Dynamics of two planets in co-orbital motion

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities; we also assume that both planets share the same orbital plane. Initially, we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analysed in more detail using a semi-analytical model. Apart from the well-known quasi-satellite orbits and the classical equilibrium Lagrangian points L(4) and L(5), we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at (delta lambda, delta pi) = (+/- 60 degrees, -/+ 120 degrees), where delta lambda is the difference in mean longitudes and delta pi is the difference in longitudes of pericentre. The position of these anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities and are found for eccentricities as high as similar to 0.7. Finally, we also applied a slow mass variation to one of the planets and analysed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.

Precession and nutation in the eta Carinae binary system: evidence from the X-ray light curve

It is believed that eta Carinae is actually a massive binary system, with the wind-wind interaction responsible for the strong X-ray emission. Although the overall shape of the X-ray light curve can be explained by the high eccentricity of the binary orbit, other features like the asymmetry near periastron passage and the short quasi-periodic oscillations seen at those epochs have not yet been accounted for. In this paper we explain these features assuming that the rotation axis of eta Carinae is not perpendicular to the orbital plane of the binary system. As a consequence, the companion star will face eta Carinae on the orbital plane at different latitudes for different orbital phases and, since both the mass-loss rate and the wind velocity are latitude dependent, they would produce the observed asymmetries in the X-ray flux. We were able to reproduce the main features of the X-ray light curve assuming that the rotation axis of eta Carinae forms an angle of 29 degrees +/- 4 degrees with the axis of the binary orbit. We also explained the short quasi-periodic oscillations by assuming nutation of the rotation axis, with an amplitude of about 5 degrees and a period of about 22 days. The nutation parameters, as well as the precession of the apsis, with a period of about 274 years, are consistent with what is expected from the torques induced by the companion star.

Two-dimensional electron states bound to an off-plane donor in a magnetic field

The states of an electron confined in a two-dimensional (2D) plane and bound to an off-plane donor impurity center, in the presence of a magnetic field, are investigated. The energy levels of the ground state and the first three excited states are calculated variationally. The binding energy and the mean orbital radius of these states are obtained as a function of the donor center position and the magnetic field strength. The limiting cases are discussed for an in-plane donor impurity (i.e. a 2D hydrogen atom) as well as for the donor center far away from the 2D plane in strong magnetic fields, which corresponds to a 2D harmonic oscillator.

A retrospective study of zygomatico-orbital complex and/or zygomatic arch fractures over a 71-month period

Background/Aim: The aim of this retrospective study was to evaluate the epidemiology, treatment, and complications of zygomatico-orbital complex (ZOC) and/or zygomatic arch (ZA) fractures either associated with other facial fractures or not over a 71-month period. Material and methods: This survey was performed in three hospitals of Ribeirao Preto in Sao Paulo, Brazil, from August 2002 to July 2008. The records of 1575 patients with facial trauma were reviewed. There were 140 cases of ZOC and ZA fractures either associated with other facial fractures or not. Data regarding gender, age, race, addictions, day of trauma, etiology, signs and symptoms, oral hygiene condition, day of initial evaluation, hospital admission, day of surgery, surgery approach, pattern of fractures, treatment performed, post-operative antibiotic therapy, day of hospital discharge, and post-operative complications were collected. The data were subjected to descriptive statistical analyses. Results: The most frequent fractures affected Caucasian men and occurred during the fourth decade of life. The most frequent etiology was traffic accident, and symptoms and signs included pain and edema. Type I fractures were the main injury observed, and the treatment of choice was always rigid internal fixation. Post-operative antibiotic therapy was solely employed when there was an indication. Complications were observed in 13.1% of the cases. Conclusions: The treatment protocol yielded suitable post-operative results and also showed success rates comparable to published data around the world.

Reliability of orbital fits for resonant extrasolar planetary systems: the case of HD82943

We perform a statistical study of the process of orbital determination of the HD82943 extrasolar planetary system, using the current observational data set of N = 165 radial velocity (RV) measurements. Our aim is to analyse the dispersion of possible orbital fits leading to residuals compatible with the best solution, and to discuss the sensitivity of the results with respect to both the data set and the error distribution around the best fit. Although some orbital parameters (e.g. semimajor axis) appear well constrained, we show that the best fits for the HD82943 system are not robust, and at present it is not possible to estimate reliable solutions for these bodies. Finally, we discuss the possibility of a third planet, with a mass of 0.35M(Jup) and an orbital period of 900 d. Stability analysis and simulations of planetary migration indicate that such a hypothetical three-planet system could be locked in a double 2/1 mean-motion resonance, similar to the so-called Laplace resonance of the three inner Galilean satellites of Jupiter.

