More Than 1700 Years of Word Equations

Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical study of word equations began only in the 20th century. So, the title of the present article does not seem to be justified at all. However, a linear Diophantine equation can be viewed as a special case of a system of word equations over a unary alphabet, and, more importantly, a word equation can be viewed as a special case of a Diophantine equation. Hence, the problem WordEquations: "Is a given word equation solvable?" is intimately related to Hilbert's 10th problem on the solvability of Diophantine equations. This became clear to the Russian school of mathematics at the latest in the mid 1960s, after which a systematic study of that relation began. Here, we review some recent developments which led to an amazingly simple decision procedure for WordEquations, and to the description of the set of all solutions as an EDT0L language.Comment: The paper will appear as an invited address in the LNCS proceedings of CAI 2015, Stuttgart, Germany, September 1 - 4, 201

Selective conversion of nitroarenes using a carbon nanotube-ruthenium nanohybrid

International audienceRuthenium nanoparticles were assembled on carbon nanotubes and the resulting nanohybrid was used in the hydrazine-mediated catalytic hydrogenation of various nitroarenes, at room temperature. Depending on the solvent, a selective transformation occurred, giving either access to the corresponding aniline or hydroxylamine derivative

Room temperature Suzuki coupling of aryl iodides, bromides, and chlorides using a heterogeneous carbon nanotube-palladium nanohybrid catalyst

International audiencePalladium nanoparticles were immobilized on multi-walled carbon nanotubes by a layer-by-layer approach, resulting in a well-defined assembly. The nanohybrid was found effective in promoting Suzuki cross couplings of various halogenated aromatics, including chlorinated ones, with arylboronic acids under sustainable conditions. The heterogeneous catalyst could also easily be recovered from the reaction mixture and reused with no loss of activity over several cycles

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

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&

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

Far-Infrared to Millimeter Astrophysical Dust Emission. II: Comparison of the Two-Level Systems (TLS) model with Astronomical Data

In a previous paper we proposed a new model for the emission by amorphous astronomical dust grains, based on solid-state physics. The model uses a description of the Disordered Charge Distribution (DCD) combined with the presence of Two-Level Systems (TLS) defects in the amorphous solid composing the grains. The goal of this paper is to confront this new model to astronomical observations of different Galactic environments in the FIR/submm, in order to derive a set of canonical model parameters to be used as a Galactic reference to be compared to in future Galactic and extragalactic studies. We confront the TLS model with existing astronomical data. We consider the average emission spectrum at high latitudes in our Galaxy as measured with FIRAS and WMAP, as well as the emission from Galactic compact sources observed with Archeops, for which an inverse relationship between the dust temperature and the emissivity spectral index has been evidenced. We show that, unlike models previously proposed which often invoke two dust components at different temperatures, the TLS model successfully reproduces both the shape of the Galactic SED and its evolution with temperature as observed in the Archeops data. The best TLS model parameters indicate a charge coherence length of \simeq 13 nm and other model parameters in broad agreement with expectations from laboratory studies of dust analogs. We conclude that the millimeter excess emission, which is often attributed to the presence of very cold dust in the diffuse ISM, is likely caused solely by TLS emission in disordered amorphous dust grains. We discuss the implications of the new model, in terms of mass determinations from millimeter continuum observations and the expected variations of the emissivity spectral index with wavelength and dust temperature. The implications for the analysis of the Herschel and Planck satellite data are discussed.Comment: Accepted for publication in A&A (16 pages, 9 figures, 6 tables

A Corona Australis cloud filament seen in NIR scattered light I. Comparison with extinction of background stars

With current near-infrared (NIR) instruments the near-infrared light scattered from interstellar clouds can be mapped over large areas. The surface brightness carries information on the line-of-sight dust column density. Therefore, scattered light could provide an important tool to study mass distribution in quiescent interstellar clouds at a high, even sub-arcsecond resolution. We wish to confirm the assumption that light scattering dominates the surface brightness in all NIR bands. Furthermore, we want to show that scattered light can be used for an accurate estimation of dust column densities in clouds with Av in the range 1-15mag. We have obtained NIR images of a quiescent filament in the Corona Australis molecular cloud. The observations provide maps of diffuse surface brightness in J, H, and Ks bands. Using the assumption that signal is caused by scattered light we convert surface brightness data into a map of dust column density. The same observations provide colour excesses for a large number of background stars. These data are used to derive an extinction map of the cloud. The two, largely independent tracers of the cloud structure are compared. Results. In regions below Av=15m both diffuse surface brightness and background stars lead to similar column density estimates. The existing differences can be explained as a result of normal observational errors and bias in the sampling of extinctions provided by the background stars. There is no indication that thermal dust emission would have a significant contribution even in the Ks band. The results show that, below Av=15mag, scattered light does provide a reliable way to map cloud structure. Compared with the use of background stars it can also in practice provide a significantly higher spatial resolution.Comment: 14 pages, 15 figures, accepted to A&A, the version includes small changes in the text and an added appendi

Submillimeter Emission from Water in the W3 Region

We have mapped the submillimeter emission from the 1(10)-1(01) transition of ortho-water in the W3 star-forming region. A 5'x5' map of the W3 IRS4 and W3 IRS5 region reveals strong water lines at half the positions in the map. The relative strength of the Odin lines compared to previous observations by SWAS suggests that we are seeing water emission from an extended region. Across much of the map the lines are double-peaked, with an absorption feature at -39 km/s; however, some positions in the map show a single strong line at -43 km/s. We interpret the double-peaked lines as arising from optically thick, self-absorbed water emission near the W3 IRS5, while the narrower blue-shifted lines originate in emission near W3 IRS4. In this model, the unusual appearance of the spectral lines across the map results from a coincidental agreement in velocity between the emission near W3 IRS4 and the blue peak of the more complex lines near W3 IRS5. The strength of the water lines near W3 IRS4 suggests we may be seeing water emission enhanced in a photon-dominated region.Comment: Accepted to A&A Letters as part of the special Odin issue; 4 page