Confirmation of Lagrange Hypothesis for Twisted Elastic Rod

The history of structural optimization as an exact science begins possibly with the celebrated Lagrange problem: to find a curve which by its revolution about an axis in its plane determines the rod of greatest efficiency. The Lagrange hypothesis, that the optimal rod possesses the constant cross-section was abandoned for Euler buckling problem. In this Article the Lagrange hypothesis is proved to be valid for Greenhill's problem of torque buckling. The corresponding isoperimetric inequality is affirmed.Comment: 4 page

Gas Absorption Detected from the Edge-on Debris Disk Surrounding HD32297

Near-infrared and optical imaging of HD32297 indicate that it has an edge-on debris disk, similar to beta Pic. I present high resolution optical spectra of the NaI doublet toward HD32297 and stars in close angular proximity. A circumstellar absorption component is clearly observed toward HD32297 at the stellar radial velocity, which is not observed toward any of its neighbors, including the nearest only 0.9 arcmin away. An interstellar component is detected in all stars >90 pc, including HD32297, likely due to the interstellar material at the boundary of the Local Bubble. Radial velocity measurements of the nearest neighbors, BD+07 777s and BD+07 778, indicate that they are unlikely to be physically associated with HD32297. The measured circumstellar column density around HD32997, log N(NaI) ~ 11.4, is the strongest NaI absorption measured toward any nearby main sequence debris disk, even the prototypical edge-on debris disk, beta Pic. Assuming that the morphology and abundances of the gas component around HD32297 are similar to beta Pic, I estimate an upper limit to the gas mass in the circumstellar disk surrounding HD32297 of ~0.3 M_Earth.Comment: 13 pages, 2 figures; Accepted for publication in ApJ Letter

Deep imaging survey of young, nearby austral stars: VLT/NACO near-infrared Lyot-coronographic observations

Context. High contrast and high angular resolution imaging is the optimal search technique for substellar companions to nearby stars at physical separations larger than typically 10 AU. Two distinct populations of substellar companions, brown dwarfs and planets, can be probed and characterized. As a result, fossile traces of processes of formation and evolution can be revealed by physical and orbital properties, both for individual systems and as an ensemble. Aims. Since November 2002, we have conducted a large, deep imaging, survey of young, nearby associations of the southern hemisphere. Our goal is detection and characterization of substellar companions with projected separations in the range 10–500 AU. We have observed a sample of 88 stars, primarily G to M dwarfs, younger than 100 Myr, and within 100 pc of Earth. Methods. The VLT/NACO adaptive optics instrument of the ESO Paranal Observatory was used to explore the faint circumstellar environment between typically 0.1 and 10". Diffraction-limited observations in H and K_s-band combined with Lyot-coronagraphy enabled us to reach primary star-companion brightness ratios as small as 10^(-6). The existence of planetary mass companions could therefore be probed. We used a standardized observing sequence to precisely measure the position and flux of all detected sources relative to their visual primary star. Repeated observations at several epochs enabled us to discriminate comoving companions from background objects. Results. We report the discovery of 17 new close (0.1–5.0") multiple systems. HIP 108195 AB and C (F1 III-M6), HIP 84642 AB (a~14 AU, K0-M5) and TWA22 AB (a~1.8 AU; M6-M6) are confirmed comoving systems. TWA22 AB is likely to be a rare astrometric calibrator that can be used to test evolutionary model predictions. Among our complete sample, a total of 65 targets were observed with deep coronagraphic imaging. About 240 faint companion candidates were detected around 36 stars. Follow-up observations with VLT or HST for 83% of these stars enabled us to identify a large fraction of background contaminants. Our latest results that pertain to the substellar companions to GSC 08047-00232, AB Pic and 2M1207 (confirmed during this survey and published earlier), are reviewed. Finally, a statistical analysis of our complete set of coronagraphic detection limits enables us to place constraints on the physical and orbital properties of giant planets between typically 20 and 150 AU

Laser-Induced Skyrmion Writing and Erasing in an Ultrafast Cryo-Lorentz Transmission Electron Microscopy

We demonstrate that light-induced heat pulses of different duration and energy can write skyrmions in a broad range of temperatures and magnetic field in FeGe. Using a combination of camera-rate and pump-probe cryo-Lorentz Transmission Electron Microscopy, we directly resolve the spatio-temporal evolution of the magnetization ensuing optical excitation. The skyrmion lattice was found to maintain its structural properties during the laser-induced demagnetization, and its recovery to the initial state happened in the sub-{\mu}s to {\mu}s range, depending on the cooling rate of the system