The extreme physical properties of the CoRoT-7b super-Earth

The search for rocky exoplanets plays an important role in our quest for extra-terrestrial life. Here, we discuss the extreme physical properties possible for the first characterised rocky super-Earth, CoRoT-7b (R(pl) = 1.58 +/- 0.10 R(Earth), M(pl) = 6.9 +/- 1.2 M(Earth)). It is extremely close to its star (a = 0.0171 AU = 4.48 R(st)), with its spin and orbital rotation likely synchronised. The comparison of its location in the (M(pl), R(pl)) plane with the predictions of planetary models for different compositions points to an Earth-like composition, even if the error bars of the measured quantities and the partial degeneracy of the models prevent a definitive conclusion. The proximity to its star provides an additional constraint on the model. It implies a high extreme-UV flux and particle wind, and the corresponding efficient erosion of the planetary atmosphere especially for volatile species including water. Consequently, we make the working hypothesis that the planet is rocky with no volatiles in its atmosphere, and derive the physical properties that result. As a consequence, the atmosphere is made of rocky vapours with a very low pressure (P <= 1.5 Pa), no cloud can be sustained, and no thermalisation of the planet is expected. The dayside is very hot (2474 +/- 71 K at the sub-stellar point) while the nightside is very cold (50-75 K). The sub-stellar point is as hot as the tungsten filament of an incandescent bulb, resulting in the melting and distillation of silicate rocks and the formation of a lava ocean. These possible features of CoRoT-7b could be common to many small and hot planets, including the recently discovered Kepler-10b. They define a new class of objects that we propose to name ""Lava-ocean planets"". (C) 2011 Elsevier Inc. All rights reserved.

Constraining the orbital orientation of eta Carinae from H Paschen lines

During the past decade, several observational and theoretical works have provided evidence of the binary nature of eta Carinae. Nevertheless, there is still no direct determination of the orbital parameters, and the different current models give contradictory results. The orbit is, in general, assumed to coincide with the Homunculus equator although the observations are not conclusive. Among all systems, eta Car has the advantage that it is possible to observe both the direct emission of line transitions in the central source and its reflection by the Homunculus, which is dependent on the orbital inclination. In this work, we studied the orbital phase-dependent hydrogen Paschen spectra reflected by the south-east lobe of the Homunculus to constrain the orbital parameters of eta Car and determine its inclination with respect to the Homunculus axis. Assuming that the emission excess originates in the wind-wind shock region, we were able to model the latitude dependence of the spectral line profiles. For the first time, we were able to estimate the orbital inclination of eta Car with respect to the observer and to the Homunculus axis. The best fit occurs for an orbital inclination to the line of sight of i similar to 60 degrees +/- 10 degrees, and i* similar to 35 degrees +/- 10 degrees with respect to the Homunculus axis, indicating that the angular momenta of the central object and the orbit are not aligned. We were also able to fix the phase angle of conjunction as similar to -40 degrees, showing that periastron passage occurs shortly after conjunction.

DETECTABILITY AND ERROR ESTIMATION IN ORBITAL FITS OF RESONANT EXTRASOLAR PLANETS

We estimate the conditions for detectability of two planets in a 2/1 mean-motion resonance from radial velocity data, as a function of their masses, number of observations and the signal-to-noise ratio. Even for a data set of the order of 100 observations and standard deviations of the order of a few meters per second, we find that Jovian-size resonant planets are difficult to detect if the masses of the planets differ by a factor larger than similar to 4. This is consistent with the present population of real exosystems in the 2/1 commensurability, most of which have resonant pairs with similar minimum masses, and could indicate that many other resonant systems exist, but are currently beyond the detectability limit. Furthermore, we analyze the error distribution in masses and orbital elements of orbital fits from synthetic data sets for resonant planets in the 2/1 commensurability. For various mass ratios and number of data points we find that the eccentricity of the outer planet is systematically overestimated, although the inner planet`s eccentricity suffers a much smaller effect. If the initial conditions correspond to small-amplitude oscillations around stable apsidal corotation resonances, the amplitudes estimated from the orbital fits are biased toward larger amplitudes, in accordance to results found in real resonant extrasolar systems.

