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The density function and corresponding moments for the ratio of correlated gamma distributed variates were derived. A class of bivariate gamma distributions was also considered, and additional distributional results which use this class of functions were also derived. Similar results, by using a different class of bivariate gamma distributions, are presented.
We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson’s theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs–Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born–Oppenheimer molecular dynamics performed at a single temperature. In conclusion, this advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function.
Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-Z expansions for the corresponding energies of neutral atoms with atomic number Z and electron number N = Z, which are correct to leading order (–0.221 Z 5/3 and –0.021 Z ln Z respectively) even in the lowest-rung or local density approximation. We find that hydrogenic densities lead to E x (N,Z) ≈ –0.354 N 2/3 Z (as known before only for Z >> N >> 1) and E c ≈ –0.02 N ln N . These asymptotic estimates are most correct for atomic ions with large N and Z >> N, but we find that they are qualitatively and semi- quantitatively correct even for small N and for N ≈ Z. The large-N asymptotic behavior of the energy is pre-figured in small-N atoms and atomic ions, supporting the argument that widely-predictive approximate density functionals should be designed to recover the correct asymptotics. Here, it is shown that the exact Kohn-Sham correlation energy, when calculated from the pure ground-state wavefunction, should have no contribution proportional to Z in the Z → ∞ limit for any fixed N.
Abstract Mechanistic modeling indicates that stomatal conductance could be reduced to improve water use efficiency (WUE) in C4 crops. Genetic variation in stomatal density and canopy temperature was evaluated in the model C4 genus, Setaria. Recombinant inbred lines (RILs) derived from a Setaria italica×Setaria viridis cross were grown with ample or limiting water supply under field conditions in Illinois. An optical profilometer was used to rapidly assess stomatal patterning, and canopy temperature was measured using infrared imaging. Stomatal density and canopy temperature were positively correlated but both were negatively correlated with total above-ground biomass. These trait relationships suggest a likely interaction between stomatal density and the other drivers of water use such as stomatal size and aperture. Multiple quantitative trait loci (QTL) were identified for stomatal density and canopy temperature, including co-located QTL on chromosomes 5 and 9. The direction of the additive effect of these QTL on chromosome 5 and 9 was in accordance with the positive phenotypic relationship between these two traits. This, along with prior experiments, suggests a common genetic architecture between stomatal patterning and WUE in controlled environments with canopy transpiration and productivity in the field, while highlighting the potential of Setaria as a model to understand the physiology and genetics of WUE in C4 species.
Molten CaCl 2 is a useful electrolyte for certain pyroprocessing techniques, and the solubility of oxide ions in this salt is a critical characteristic of many of these techniques. CaO is a byproduct of direct oxide reduction (DOR), so the concentration of oxide ions can be used to determine the extent of these reactions. Using cyclic voltammetry (CV) with tungsten electrodes, the CaO concentration in the salt up to approximately 5 wt% was correlated to both oxidation peak height and power density values. This correlation was demonstrated in both equilibrium and transient conditions. CV is a promising method for the in situ real-time monitoring of CaO concentrations in DOR processes.
