Torsional birefringence in metric-affine Chern-Simons gravity: gravitational waves in late-time cosmology

In the context of the metric-affine Chern-Simons gravity endowed with projective invariance, we derive analytical solutions for torsion and nonmetricity in the homogeneous and isotropic cosmological case, described by a flat Friedmann-Robertson-Walker metric. We describe in some details the general properties of the cosmological solutions in the presence of a perfect fluid, such as dynamical stability and the settling of big bounce points, and we discuss the structure of some specific solutions reproducing de Sitter and power law behaviours for the scale factor. Then, we focus on first-order perturbations in the de Sitter scenario, and we study the propagation of gravitational waves in the adiabatic limit, looking at tensor and scalar polarizations. In particular, we find that metric tensor modes couple to torsion tensor components, leading to the appearance, as in the metric version of Chern-Simons gravity, of birefringence, described by different dispersion relations for the left and right circularized polarization states. As a result, the purely tensor part of torsion propagates like a wave, while nonmetricity decouples and behaves like a harmonic oscillator. Finally, we discuss scalar modes, outlining as they decay exponentially in time and do not propagate.Comment: References adde

Tactics for Reasoning modulo AC in Coq

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which constant is a neutral element.Comment: 16

Energy radiation of moving cracks

The energy radiated by moving cracks in a discrete background is analyzed. The energy flow through a given surface is expressed in terms of a generalized Poynting vector. The velocity of the crack is determined by the radiation by the crack tip. The radiation becomes more isotropic as the crack velocity approaches the instability threshold.Comment: 7 pages, embedded figure

Positioning a coarse-calibrated camera with respect to an unknown object by 2D 1/2 visual servoing

International audienceIn this paper we propose a new vision-based robot control approach halfway between the classical position-based and image-based visual servoings. It allows to avoid their respective disadvantages. The homography between some planar feature points extracted from two images (corresponding to the current and desired camera poses) is computed at each iteration. Then, an approximate partial-pose, where the translational term is known only up to a scale factor, is deduced, from which can be designed a closed-loop control law controlling the six camera d.o.f.. Contrarily to the position-based visual servoing, our scheme does not need any geometric 3D model of the object. Furthermore and contrarily to the image-based visual servoing, our approach ensures the convergence of the control law in all the task space

Crystallization of Ge2Sb2Te5 nanometric phase change material clusters made by gas-phase condensation

International audienceThe crystallization behavior of Ge2Sb2Te5 nanometric clusters was studied using X-ray diffraction with in situannealing. Clusters were made using a sputtering gas-phase condensation source, which allowed for the growth of well-defined, contaminant-free, and isolated clusters. The average size for the clusters is 5.7 ± 1 nm. As-deposited amorphous clusters crystallize in the fcc cubic phase at 180 °C, while for thin films, the phase change temperature is 155 °C. This observation illustrates the scalability of the Ge2Sb2Te5phase change from the amorphous to the cubic state in three-dimensionally confined systems in this size range

Continuum field description of crack propagation

We develop continuum field model for crack propagation in brittle amorphous solids. The model is represented by equations for elastic displacements combined with the order parameter equation which accounts for the dynamics of defects. This model captures all important phenomenology of crack propagation: crack initiation, propagation, dynamic fracture instability, sound emission, crack branching and fragmentation.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett. Additional information can be obtained from http://gershwin.msd.anl.gov/theor

Crack Front Waves and the dynamics of a rapidly moving crack

Crack front waves are localized waves that propagate along the leading edge of a crack. They are generated by the interaction of a crack with a localized material inhomogeneity. We show that front waves are nonlinear entities that transport energy, generate surface structure and lead to localized velocity fluctuations. Their existence locally imparts inertia, which is not incorporated in current theories of fracture, to initially "massless" cracks. This, coupled to crack instabilities, yields both inhomogeneity and scaling behavior within fracture surface structure.Comment: Embedded Latex file including 4 figure

Elastic forces that do no work and the dynamics of fast cracks

Elastic singularities such as crack tips, when in motion through a medium that is itself vibrating, are subject to forces orthogonal to the direction of motion and thus impossible to determine by energy considerations alone. This fact is used to propose a universal scenario, in which three dimensionality is essential, for the dynamic instability of fast cracks in thin brittle materials.Comment: 8 pages Latex, 1 Postscript figur

A Corona Australis cloud filament seen in NIR scattered light II: Comparison with sub-millimeter data

We study a northern part of the Corona Australis molecular cloud that consists of a filament and a dense sub-millimetre core inside the filament. Our aim is to measure dust temperature and sub-mm emissivity within the region. We also look for confirmation that near-infrared (NIR) surface brightness can be used to study the structure of even very dense clouds. We extend our previous NIR mapping south of the filament. The dust colour temperatures are estimated using Spitzer 160um and APEX/Laboca 870um maps. The column densities derived based on the reddening of background stars, NIR surface brightness, and thermal sub-mm dust emission are compared. A three dimensional toy model of the filament is used to study the effect of anisotropic illumination on near-infrared surface brightness and the reliability of dust temperature determination. Relative to visual extinction, the estimated emissivity at 870um is kappa(870) = (1.3 +- 0.4) x 10^{-5} 1/mag. This is similar to the values found in diffuse medium. A significant increase in the sub-millimetre emissivity seems to be excluded. In spite of saturation, NIR surface brightness was able to accurately pinpoint, and better than measurements of the colour excesses of background stars, the exact location of the column density maximum. Both near- and far-infrared data show that the intensity of the radiation field is higher south of the filament.Comment: 9 pages, 9 figures, accepted to A&

Arrested Cracks in Nonlinear Lattice Models of Brittle Fracture

We generalize lattice models of brittle fracture to arbitrary nonlinear force laws and study the existence of arrested semi-infinite cracks. Unlike what is seen in the discontinuous case studied to date, the range in driving displacement for which these arrested cracks exist is very small. Also, our results indicate that small changes in the vicinity of the crack tip can have an extremely large effect on arrested cracks. Finally, we briefly discuss the possible relevance of our findings to recent experiments.Comment: submitted to PRE, Rapid Communication