Plane curve diagrams and geometrical applications

We look at plane curve diagrams (f,alpha), which are given by a plane curve multigerm alpha : (R, S) -> R(2) and a function on it f : (R, S) -> R. We obtain a classification of all such diagrams, where alpha has e-codimension <= 2 and f has finite order. Then we define an equivalence between plane curves which we call Ah(alpha)-equivalence and which is determined by the class of the diagram (h(alpha), alpha). Here, h alpha denotes the height function of alpha with respect to its normal vector. This is an equivalence which not only takes into account the topology of the singularity of alpha, but also its flat geometry. Finally, we apply our results in order to obtain a classification of all the plane projections of a generic space curve gamma embedded in R(3).

Influence of quantum-dots density on average in-plane strain of optoelectronic devices investigated by high-resolution X-ray diffraction

High-resolution X-ray diffractometry is used to probe the nature of a diffraction-peak broadening previously noticed in quantum dots (QDs) systems with freestanding InAs islands on top of GaAs (001) substrates [Freitas et al., Phys. Status Solidi (A) 204, 2548 (2007)]. The procedure is hence extended to further investigate the capping process of InAs/GaAs QDs. A direct correlation is established between QDs growth rates and misorientation of lattice-planes at the samples surfaces. This effect provides an alternative too] for studying average strain fields on QDs systems in standard triple axis diffractometers running on X-ray tube sources, which are much more common than synchrotron facilities. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Synthesis, mechanism of formation, and molecular orbital calculations of arylamidoximes

A simple and easy synthesis of ten arylamidoximes from arylnitriles and hydroxylamine is described. The formation of the arylamides has been observed to a much lesser extent in the present work. A new mechanism for the formation of arylamidoximes, as well as arylamides, from arylnitriles and hydroxylamine is suggested. Quantum mechanical calculations have been carried out to support this mechanism. The enthalpy of formation in conjunction with atomic charges of the reactants and intermediates helped to understand more about the generation of the products.

Structural, electronic, and magnetic entropy contributions of the orbital order-disorder transition in LaMnO(3)

Measurements of X-ray diffraction, electrical resistivity, and magnetization are reported across the Jahn-Teller phase transition in LaMnO(3). Using a thermodynamic equation, we obtained the pressure derivative of the critical temperature (T(JT)), dT(JT)/dP = -28.3 K GPa(-1). This approach also reveals that 5.7(3)J(mol K)(-1) comes from the volume change and 0.8(2)J(mol K)(-1) from the magnetic exchange interaction change across the phase transition. Around T(JT), a robust increase in the electrical conductivity takes place and the electronic entropy change, which is assumed to be negligible for the majority of electronic systems, was found to be 1.8(3)J(mol K)(-1).

Electric field gradients in (111)In-doped (Hf/Zr)(3)Al(2) and (Hf/Zr)(4)Al(3) mixed compounds: ab initio calculations, perturbed angular correlation measurements and site preference

The quadrupolar hyperfine interactions of in-diffused (111)In -> (111)Cd probes in polycrystalline isostructural Zr(4)Al(3) and Hf(4)Al(3) samples containing small admixtures of the phases (Zr/Hf)(3)Al(2) were investigated. A strong preference of (111)In solutes for the contaminant (Zr/Hf)(3)Al(2) minority phases was observed. Detailed calculations of the electric field gradient (EFG) at the Cd nucleus using the full-potential augmented plane wave + local orbital formalism allowed us to assign the observed EFG fractions to the various lattice sites in the (Zr/Hf)(3)Al(2) compounds and to understand the preferential site occupation of the minority phases by the (111)In atoms. The effects of the size of the supercell and relaxation around the oversized In and Cd probe atoms were investigated in detail.

Semiclassical and quantum motions on the non-commutative plane

We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man`ko states and circular squeezed states. The relation between these states and the ""classical"" trajectories is investigated, and we present numerical explorations of some semiclassical quantities. (C) 2009 Elsevier B.V. All rights reserved.

The electronic and optical properties of sodalite (Na(8)Al(6)Si(6)O(24)Cl(2)) from first principles

This study reports the results of ab initio electronic and optical calculations for pure socialite crystal using the linear augmented plane wave (LAPW) method within density functional theory (DFT). The calculated electronic structure revealed predominantly orbital characters of the valence band and the conduction band, and enabled us to determine the type and the value of the fundamental gap of the compound. The imaginary part of the dielectric tensor, extinction coefficient and refraction index were calculated as functions of the incident radiation wavelength. It is shown that the O 2p states and Na 3s states play the major role in optical transitions as initial and final states, respectively. The absorption spectrum is localized in the ultraviolet range between 40 and 250 nm. Furthermore, we concluded that the material does not absorb radiation in the visible range. (C) 2009 Elsevier Ltd. All rights reserved.