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All sourcesNASA NTRSDOE OSTI
NASA NTRS1958

Statistical Study of Turbulence: Spectral Functions and Correlation Coefficients

In reading the publications on turbulence of different authors, one often runs the risk of confusing the various correlation coefficients and turbulence spectra. We have made a point of defining, by appropriate concepts, the differences which exist between these functions. Besides, we introduce in the symbols a few new characteristics of turbulence. In the first chapter, we study some relations between the correlation coefficients and the different turbulence spectra. Certain relations are given by means of demonstrations which could be called intuitive rather than mathematical. In this way we demonstrate that the correlation coefficients between the simultaneous turbulent velocities at two points are identical, whether studied in Lagrange's or in Euler's systems. We then consider new spectra of turbulence, obtained by study of the simultaneous velocities along a straight line of given direction. We determine some relations between these spectra and the correlation coefficients. Examining the relation between the spectrum of the turbulence measured at a fixed point and the longitudinal-correlation curve given by G. I. Taylor, we find that this equation is exact only when the coefficient is very small.

Frenkiel, Francois N.↗
NASA NTRS1993

The three-point function as a probe of models for large-scale structure

The consequences of models of structure formation for higher-order (n-point) galaxy correlation functions in the mildly non-linear regime are analyzed. Several variations of the standard Omega = 1 cold dark matter model with scale-invariant primordial perturbations were recently introduced to obtain more power on large scales, R(sub p) is approximately 20 h(sup -1) Mpc, e.g., low-matter-density (non-zero cosmological constant) models, 'tilted' primordial spectra, and scenarios with a mixture of cold and hot dark matter. They also include models with an effective scale-dependent bias, such as the cooperative galaxy formation scenario of Bower, etal. It is shown that higher-order (n-point) galaxy correlation functions can provide a useful test of such models and can discriminate between models with true large-scale power in the density field and those where the galaxy power arises from scale-dependent bias: a bias with rapid scale-dependence leads to a dramatic decrease of the hierarchical amplitudes Q(sub J) at large scales, r is approximately greater than R(sub p). Current observational constraints on the three-point amplitudes Q(sub 3) and S(sub 3) can place limits on the bias parameter(s) and appear to disfavor, but not yet rule out, the hypothesis that scale-dependent bias is responsible for the extra power observed on large scales.

Frieman, Joshua A.↗
DOE OSTI2020

Machine learning the Hubbard U parameter in DFT+U using Bayesian optimization

Abstract Within density functional theory (DFT), adding a Hubbard U correction can mitigate some of the deficiencies of local and semi-local exchange-correlation functionals, while maintaining computational efficiency. However, the accuracy of DFT+U largely depends on the chosen Hubbard U values. We propose an approach to determining the optimal U parameters for a given material by machine learning. The Bayesian optimization (BO) algorithm is used with an objective function formulated to reproduce the band structures produced by more accurate hybrid functionals. This approach is demonstrated for transition metal oxides, europium chalcogenides, and narrow-gap semiconductors. The band structures obtained using the BO U values are in agreement with hybrid functional results. Additionally, comparison to the linear response (LR) approach to determining U demonstrates that the BO method is superior.

Chemistry↗
DOE OSTI2019

Ab initio molecular dynamics simulation of supercritical aqueous ionic solutions: Spectral diffusion of water in the vicinity of Br¯ and I¯ ions

Supercritical aqueous ionic solutions containing bromide (Br¯) and iodide (I¯) ions have been studied using Car-Parrinello molecular dynamics simulation at two different concentrations and at two different densities. The time dependent trajectory has been used for calculating vibrational spectral diffusion, structural properties and, for other dynamical properties such as hydrogen bond dynamics, orientational relaxation and residence dynamics. The vibrational spectral diffusion of fluctuating OD stretch mode inside the solvation shell of the ions and in the bulk has been studied using frequency-frequency time correlation function. Hydrogen bond dynamics, orientational relaxation and residence dynamics of Sc-water have been investigated using population correlation function approach. The water molecules inside the solvation shell of Br¯ and I¯ ions are found to show complex molecular dynamics in comparison to the water-water dynamics. The concentration dependent spectral diffusion has been observed and it occurs in multiple time scales in the solvation shell of Br¯ and I¯ ions. Here, at supercritical condition, the ion-water hydrogen bond shows faster dynamics with respect to the same at ambient condition and slower dynamics with respect to the water-water hydrogen bond dynamics at supercritical condition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Aspects of propagator sparsening in lattice QCD

In lattice field theory, field sparsening aims to replace quantum fields, or objects constructed from them, with approximations that preserve the appropriate symmetries and maintain many aspects of the physics that the fields determine. For example, an effective sparsening of a quark propagator provides an efficient map from a quark propagator on a fine lattice geometry to a quark propagator defined on a coarser geometry in order to reduce storage and computational costs of subsequent calculational stages while maintaining long-distance correlations and corresponding low-energy physical information. Previous studies have focused on decimating lattice sites or randomly sampling lattice sites to reduce the size of the propagator and subsequent costs of Wick contractions. Here, we extend the study of sparsening to incorporate covariant averaging of spatial sites and examine the effects on two-point and three-point correlation functions involving various hadrons. We find that sparsening is most effective in reproducing the unsparsened versions of these correlation functions when weighted covariant-averaging is sequentially applied many times.