A new all-electronic Particle Image Velocimetry technique that can efficiently map high speed gas flows has been developed in-house at the NASA Lewis Research Center. Particle Image Velocimetry is an optical technique for measuring the instantaneous two component velocity field across a planar region of a seeded flow field. A pulsed laser light sheet is used to illuminate the seed particles entrained in the flow field at two instances in time. One or more charged coupled device (CCD) cameras can be used to record the instantaneous positions of particles. Using the time between light sheet pulses and determining either the individual particle displacements or the average displacement of particles over a small subregion of the recorded image enables the calculation of the fluid velocity. Fuzzy logic minimizes the required operator intervention in identifying particles and computing velocity. Using two cameras that have the same view of the illumination plane yields two single exposure image frames. Two competing techniques that yield unambiguous velocity vector direction information have been widely used for reducing the single-exposure, multiple image frame data: (1) cross-correlation and (2) particle tracking. Correlation techniques yield averaged velocity estimates over subregions of the flow, whereas particle tracking techniques give individual particle velocity estimates. For the correlation technique, the correlation peak corresponding to the average displacement of particles across the subregion must be identified. Noise on the images and particle dropout result in misidentification of the true correlation peak. The subsequent velocity vector maps contain spurious vectors where the displacement peaks have been improperly identified. Typically these spurious vectors are replaced by a weighted average of the neighboring vectors, thereby decreasing the independence of the measurements. In this work, fuzzy logic techniques are used to determine the true correlation displacement peak even when it is not the maximum peak, hence maximizing the information recovery from the correlation operation, maintaining the number of independent measurements, and minimizing the number of spurious velocity vectors. Correlation peaks are correctly identified in both high and low seed density cases. The correlation velocity vector map can then be used as a guide for the particle-tracking operation. Again fuzzy logic techniques are used, this time to identify the correct particle image pairings between exposures to determine particle displacements, and thus the velocity. Combining these two techniques makes use of the higher spatial resolution available from the particle tracking. Particle tracking alone may not be possible in the high seed density images typically required for achieving good results from the correlation technique. This two-staged velocimetric technique can measure particle velocities with high spatial resolution over a broad range of seeding densities.
Particle Image Velocimetry provides a means of measuring the instantaneous 2-component velocity field across a planar region of a seeded flowfield. In this work only two camera, single exposure images are considered where both cameras have the same view of the illumination plane. Two competing techniques which yield unambiguous velocity vector direction information have been widely used for reducing the single exposure, multiple image data: cross-correlation and particle tracking. Correlation techniques yield averaged velocity estimates over subregions of the flow, whereas particle tracking techniques give individual particle velocity estimates. The correlation technique requires identification of the correlation peak on the correlation plane corresponding to the average displacement of particles across the subregion. Noise on the images and particle dropout contribute to spurious peaks on the correlation plane, leading to misidentification of the true correlation peak. The subsequent velocity vector maps contain spurious vectors where the displacement peaks have been improperly identified. Typically these spurious vectors are replaced by a weighted average of the neighboring vectors, thereby decreasing the independence of the measurements. In this work fuzzy logic techniques are used to determine the true correlation displacement peak even when it is not the maximum peak on the correlation plane, hence maximizing the information recovery from the correlation operation, maintaining the number of independent measurements and minimizing the number of spurious velocity vectors. Correlation peaks are correctly identified in both high and low seed density cases. The correlation velocity vector map can then be used as a guide for the particle tracking operation. Again fuzzy logic techniques are used, this time to identify the correct particle image pairings between exposures to determine particle displacements, and thus velocity. The advantage of this technique is the improved spatial resolution which is available from the particle tracking operation. Particle tracking alone may not be possible in the high seed density images typically required for achieving good results from the correlation technique. This two staged approach offers a velocimetric technique capable of measuring particle velocities with high spatial resolution over a broad range of seeding densities.
Spectral analysis is very useful in determining the frequency characteristics of many turbulent flows, for example, vortex flows, tail buffeting, and other pulsating flows. It is also used for obtaining turbulence spectra from which the time and length scales associated with the turbulence structure can be estimated. These estimates, in turn, can be helpful for validation of theoretical/numerical flow turbulence models. Laser velocimetry (LV) is being extensively used in the experimental investigation of different types of flows, because of its inherent advantages; nonintrusive probing, high frequency response, no calibration requirements, etc. Typically, the output of an individual realization laser velocimeter is a set of randomly sampled velocity data. Spectral analysis of such data requires special techniques to obtain reliable estimates of correlation and power spectral density functions that describe the flow characteristics. FORTRAN codes for obtaining the autocorrelation and power spectral density estimates using the correlation-based slotting technique were developed. Extensive studies have been conducted on simulated first-order spectrum and sine signals to improve the spectral estimates. A first-order spectrum was chosen because it represents the characteristics of a typical one-dimensional turbulence spectrum. Digital prefiltering techniques, to improve the spectral estimates from randomly sampled data were applied. Studies show that the spectral estimates can be increased up to about five times the mean sampling rate.
