Characteristics of transitional multicomponent gaseous and drop-laden mixing layers from direct numerical simulation: Composition effects

Transitional states are obtained by exercising a model of multicomponent-liquid (MC-liquid) drop evaporation in a three-dimensional mixing layer at larger Reynolds numbers, Re, than in a previous study. The gas phase is followed in an Eulerian frame and the multitude of drops is described in a Lagrangian frame. Complete dynamic and thermodynamic coupling between phases is included. The liquid composition, initially specified as a single-Gamma (SG) probability distribution function (PDF) depending on the molar mass, is allowed to evolve into a linear combination of two SGPDFs, called the double-Gamma PDF (DGPDF). The compositions of liquid and vapor emanating from the drops are calculated through four moments of their PDFs, which are drop-specific and location-specific, respectively. The mixing layer is initially excited to promote the double pairing of its four initial spanwise vortices, resulting into an ultimate vortex in which small scales proliferate. Simulations are performed for four liquids of different compositions, and the effects of the initial mass loading and initial free-stream gas temperature are explored. For reference, simulations are also performed for gaseous multicomponent mixing layers for which the effect of Re is investigated in the direct-numerical-simulation–accessible regime. The results encompass examination of the global layer characteristics, flow visualizations, and homogeneous-plane statistics at transition. Comparisons are performed with previous pretransitional MC-liquid simulations and with transitional single-component (SC) liquid-drop-laden mixing layer studies. Contrasting to pretransitional MC flows, the vorticity and drop organization depend on the initial gas temperature, this being due to drop/turbulence coupling. The vapor-composition mean molar mass and standard deviation distributions strongly correlate with the initial liquid-composition PDF. Unlike in pretransitional situations, regions of large composition standard deviation no longer necessarily coincide with those of large mean molar mass. The rotational and composition characteristics are all liquid-specific and the variation among liquids is amplified with increasing free-stream gas temperature. The classical energy cascade is found to be of similar strength, but the smallest scales contain orders of magnitude less energy than SC flows, which is confirmed by the larger viscous dissipation for MC flows. The kinetic energy and dissipation are liquid-specific and the variation among liquids is amplified with increasing free-stream gas temperature. The gas composition, of which the first four moments are calculated, is shown to be close to, but distinct from, a SGPDF. Eulerian and Lagrangian statistics of gas-phase quantities show that the different observation framework may affect the perception of the flow

Asymptotic laws for compositions derived from transformed subordinators

A random composition of $n$ appears when the points of a random closed set $\widetilde{\mathcal{R}}\subset[0,1]$ are used to separate into blocks $n$ points sampled from the uniform distribution. We study the number of parts $K_n$ of this composition and other related functionals under the assumption that $\widetilde{\mathcal{R}}=\phi(S_{\bullet})$, where $(S_t,t\geq0)$ is a subordinator and $\phi:[0,\infty]\to[0,1]$ is a diffeomorphism. We derive the asymptotics of $K_n$ when the L\'{e}vy measure of the subordinator is regularly varying at 0 with positive index. Specializing to the case of exponential function $\phi(x)=1-e^{-x}$, we establish a connection between the asymptotics of $K_n$ and the exponential functional of the subordinator.Comment: Published at http://dx.doi.org/10.1214/009117905000000639 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Electron dynamics in InNxSb1–x

Electron transport properties in InNxSb1–x are investigated for a range of alloy compositions. The band structure of InNxSb1–x is modeled using a modified k·p Hamiltonian. This enables the semiconductor statistics for a given x value to be calculated from the dispersion relation of the E– subband. These calculations reveal that for alloy compositions in the range 0.001<=x<=0.02 there is only a small variation of the carrier concentration at a given plasma frequency. A similar trend is observed for the effective mass at the Fermi level. Measurements of the plasma frequency and plasmon lifetime for InNxSb1–x alloys enable the carrier concentration and the effective mass at the Fermi level to be determined and a lower limit for the electron mobility to be estimated

