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General theorems concerning the strong consistency of the MLE of exponential mixture parameters are proved. These theorems imply the strong consistency of the MLE of normal mixture parameters when the data is organized into fields each of which is a random sample from one of the component normal distributions.
The evolution of weak disturbances in inert binary mixtures is determined for the one-dimensional piston problem. The interaction of the dissipative and nonlinear mechanisms is described by Burgers' equation. The binary mixture diffusion mechanisms enter as an additive term in an effective diffusivity. Results for the impulsive motion of a piston moving into an ambient medium and the sinusoidally oscillating piston are used to illustrate the results and elucidate the incorrect behavior pertaining to the associated linear theory.
Recent measurements on the dielectric constants of soil-water mixtures show the existence of two frequency regions in which the dielectric behavior of these mixtures was quite different. At the frequencies of 1.4 GHz to 5 GHz, there were strong evidences that the variations of the dielectric (epsilon) with water content (W) depended on soil type. While the real part of epsilon for sandy soils rose rapidly with the increase in W, epsilon for the high-clay content soils rose only slowly with W. As a consequence, epsilon was generally higher for the sandy soils than for the high-clay content soils at a given W. On the other hand, most of the measurements at frequencies 1 GHz indicated the increase of epsilon with W independent of soil types. At a given W, epsilon' (sandy soil) approximately equals epsilon (high-clay content soil) within the precision of the measurements. These observational features can be satisfactorily interpreted in terms of a simple dielectric relaxation model, with an appropriate choice of the mean relaxation frequency f(m) and the range of the activation energy (beta). It was found that smaller f(m) and larger beta were required for the high-clay content soils than the sandy soils in order to be consistent with the measured data.
This work explores the concept of blackbody radiation pumping of CO2 gas as a step toward utilization of solar radiation as a pumping source for laser action. To demonstrate this concept, an experiment was performed in which laser gas mixtures were exposed to 1500 K thermal radiation for brief periods of time. A gain of 2.8 x 10 to the -3rd reciprocal centimeters has been measured at 10.6 microns in a CO2-He gas mixture of 1 Torr pressure. A simple analytical model is used to describe the rate of change of energy of the vibrational modes of CO2 and to predict the gain. Agreement between the prediction and experiment is good.
Adsorption interference in binary and ternary mixtures of trace contaminants in a helium carrier gas flowing through activated carbon adsorber beds are studied. The isothermal transmission, which is the ratio of the outlet to the inlet concentration, of each component is measured. Interference between co-adsorbing gases occurs when the components are adsorbed strongly. Displacement of one component by another is manifested by a transmission greater than unity for the displaced component over some range of eluted volume. Interference is evidenced not only by a reduction of the adsorption capacity of each component in the mixture in comparison with the value obtained in a single-component experiment, but also by a change in the slope of the transmission curve of each component experiment.
The so-called miscibility gap that exists below the critical point in liquid He-3 - H-4 mixtures makes it possible to study binary phase composition, and the ensuing dispersions, in a system possessing an additional order parameter in one of the components. The physical behavior of a superfluid dispersion produced by pressure quenching an He-3 - He-4 mixture into the miscibility gap is described. The description applies both to quenches of homogeneous and phase-separated initial states in various regions of the miscibility gap.
Corrosion of SAE 310 stainless steel in H2-H2O-H2S gas mixtures was studied at a constant temperature of 1150 K. Reactive gas mixtures were chosen to yield a constant oxygen potential of approximately 6 x 10 to the minus 13th power/cu Nm and sulfur potentials ranging from 0.19 x 10 to the minus 2nd power/cu Nm to 33 x 10 to the minus 2nd power/cu Nm. The kinetics of corrosion were determined using a thermobalance, and the scales were analyzed using metallography, scanning electron microscopy, and energy dispersive X-ray analysis. Two corrosion regimes, which were dependent on sulfur potential, were identified. At high sulfur potentials (p sub S sub 2 less than or equal to 2.7 x 10 to the minus 2nd power/cu Nm) the corrosion rates were high, the kinetics obeyed a linear rate equation, and the scales consisted mainly of sulfide phases similar to those observed from pure sulfication. At low sulfur potentials (P sub S sub 2 less than or equal to 0.19 x 10 to the minus 2nd power/cu Nm) the corrosion rates were low, the kinetics obeyed a parabolic rate equation, and scales consisted mainly of oxide phases.
An analysis was conducted of the effect of flameholding devices on the precombustion fuel-air characteristics and on oxides of nitrogen (NOx) emissions for combustion of premixed partially vaporized mixtures. The analysis includes the interrelationships of flameholder droplet collection efficiency, reatomization efficiency and blockage, and the initial droplet size distribution and accounts for the contribution of droplet combustion in partially vaporized mixtures to NOx emissions. Application of the analytical procedures is illustrated and parametric predictions of NOx emissions are presented.
The similarity solutions of a strong shock wave propagation in a mixture of a gas and small solid particles have been investigated. Similarity solution exists only when the shock is very strong and the surrounding medium is of a constant density and at rest and with negligible counterpressure. The non-dimensional fundamental equations are derived and studied. The results depend on three non-dimensional parameters; i.e. (1) the ratio of the specific heats of the gas, (2) the mass concentration of the solid particles in the mixture and (3) the ratio of the density of the solid to that of initial density of the gas. Numerical solutions for various values of these parameters are presented and discussed. The speeds of the shock wave front and its location with various energy releases are given.