In universes with significant curvature or cosmological constant, cosmic microwave background (CMB) anisotropies are created very recently via the Rees-Sciama or integrated Sachs-Wolfe effects. This causes the CMB anisotropies to become partially correlated with the local matter density (z less than 4). We examine the prospects of using the hard (2- 10 keV) X-ray background as a probe of the local density and the measured correlation between the HEAO1 A2 X-ray survey and the 4-year COBE-DMR map to obtain a constraint on the cosmological constant. The 95% confidence level upper limit on the cosmological constant is OMega(sub Lambda) less than or equal to 0.5, assuming that the observed fluctuations in the X-ray map result entirely from large scale structure. (This would also imply that the X-rays trace matter with a bias factor of b(sub x) approx. = 5.6 Omega(sub m, sup 0.53)). This bound is weakened considerably if a large portion of the X-ray fluctuations arise from Poisson noise from unresolved sources. For example, if one assumes that the X-ray bias is b(sub x) = 2, then the 95% confidence level upper limit is weaker, Omega(sub Lambda) less than or equal to 0.7. More stringent limits should be attainable with data from the next generation of CMB and X-ray background maps.
We analyze the resolved stellar populations of 473 massive star-forming galaxies at 0.7 < z < 1.5, with multiwavelength broadband imaging from CANDELS andHalpha surface brightness profiles at the same kiloparsec resolution from 3D-HST. Together, this unique data set sheds light on how the assembled stellar mass is distributed within galaxies, and where new stars are being formed. We find the Halpha morphologies to resemble more closely those observed in the ACS I band than in the WFC3 H band, especially for the larger systems. We next derive a novel prescription for Halpha dust corrections, which accounts for extra extinction toward H II regions. The prescription leads to consistent star formation rate (SFR) estimates and reproduces the observed relation between the Halpha/UV luminosity ratio and visual extinction, on both a pixel-by-pixel and a galaxy-integrated level. We find the surface density of star formation to correlate with the surface density of assembled stellar mass for spatially resolved regions within galaxies, akin to the so-called "main sequence of star formation" established on a galaxy-integrated level. Deviations from this relation toward lower equivalent widths are found in the inner regions of galaxies. Clumps and spiral features, on the other hand, are associated with enhanced H alpha equivalent widths, bluer colors, and higher specific SFRs compared to the underlying disk. Their Halpha/UV luminosity ratio is lower than that of the underlying disk, suggesting that the ACS clump selection preferentially picks up those regions of elevated star formation activity that are the least obscured by dust. Our analysis emphasizes that monochromatic studies of galaxy structure can be severely limited by mass-to-light ratio variations due to dust and spatially inhomogeneous star formation histories.
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Here, we apply the Gamow shell model to study 25–31 F isotopes. As both internucleon correlations and continuum coupling are properly treated therein, the structure shape of 31 F at large distance can be analyzed precisely. For this, one-nucleon densities, root-mean-square radii, and correlation densities are calculated in neutron-rich fluorine isotopes. It is then suggested that 31 F exhibits a two-neutron halo structure, built from both continuum coupling and nucleon-nucleon correlations.
Studies were conducted utilizing six different film and filter combinations to quantitatively detect chlorophyll and turbidity in six farm ponds. The low range of turbidity from 0-35 JTU correlated well with the density readings from the green band of normal color film and the high range above 35 JTU was found to correlate with density readings in the red band of color infrared film. The effect of many of the significant variables can be reduced by using standardized procedures in taking the photography. Attempts to detect chlorophyll were masked by the turbidity. The ponds which were highly turbid also had high chlorophyll concentrations; whereas, the ponds with low turbidity also had low chlorophyll concentrations. This prevented a direct correlation for this parameter. Several suggested approaches are cited for possible future investigations.
