 1 and 2, while 85% of the high-mass companion sample does. The other 15\% showed Mg/Si values below 1. No stars with planets were found with Mg/Si > 2. Planet hosts with low-mass companions present C/O and Mg/Si ratios similar to those found in the Sun, whereas stars with high-mass companions have lower C/O.Comment: 9 pages, 12 figues. Accepted in A&