Liquid transport in scale space

International audienceWhen a liquid stream is injected into a gaseous atmosphere, it destabilizes and continuously passes through different states characterized by different morphologies. Throughout this process, the flow dynamics may be different depending on the region of the flow and the scales of the involved liquid structures. Exploring this multi-scale, multi-dimensional phenomenon requires some new theoretical tools, some of which need yet to be elaborated. Here, a new analytical framework is proposed on the basis of two-point statistical equations of the liquid volume fraction. This tool, which originates from single phase turbulence, allows us notably to decompose the fluxes of liquid in flow–position space and scale space. Direct numerical simulations of liquid–gas turbulence decaying in a triply periodic domain are then used to characterize the time and scale evolution of the liquid volume fraction. It is emphasized that two-point statistics of the liquid volume fraction depend explicitly on the geometrical properties of the liquid–gas interface and in particular its surface density. The stretch rate of the liquid–gas interface is further shown to be the equivalent for the liquid volume fraction (a non-diffusive scalar) of the scalar dissipation rate. Finally, a decomposition of the transport of liquid in scale space highlights that non-local interactions between non-adjacent scales play a significant role

Liquid transport in scale space

When a liquid stream is injected into a gaseous atmosphere, it destabilizes and continuously passes through different states characterized by different morphologies. Throughout this process, the flow dynamics may be different depending on the region of the flow and the scales of the involved liquid structures. Exploring this multi-scale, multi-dimensional phenomenon requires some new theoretical tools, some of which need yet to be elaborated. Here, a new analytical framework is proposed on the basis of two-point statistical equations of the liquid volume fraction. This tool, which originates from single phase turbulence, allows notably to decompose the fluxes of liquid in flow-position space and scale space. Direct Numerical Simulations of liquid-gas turbulence decaying in a triply periodic domain are then used to characterize the time and scale evolution of the liquid volume fraction. It is emphasized that two-point statistics of the liquid volume fraction depend explicitly on the geometrical properties of the liquid-gas interface and in particular its surface density. The stretch rate of the liquid-gas interface is further shown to be the equivalent for the liquid volume fraction (a non diffusive scalar) of the scalar dissipation rate. Finally, a decomposition of the transport of liquid in scale space highlights that non-local interactions between non adjacent scales play a significant role

Stratified NH and ND emission in the prestellar core 16293E in L1689N

Context. High degrees of deuterium fractionation are commonly found in cold prestellar cores and in the envelopes around young protostars. As it brings strong constraints to chemical models, deuterium chemistry is often used to infer core history or molecule formation pathways. Whereas a large number of observations are available regarding interstellar deuterated stable molecules, relatively little is known about the deuteration of hydride radicals, as their fundamental rotational transitions are at high frequencies where the atmosphere is mostly opaque. Aims. Nitrogen hydride radicals are important species in nitrogen chemistry, as they are thought to be related to ammonia formation. Observations have shown that ammonia is strongly deuterated, with [NH_2D]/[NH_3] ~ 10%. Models predict similarly high [ND]/[NH] ratios, but so far only one observational determination of this ratio is available, towards the envelope of the protostar IRAS16293-2422. To test model predictions, we aim here to determine [ND]/[NH] in a dense, starless core. Methods. We observed NH and ND in 16293E with the HIFI spectrometer on board the Herschel Space Observatory as part of the CHESS guaranteed time key programme, and derived the abundances of these two species using a non local thermodynamic equilibrium radiative transfer model. Results. Both NH and ND are detected in the source, with ND in emission and NH in absorption against the continuum that arises from the cold dust emission. Our model shows, however, that the ND emission and the NH absorption originate from different layers in the cloud, as further evidenced by their different velocities. In the central region of the core, we can set a lower limit to the [ND]/[NH] ratio of ≳2%. This estimate is consistent with recent pure gas-phase models of nitrogen chemistry

Dense molecular gas toward W49A: A template for extragalactic starbursts?

The HCN, HCO+, and HNC molecules are commonly used as tracers of dense star-forming gas in external galaxies, but such observations are spatially unresolved. Reliably inferring the properties of galactic nuclei and disks requires detailed studies of sources whose structure is spatially resolved. We compare the spatial distributions and abundance ratios of HCN, HCO+, and HNC in W49A, the most massive and luminous star-forming region in the Galactic disk, based on maps of a 2' (6.6 pc) field at 14" (0.83 pc) resolution of the J=4-3 transitions of HCN, H13CN, HC15N, HCO+, H13CO+, HC18O+ and HNC. The kinematics of the molecular gas in W49A appears complex, with a mixture of infall and outflow motions. Both the line profiles and comparison of the main and rarer species show that the main species are optically thick. Two 'clumps' of infalling gas appear to be at ~40 K, compared to ~100 K at the source centre, and may be ~10x denser than the rest of the outer cloud. Chemical modelling suggests that the HCN/HNC ratio probes the current gas temperature, while the HCN/HCO+ ratio and the deuterium fractionation were set during an earlier, colder phase of evolution. The data suggest that W49A is an appropriate analogue of an extragalactic star forming region. Our data show that the use of HCN/HNC/HCO+ line ratios as proxies for the abundance ratios is incorrect for W49A, suggesting the same for galactic nuclei. Our observed isotopic line ratios such as H13CN/H13CO+ approach our modeled abundance ratios quite well in W49A. The 4-3 lines of HCN and HCO+ are much better tracers of the dense star-forming gas in W49A than the 1-0 lines. Our observed HCN/HNC and HCN/HCO+ ratios in W49A are inconsistent with homogeneous PDR or XDR models, indicating that irradiation hardly affects the gas chemistry in W49A. Overall, the W49A region appears to be a useful template for starburst galaxies.Comment: Accepted by A&A; 17 pages, 15 figure

Extended warm and dense gas towards W49A: starburst conditions in our Galaxy?