A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram

Crystal structure and chemistry of barium-graphite intercalation compounds

Graphite can accommodate various chemical species between graphene layers to form graphite intercalation compounds (GIC) [1]. Alkali metals can easily lead to bulk stage-1 intercalation compounds by vapor transport but for more electronegative elements, such as alkaline-earth metals or lanthanides, only a superficial intercalation is obtained and other synthesis methods have to be envisaged. Molten alloys, formed between an alkali metal and the targeted metal, have demonstrated their efficiency to prepare bulk and homogeneous GIC from these latter elements, for example the superconducting CaC6 phase [2], but some elements remain difficult to intercalate by this method. More recently, our team developed a method based on the work of Hagiwara et al., consisting in using a LiCl-KCl eutectic molten medium [3], which for example allowed to prepare for the first time a bulk SrC6 compound [4]. This work is focused on the intercalation of barium into graphite from the LiCl-KCl molten salts method. A bulk stage-1 BaC6 compound has been prepared and X-ray diffraction measurements confirmed its crystal structure [5]. Moreover, by varying the experimental conditions, two completely novel phases, denoted α and β, have been isolated. From ion beam analyses, Li0,2K0,6Ba0,35C6 and Li0,2K0,75Ba0,6C6 chemical formulae have been determined for α and β phases, respectively, showing that lithium and potassium are intercalated together with barium. X- ray diffraction led to the determination of the stacking sequence of each compound, and their planar unit cells. Lastly, a reaction mechanism is proposed, which explains the formation of the different phases observed in this study

On Virtual Displacement and Virtual Work in Lagrangian Dynamics

The confusion and ambiguity encountered by students, in understanding virtual displacement and virtual work, is discussed in this article. A definition of virtual displacement is presented that allows one to express them explicitly for holonomic (velocity independent), non-holonomic (velocity dependent), scleronomous (time independent) and rheonomous (time dependent) constraints. It is observed that for holonomic, scleronomous constraints, the virtual displacements are the displacements allowed by the constraints. However, this is not so for a general class of constraints. For simple physical systems, it is shown that, the work done by the constraint forces on virtual displacements is zero. This motivates Lagrange's extension of d'Alembert's principle to system of particles in constrained motion. However a similar zero work principle does not hold for the allowed displacements. It is also demonstrated that d'Alembert's principle of zero virtual work is necessary for the solvability of a constrained mechanical problem. We identify this special class of constraints, physically realized and solvable, as {\it the ideal constraints}. The concept of virtual displacement and the principle of zero virtual work by constraint forces are central to both Lagrange's method of undetermined multipliers, and Lagrange's equations in generalized coordinates.Comment: 12 pages, 10 figures. This article is based on an earlier article physics/0410123. It includes new figures, equations and logical conten

Students’ Evolving Meaning About Tangent Line with the Mediation of a Dynamic Geometry Environment and an Instructional Example Space

In this paper I report a lengthy episode from a teaching experiment in which fifteen Year 12 Greek students negotiated their definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the notion of derivative and to the general case of tangent to a function graph. Its design was based on previous research results on students’ perspectives on tangency, especially in their transition from Geometry to Analysis. In this experiment an instructional example space of functions was used in an electronic environment utilising Dynamic Geometry software with Function Grapher tools. Following the Vygotskian approach according to which students’ knowledge develops in specific social and cultural contexts, students’ construction of the meaning of tangent line was observed in the classroom throughout the experiment. The analysis of the classroom data collected during the experiment focused on the evolution of students’ personal meanings about tangent line of function graph in relation to: the electronic environment; the pre-prepared as well as spontaneous examples; students’ engagement in classroom discussion; and, the role of researcher as a teacher. The analysis indicated that the evolution of students’ meanings towards a more sophisticated understanding of tangency was not linear. Also it was interrelated with the evolution of the meaning they had about the inscriptions in the electronic environment; the instructional example space; the classroom discussion; and, the role of the teacher

Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories

We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, that can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form, so as to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that is at basis of the analytic part of the Nekhoroshev's theorem, so as to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller.Comment: 31 pages, 2 figures. arXiv admin note: text overlap with arXiv:1010.260

A new interferometric study of four exoplanet host stars : {\theta} Cygni, 14 Andromedae, {\upsilon} Andromedae and 42 Draconis

Studying exoplanet host stars is of the utmost importance to establish the link between the presence of exoplanets around various types of stars and to understand the respective evolution of stars and exoplanets. Using the limb-darkened diameter (LDD) obtained from interferometric data, we determine the fundamental parameters of four exoplanet host stars. We are particularly interested in the F4 main-sequence star, {\theta} Cyg, for which Kepler has recently revealed solar-like oscillations that are unexpected for this type of star. Furthermore, recent photometric and spectroscopic measurements with SOPHIE and ELODIE (OHP) show evidence of a quasi-periodic radial velocity of \sim150 days. Models of this periodic change in radial velocity predict either a complex planetary system orbiting the star, or a new and unidentified stellar pulsation mode. We performed interferometric observations of {\theta} Cyg, 14 Andromedae, {\upsilon} Andromedae and 42 Draconis for two years with VEGA/CHARA (Mount Wilson, California) in several three-telescope configurations. We measured accurate limb darkened diameters and derived their radius, mass and temperature using empirical laws. We obtain new accurate fundamental parameters for stars 14 And, {\upsilon} And and 42 Dra. We also obtained limb darkened diameters with a minimum precision of \sim 1.3%, leading to minimum planet masses of Msini=5.33\pm 0.57, 0.62 \pm 0.09 and 3.79\pm0.29 MJup for 14 And b, {\upsilon} And b and 42 Dra b, respectively. The interferometric measurements of {\theta} Cyg show a significant diameter variability that remains unexplained up to now. We propose that the presence of these discrepancies in the interferometric data is caused by either an intrinsic variation of the star or an unknown close companion orbiting around it.Comment: 10 pages + 2 pages appendix, 16 figures, accepted for publication in A&