Optical absorption-line techniques have been applied to the study of a number of translucent molecular clouds in which the total column densities are large enough that substantial molecular abundances can be maintained. Results are presented for a survey of absorption lines of interstellar C2, CH, and CN. Detections of CN through the A 2Pi-X 2Sigma(+) (1,O) and (2,O) bands of the red system are reported and compared with observations of the violet system for one line of sight. The population distributions in C2 provide diagnostic information on temperature and density. The measured column densities of the three species can be used to test details of the theory of molecule formation in clouds where photoprocesses still play a significant role. The C2 and CH column densities are strongly correlated with each other and probably also with the H2 column density. In contrast, the CN column densities are found to vary greatly from cloud to cloud. The observations are discussed with reference to detailed theoretical models.
Dark matter, if it exists, accounts for five times as much as the ordinary baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter might possess the widest presence in our universe. This paper presents a statistical theory for the flow of dark matter that is compared with N-body simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is self-gravitating, long-range, and collisionless with a scale-dependent flow behavior. The peculiar velocity field is of constant divergence nature on small scale and irrotational on large scale. The statistical measures, i.e., correlation, structure, dispersion, and spectrum functions, are modeled on both small and large scales, respectively. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. Incompressible and constant divergence flow share the same kinematic relations for even order correlations. The limiting correlation of velocity $\mathrm{ρ_{L}=1/2}$ on the smallest scale ( r = 0) is a unique feature of collisionless flow ($\mathrm{ρ_{L}=1}$ for incompressible flow). On large scale, transverse velocity correlation has an exponential form $T_{2}∝e^{–r/r_2}$ with a constant comoving scale r 2 =21.3 Mpc/h that may be related to the horizon size at matter–radiation equality. All other correlation, structure, dispersion, and spectrum functions for velocity, density, and potential fields are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of ${S}_{2}^{1}∝r^{1/4}$. All other statistical measures can be obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for scale r between 1 and 7 Mpc/h. Divergence is negatively correlated for r > 30 Mpc/h that leads to a negative density correlation.
A survey is reported of interstellar densities, abundances, and cloud structure in the Galaxy, using the IUE and IRAS satellites. Heavy element depletions are discussed along with their correlations with mean density, reddening, and galactic location. Interesting correlations between the Fe/Si abundance ratio and the infrared diffuse cirrus is also reported, which may provide information on the history and formation of grains in the galactic halo.
The O IV density sensitive emission lines around 1400 A, using the solar ultraviolet measurement of emitted radiation (SUMER) instrument onboard the Solar and Heliospheric Observatory (SOHO), are reported on. The data for the quiet sun, obtained close to the disk center and the solar limb were acquired. A systematic correlation between a density sensitive emission line ratio and Doppler shift across the same emission profiles was obtained. The correlation is such that the density is higher in the downflowing than in the upflowing plasma. The results are in good agreement with the simulations of downward propagating waves.
Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic pair densities and pairing fields are introduced. Many pairing functionals currently used can be traced back to zero-range nucleon-nucleon interactions. Unfortunately, such functionals are plagued by deficiencies that become apparent in large model spaces that contain unbound single-particle (continuum) states. In particular, the underlying computational schemes diverge as the single-particle space increases, and the results depend on how marginally occupied states are incorporated. These problems become more pronounced for pairing functionals that contain gradient-density dependence, such as in the Fayans functional. To remedy this, finite-range pairing functionals are introduced. In this study, this is done by folding the pair density with Gaussians. Here, we show that a folding radius of about 1 fm offers the best compromise between quality and stability, and substantially reduces the pathological behavior in different numerical applications.