Laboratory reflectance spectra in the 0.325-2.5 micron region of bound water, water-mineral mixtures, mineral grains on frost, and frost on minerals are presented. The materials used in this study are montmorillonite, kaolinite, beryl, Mauna Kea red cinder, and black charcoal. It is found that the wavelengths of bound water and bound OH absorptions do not shift appreciably with temperature and can be detected when large amounts of free water ice are present. The decrease in the visible reflectance seen in many planetary reflectance spectra containing strong water ice absorptions can be explained by water-mineral mixtures, mineral grains on frost, or frost on mineral grains. Mineral grains on frost are detectable in very small quantities (fractional areal coverage less than approximately 0.005) depending on the mineral reflectance features, while it takes a thick layer of frost (greater than approximately 1 mm) to mask a mineral below 1.4 microns, again depending on the mineral reflectance. Frost on a very dark surface (albedo about 6%) is easily seen; however, a dark mineral mixed with water could completely mask the water absorptions (shortward of 2.5 microns).
A method is proposed for predicting the translational component of the thermal conductivity of partially ionized gas mixtures. It is approximate but simple in form and offers a significant improvement over commonly utilized approximations. It does not require large computer run times nor storage, thus it is suitable for use with complex flow fields and heat transfer calculations. Results for gas mixtures which are representative of the atmosphere of Jupiter, Earth, and Venus are presented and they compare favorably with results from detailed kinetic theory analyses.
The evaluation of the thermodynamic properties of a gas mixture can be performed using a generalized correlation which makes use of the second virial coefficient. This coefficient is based on statistical mechanics and is a function of temperature and composition, but not of pressure. The method provides results accurate to within 3 percent for gases which are nonpolar or only slightly polar. When applied to highly polar gases, errors of 5 to 10 percent may result. For gases which associate, even larger errors are possible. The sequences of calculations can be routinely programmed for a digital computer. The thermodynamic properties of a mixture of neon, argon and ethane were calculated by such a program. The result will be used for the design of the gas replenishment system for the Energetic Gamma Ray Experiment Telescope.
A Gaussian mixture density arises when a discrete variable (e.g., a photodetector count variable) is added to a continuous Gaussian variable (e.g., thermal noise). Making use of some properties of photomultiplier Gaussian mixture distributions, some approximate error probability formulas can be derived. These appear as averages of M-ary orthogonal Gaussian error probabilities. The use of a pure Gaussian assumption is considered, and when properly defined, appears as an accurate upper bound to performance.
Some candidates for alkali metal and alkali halide mixtures suitable for thermal energy storage at temperatures 600 C are identified. A solar thermal system application which offer advantages such as precipitation of salt crystals away from heat transfer surfaces, increased thermal conductivity of phase change materials, corrosion inhibition, and a constant monotectic temperature, independent of mixture concentrations. By using the lighters, metal rich phase as a heat transfer medium and the denser, salt rich phase as a phase change material for latent heat storage, undesirable solidification on the heat transfer surface may be prevented, is presented.
Recent ion-induced nucleation studies in a binary mixture of H2O and H2SO4 vapors indicate that conventional classical nucleation theories cannot account for the experimentally observed ion-H2O-H2SO4 microcluster spectra. An empirical-analytical, semi-molecular theory of nucleation of a binary mixture of vapors on ions has been developed. This theory includes molecular approach to ion-induced changes in dielectric properties in the immediate neighborhood of an ion core as well as the size dependence of the surface tension of the microcluster. In addition to gaseous sulfuric acid and water molecules, the effect of ion-hydrates and sulfuric acid hydrates has also been considered. This theory is further simplified by using an empirical correction factor for the electrostatic term. This correction factor has been obtained by comparing the simplified model with the molecular dynamics calculations for selected ion hydrate formation. These two theoretical models are then compared with the classical theory for a variety of experimental conditions.
A physical-chemical model is developed and used to investigate gaseous absorption by water droplets from trace gas mixtures. The model is an extension of that of Carmichael and Peters (1979) and includes the simultaneous absorption of SO2, NH3, HNO3, CO2, and HCl. Gas phase depletion is also considered. Presented results demonstrate that the absorption behavior of raindrops is strongly dependent on drop size, fall distance, trace gas concentrations, and the chemical and physical properties of the constituents of the mixture. In addition, when gas phase depletion is considered, the absorption rates and equilibrium values are also dependent on the precipitation rate itself. Also, the trace constituents liquid phase concentrations may be a factor of six or more lower when gas depletion is considered then when the depletion is ignored. However, the hydrogen ion concentration may be insensitive to the gas phase depletion.
Flame configurations, flame-front cellular instability, and extinction of propane/air mixtures in the stagnation-point flow are experimentally studied for their dependence on downstream heat loss, preferential diffusion, and flame stretch. Boundaries for lean- and rich-limit extinction, stabilization of corrugated flames, and local extinction caused by sharp curvatures are mapped for varying propane concentrations and freestream velocities. Flame location and temperature at extinction are determined as functions of stagnation surface temperature, extent of preheating, propane concentration, and freestream velocity. Results substantiate the theoretical predictions of the different extinction modes for lean and rich flames in the absence of downstream heat loss, and yield useful insight on the extinction characteristics when finite downstream heat loss does exist. It is further shown that flame-front instability occurs only for rich mixtures in accordance with preferential diffusion considerations, and that flame stretch has a stabilizing effect such that flame-front instability is completely inhibited before the onset of extinction.
Alkali metal and alkali halide mixtures are identified which may be suitable for thermal energy storage at temperatures above 600 C. The use of metal-halides is appropriate because of their tendency to form two immiscible melts with a density difference, which reduces scale formation and solidification on heat transfer surfaces. Also, the accumulation of phase change material along the melt interface is avoided by the self-dispersing characteristic of some metal-halides, in particular Sr-SrCl2, Ba-BaCl2, and Ba-BaBr2 mixtures. Further advantages lie in their high thermal conductivities, ability to cope with thermal shock, corrosion inhibition, and possibly higher energy densities.