Towards a covariant canonical formulation for closed topological defects without boundaries

On the basis of the covariant description of the canonical formalism for quantization, we present the basic elements of the symplectic geometry for a restricted class of topological defects propagating on a curved background spacetime. We discuss the future extensions of the present results.Comment: LaTeX, 12 pages, submitted to Phys. Lett. B. (2002

Interpreting the photometry and spectroscopy of directly imaged planets: a new atmospheric model applied to beta Pictoris b and SPHERE observations

We aim to interpret future photometric and spectral measurements from these instruments, in terms of physical parameters of the planets, with an atmospheric model using a minimal number of assumptions and parameters. We developed Exoplanet Radiative-convective Equilibrium Model (Exo-REM) to analyze the photometric and spectro- scopic data of directly imaged planets. The input parameters are a planet's surface gravity (g), effective temperature (Teff ), and elemental composition. The model predicts the equilibrium temperature profile and mixing ratio profiles of the most important gases. Opacity sources include the H2-He collision-induced absorption and molecular lines from eight compounds (including CH4 updated with the Exomol line list). Absorption by iron and silicate cloud particles is added above the expected condensation levels with a fixed scale height and a given optical depth at some reference wavelength. Scattering was not included at this stage. We applied Exo-REM to photometric and spectral observations of the planet beta Pictoris b obtained in a series of near-IR filters. We derived Teff = 1550 +- 150 K, log(g) = 3.5 +- 1, and radius R = 1.76 +- 0.24 RJup (2-{\sigma} error bars from photometric measurements). These values are comparable to those found in the literature, although with more conservative error bars, consistent with the model accuracy. We were able to reproduce, within error bars, the J- and H-band spectra of beta Pictoris b. We finally investigated the precision to which the above parameterComment: 15 pages, 14 figures, accepted by A&

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

Understanding amorphous phase-change materials from the viewpoint of Maxwell rigidity

Phase-change materials (PCMs) are the subject of considerable interest because they have been recognized as potential active layers for next-generation non-volatile memory devices, known as Phase Change Random Access Memories (PRAMs). By analyzing First Principles Molecular Dynamics simulations we develop a new method for the enumeration of mechanical constraints in the amorphous phase and show that the phase diagram of the most popular system (Ge-Sb-Te) can be split into two compositional regions having a well-defined mechanical character: a Tellurium rich flexible phase, and a stressed rigid phase that encompasses the known PCMs. This sound atomic scale insight should open new avenues for the understanding of PCMs and other complex amorphous materials from the viewpoint of rigidity.Comment: 5 pages, 4 figures in EP

Rigidity transitions and constraint counting in amorphous networks: beyond the mean-field approach

Subj-class: Disordered Systems and Neural NetworksComment: 12 pages, revtex, 3 figure

Sparse aperture masking at the VLT II. Detection limits for the eight debris disks stars β\beta Pic, AU Mic, 49 Cet, η\eta Tel, Fomalhaut, g Lup, HD181327 and HR8799

Context. The formation of planetary systems is a common, yet complex mechanism. Numerous stars have been identified to possess a debris disk, a proto-planetary disk or a planetary system. The understanding of such formation process requires the study of debris disks. These targets are substantial and particularly suitable for optical and infrared observations. Sparse Aperture masking (SAM) is a high angular resolution technique strongly contributing to probe the region from 30 to 200 mas around the stars. This area is usually unreachable with classical imaging, and the technique also remains highly competitive compared to vortex coronagraphy. Aims. We aim to study debris disks with aperture masking to probe the close environment of the stars. Our goal is either to find low mass companions, or to set detection limits. Methods. We observed eight stars presenting debris disks ( $\beta$ Pictoris, AU Microscopii, 49 Ceti, $\eta$ Telescopii, Fomalhaut, g Lupi, HD181327 and HR8799) with SAM technique on the NaCo instrument at the VLT. Results. No close companions were detected using closure phase information under 0.5 of separation from the parent stars. We obtained magnitude detection limits that we converted to Jupiter masses detection limits using theoretical isochrones from evolutionary models. Conclusions. We derived upper mass limits on the presence of companions in the area of few times the diffraction limit of the telescope around each target star.Comment: 7 pages, All magnitude detection limits maps are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5

3 - 14 Micron Spectroscopy of Comets C/2002 O4 (Honig), C/2002 V1 (NEAT), C/2002 X5 (Kudo-Fujikawa), C/2002 Y1 (Juels-Holvorcem), 69P/Taylor, and the Relationships among Grain Temperature, Silicate Band Strength and Structure among Comet Families

We report 3 - 13 micron spectroscopy of 4 comets observed between August 2002 and February 2003: C/2002 O4 (Honig) on August 1, 2002, C/2002 V1 (NEAT) on Jan. 9 and 10, 2003, C/2002 X5 (Kudo-Fujikawa) on Jan. 9 and 10, 2003, and C/2002 Y1 (Juels-Holvorcem) on Feb. 20, 2003. In addition, we include data obtained much earlier on 69P/Taylor (February 9, 1998) but not previously published. For Comets Taylor, Honig, NEAT, and Kudo-Fujikawa, the silicate emission band was detected, being approximately 23%, 12%, 15%, and 10%, respectively, above the continuum. The data for Comet Juels-Holvorcem were of insufficient quality to detect the presence of a silicate band of comparable strength to the other three objects, and we place an upper limit of 24% on this feature. The silicate features in both NEAT and Kudo-Fujikawa contained structure indicating the presence of crystalline material. Combining these data with those of other comets, we confirm the correlation between silicate band strength and grain temperature of Gehrz & Ney (1992) and Williams et al. (1997) for dynamically new and long period comets, but the majority of Jupiter family objects may deviate from this relation. The limited data available on Jupiter family objects suggest that they may have silicate bands that are slightly different from the former objects. Finally, when compared to the silicate emission bands observed in pre-main sequence stars, the dynamically new and long period comets most closely resemble the more evolved stellar systems, while the limited data (in quantity and quality) on Jupiter family objects seem to suggest that these have spectra more like the less-evolved stars.Comment: 45 pages, 12 figure

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