Baseline groundwater chemistry : the Sherwood Sandstone of Devon and Somerset

This report describes the regional geochemistry of groundwater from the Sherwood Sandstone aquifer of Devon and Somerset. In order to assess the likely natural baseline chemistry of the groundwater in the area, information has been gathered from the strategic collection of 21 new groundwater samples, and from collation of existing groundwater, rainfall, mineralogical and geochemical data. The Sherwood Sandstone aquifer results from continental deposition during the early Triassic period. The deposition comprised thick clastic deposits in basins created during the late Permian. There are two distinct units: the Otter Sandstone Formation and the underlying Budleigh Salterton Pebble Beds Formation. These units form the most important aquifer in south-west England. The main chemical properties of the groundwater are determined by rainwater recharge reacting with the aquifer minerals. Of these minerals carbonates are the dominant influence on the water chemistry. While Ca is dominant in groundwaters from both aquifer units, the water types from the two units can be distinguished: the Otter Sandstone Formation aquifer has mainly Ca-HCO3 type waters, with some mixing towards Mg, and the groundwaters in the Budleigh Salterton Pebble Beds Formation aquifer are of Ca-HCO3 type to Na+K-Cl type. There is little variation in the major ion proportion of the groundwaters from the Otter Sandstone Formation, most likely as these represent groundwater in equilibrium with the minerals which give it this character. There is greater variation in the Budleigh Salterton Pebble Beds Formation groundwaters. Besides the difference in groundwater types, the groundwater from the Budleigh Salterton Pebble Beds Formation is more acidic, more oxic, has lower SEC values, and HCO3, Cr, U and Mg concentrations, and higher concentrations of Al, Be, Cd, Cr, Co, Tl and REE than the groundwater from the Otter Sandstone Formation. Human impacts on the water quality are evident. These are mainly visible in the presence of indicator contaminants, such as nitrate. The widespread presence and changes of nitrate concentrations over time indicate the extent to which the unconfined aquifer is influenced by modern farming practices or urban pollution. Concentrations of NO3-N exceeded the current drinking water limit of 11.3 mg L-1 in 25% of the sampled groundwaters, which probably reflects the intensification of agriculture in the study area over the last few decades. Indeed, the dominant land uses of the area are agriculture and grassland. However, recent legislation and the drive towards intelligent farming have meant that in some groundwaters the concentrations of nitrate are decreasing. While many of the groundwaters investigated in this study are of good inorganic quality there are some notable exceptions which contain elevated concentrations of Fe, SO4, Ni, Co and NO3. The distribution of the poor-quality is generally so sporadic that water quality would be difficult to predict prior to drilling a borehole. For many analytes, the 95th percentile of the distributions has been taken as a first approximation of an upper limit of baseline concentrations as this serves to eliminate the most extreme outlier concentrations that likely represent a distinct population

Modelling Spatial Compositional Data: Reconstructions of past land cover and uncertainties

In this paper, we construct a hierarchical model for spatial compositional data, which is used to reconstruct past land-cover compositions (in terms of coniferous forest, broadleaved forest, and unforested/open land) for five time periods during the past $6\,000$ years over Europe. The model consists of a Gaussian Markov Random Field (GMRF) with Dirichlet observations. A block updated Markov chain Monte Carlo (MCMC), including an adaptive Metropolis adjusted Langevin step, is used to estimate model parameters. The sparse precision matrix in the GMRF provides computational advantages leading to a fast MCMC algorithm. Reconstructions are obtained by combining pollen-based estimates of vegetation cover at a limited number of locations with scenarios of past deforestation and output from a dynamic vegetation model. To evaluate uncertainties in the predictions a novel way of constructing joint confidence regions for the entire composition at each prediction location is proposed. The hierarchical model's ability to reconstruct past land cover is evaluated through cross validation for all time periods, and by comparing reconstructions for the recent past to a present day European forest map. The evaluation results are promising and the model is able to capture known structures in past land-cover compositions

The Bernoulli sieve revisited

We consider an occupancy scheme in which "balls" are identified with $n$ points sampled from the standard exponential distribution, while the role of "boxes" is played by the spacings induced by an independent random walk with positive and nonlattice steps. We discuss the asymptotic behavior of five quantities: the index $K_n^*$ of the last occupied box, the number $K_n$ of occupied boxes, the number $K_{n,0}$ of empty boxes whose index is at most $K_n^*$, the index $W_n$ of the first empty box and the number of balls $Z_n$ in the last occupied box. It is shown that the limiting distribution of properly scaled and centered $K_n^*$ coincides with that of the number of renewals not exceeding $\log n$. A similar result is shown for $K_n$ and $W_n$ under a side condition that prevents occurrence of very small boxes. The condition also ensures that $K_{n,0}$ converges in distribution. Limiting results for $Z_n$ are established under an assumption of regular variation.Comment: Published in at http://dx.doi.org/10.1214/08-AAP592 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Coordinated Analyses of Presolar Grains in the Allan Hills 77307 and Queen Elizabeth Range 99177 Meteorites

We report the identification of presolar silicates (~177 ppm), presolar oxides (~11 ppm), and one presolar SiO2 grain in the Allan Hills (ALHA) 77307 chondrite. Three grains having Si isotopic compositions similar to SiC X and Z grains were also identified, though the mineral phases are unconfirmed. Similar abundances of presolar silicates (~152 ppm) and oxides (~8 ppm) were also uncovered in the primitive CR chondrite Queen Elizabeth Range (QUE) 99177, along with 13 presolar SiC grains and one presolar silicon nitride. The O isotopic compositions of the presolar silicates and oxides indicate that most of the grains condensed in low-mass red giant and asymptotic giant branch stars. Interestingly, unlike presolar oxides, few presolar silicate grains have isotopic compositions pointing to low-metallicity, low-mass stars (Group 3). The 18O-rich (Group 4) silicates, along with the few Group 3 silicates that were identified, likely have origins in supernova outflows. This is supported by their O and Si isotopic compositions. Elemental compositions for 74 presolar silicate grains were determined by scanning Auger spectroscopy. Most of the grains have non-stoichiometric elemental compositions inconsistent with pyroxene or olivine, the phases commonly used to fit astronomical spectra, and have comparable Mg and Fe contents. Non-equilibrium condensation and/or secondary alteration could produce the high Fe contents. Transmission electron microscopic analysis of three silicate grains also reveals non-stoichiometric compositions, attributable to non-equilibrium or multistep condensation, and very fine scale elemental heterogeneity, possibly due to subsequent annealing. The mineralogies of presolar silicates identified in meteorites thus far seem to differ from those in interplanetary dust particles.Comment: 23 pages, 16 figure