The star formation rates in starburst galaxies are orders of magnitude higher than in local star-forming regions, and the origin of this difference is not well understood. We use sub-mm spectral line maps to characterize the physical conditions of the molecular gas in the luminous Galactic star-forming region W49A and compare them with the conditions in starburst galaxies. We probe the temperature and density structure of W49A using H_2CO and HCN line ratios over a 2'x2' (6.6x6.6 pc) field with an angular resolution of 15" (~0.8 pc) provided by the JCMT Spectral Legacy Survey. We analyze the rotation diagrams of lines with multiple transitions with corrections for optical depth and beam dilution, and estimate excitation temperatures and column densities. Comparing the observed line intensity ratios with non-LTE radiative transfer models, our results reveal an extended region (about 1'x1', equivalent to ~3x3 pc at the distance of W49A) of warm (> 100 K) and dense (>10^5 cm^-3) molecular gas, with a mass of 2x10^4 - 2x10^5 M_Sun (by applying abundances derived for other regions of massive star-formation). These temperatures and densities in W49A are comparable to those found in clouds near the center of the Milky Way and in starburst galaxies. The highly excited gas is likely to be heated via shocks from the stellar winds of embedded, O-type stars or alternatively due to UV irradiation, or possibly a combination of these two processes. Cosmic rays, X-ray irradiation and gas-grain collisional heating are less likely to be the source of the heating in the case of W49A.Comment: Accepted for publication in A&A; 11 pages, 9 figure

Social networks and labour productivity in Europe: An empirical investigation

This paper uses firm-level data recorded in the AMADEUS database to investigate the distribution of labour productivity in different European countries. We find that the upper tail of the empirical productivity distributions follows a decaying power-law, whose exponent $\alpha$ is obtained by a semi-parametric estimation technique recently developed by Clementi et al. (2006). The emergence of "fat tails" in productivity distribution has already been detected in Di Matteo et al. (2005) and explained by means of a model of social network. Here we show that this model is tested on a broader sample of countries having different patterns of social network structure. These different social attitudes, measured using a social capital indicator, reflect in the power-law exponent estimates, verifying in this way the existence of linkages among firms' productivity performance and social network.Comment: LaTeX2e; 18 pages with 3 figures; Journal of Economic Interaction and Coordination, in pres

On the influence of collisional rate coefficients on the water vapour excitation

Water is a key molecule in many astrophysical studies. Its high dipole moment makes this molecule to be subthermally populated under the typical conditions of most astrophysical objects. This motivated the calculation of various sets of collisional rate coefficients (CRC) for H$_2$O (with He or H$_2$) which are necessary to model its rotational excitation and line emission. We performed accurate non--local non--LTE radiative transfer calculations using different sets of CRC in order to predict the line intensities from transitions that involve the lowest energy levels of H$_2$O (E $<$ 900 K). The results obtained from the different CRC sets are then compared using line intensity ratio statistics. For the whole range of physical conditions considered in this work, we obtain that the intensities based on the quantum and QCT CRC are in good agreement. However, at relatively low H$_2$ volume density ($n$(H$_2$) $<$ 10$^7$ cm$^{-3}$) and low water abundance ($\chi$(H$_2$O) $<$ 10$^{-6}$), these physical conditions being relevant to describe most molecular clouds, we find differences in the predicted line intensities of up to a factor of $\sim$ 3 for the bulk of the lines. Most of the recent studies interpreting early Herschel Space Observatory spectra used the QCT CRC. Our results show that although the global conclusions from those studies will not be drastically changed, each case has to be considered individually, since depending on the physical conditions, the use of the QCT CRC may lead to a mis--estimate of the water vapour abundance of up to a factor of $\sim$ 3

Molecular excitation in the Interstellar Medium: recent advances in collisional, radiative and chemical processes

We review the different excitation processes in the interstellar mediumComment: Accepted in Chem. Re

Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Study of mass and momentum transfer in diesel sprays base on X-ray mass distribution measurements and on a theoretical derivation

[EN] In this paper, a research aimed at quantifying mass and momentum transfer in the near-nozzle field of diesel sprays injected into stagnant ambient air is reported. The study combines X-ray measurements for two different nozzles and axial positions, which provide mass distributions in the spray, with a theoretical model based on momentum flux conservation, which was previously validated. This investigation has allowed the validation of Gaussian profiles for local fuel concentration and velocity near the nozzle exit, as well as the determination of Schmidt number at realistic diesel spray conditions. 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