Lattice QCD↗
DOE OSTI2025

Lanczos algorithm for lattice QCD matrix elements

Recent work [M. L. Wagman, Lanczos, the transfer matrix, and the signal-to-noise problem, .] found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for multiple states from a single correlator, and two-sided error bounds. After filtering out spurious eigenvalues and using outlier-robust estimators within a nested bootstrap framework, Lanczos estimators behave more like multistate fit results than effective masses—but without involving statistical fitting. We extend this formalism to the determination of matrix elements from three-point correlation functions and provide a physical picture of “spurious-state filtering” involving restriction to a Hermitian subspace. We demonstrate similar advantages for matrix elements as for spectroscopy through example applications to noiseless mock-data and (bare) forward matrix elements of the strange scalar current between both ground and excited states with the quantum numbers of the nucleon.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Low-temperature transport in La{sub 0.5}Ca{sub 0.4}Li{sub 0.1}MnO{sub 3} manganite in high magnetic fields (1 T ⩽ H ⩽ 14 T)

The low-temperature minimum of the resistivity of La{sub 0.5}Ca{sub 0.4}Li{sub 0.1}MnO{sub 3} manganite in high magnetic fields (up to 14 T) is analyzed quantitatively. It is shown that the behavior of the resistivity and magnetoresistance at low temperatures is successfully described by the model of intergrain spin-polarized tunnel charge transfer. In accordance with this model, the resistivity is expressed in terms of the correlation function of magnetizations of neighboring grains. The expression for the temperature- and magnetic-field dependences of this correlator, derived in [31], is thoroughly analyzed and applied for the polycrystalline manganite sample under investigation. The main parameters of the chosen model are obtained from analysis of experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1996

The Three-Dimensional Spatial Structure of Cirrus Clouds Determined from Lidar Satellite Observations

Simultaneous imagery from the University of Wisconsin Volume Imaging Lidar (VIL) and meteorological satellites were used to quantify the spatial structure of cirrus clouds with 60 m resolution. This data was used to determine the spatial distributions of cloud base altitude, cloud top altitude, and mid-cloud altitude. Two dimensional auto-correlation functions describing the mean shape of cirrus clouds were computed. Because cirrus clouds seldom have distinct edges, these correlation functions are derived as a function of a threshold value which defines the cloud edge.

Eloranta, E. W.↗
NASA NTRS2003

Concentration and Velocity Gradients in Fluidized Beds

In this work we focus on the height dependence of particle concentration, average velocity components, fluctuations in these velocities and, with the flow turned off, the sedimentation velocity. The latter quantities are measured using Particle Imaging Velocimetry (PIV). The PIV technique uses a 1-megapixel camera to capture two time-displaced images of particles in the bed. The depth of field of the imaging system is approximately 0.5 cm. The camera images a region with characteristic length of 2.6 cm for the small particles and 4.7 cm. for the large particles. The local direction of particle flow is determined by calculating the correlation function for sub-regions of 32 x 32 pixels. The velocity vector map is created from this correlation function using the time between images (we use 15 to 30 ms). The software is sensitive variations of 1/64th of a pixel. We produce velocity maps at various heights, each consisting of 3844 velocities. We break this map into three vertical zones for increased height information. The concentration profile is measured using an expanded (1 cm diameter) linearly polarized HeNe Laser incident on the fluidized bed. A COHU camera (gamma=1, AGC off) with a lens and a polarizer images the transmitted linearly polarized light to minimize the effects of multiply scattered light. The intensity profile (640 X 480 pixels) is well described by a Gaussian fit and the height of the Gaussian is used to characterize the concentration. This value is compared to the heights found for known concentrations. The sedimentation velocity is estimated using by imaging a region near the bottom of the bed and using PIV to measure the velocity as a function of time. With a nearly uniform concentration profile, the time can be converted to height information. The stable fluidized beds are made from large pseudo-monodisperse particles (silica spheres with radii (250-300) microns and (425-500) microns) dispersed in a glycerin/water mix. The Peclet number is sufficiently large that Brownian motion of the particles can be ignored and the Reynolds number sufficiently small that particle inertia is negligible. A packed particle bed is used to randomize and disperse the flowing fluid introduced by a peristaltic pump. The bed itself is a rectangular glass cell 8 cm wide (x), 0.8 cm deep and a height of 30.5 cm (z). The depth of field of the camera is approximately 0.5 cm so depth information is averaged. Over flow fluid is returned to the reservoir making a closed loop system. In these experiments the particles form a sediment approximately 5.7 cm high with the pump off and expand to 22 cm with the pump on. For the smaller particles the pump velocity is .5 millimeters per second and 1.1 millimeters per second for the large particles. At this concentration the bed has a very well defined top where particle concentration rapidly drops to zero.

McClymer, James P.↗
NASA NTRS1994

The three-point function as a probe of models for large-scale structure

We analyze the consequences of models of structure formation for higher order (n-point) galaxy correlation functions in the mildly nonlinear regime. Several variations of the standard Omega = 1 cold dark matter model with scale-invariant primordial perturbations have recently been introduced to obtain more power on large scales, R(sub p) is approximately 20/h Mpc, e.g., low matter-density (nonzero cosmological constant) models, 'tilted' primordial spectra, and scenarios with a mixture of cold and hot dark matter. They also include models with an effective scale-dependent bias, such as the cooperative galaxy formation scenario of Bower et al. We show that higher-order (n-point) galaxy correlation functions can provide a useful test of such models and can discriminate between models with true large-scale power in the density field and those where the galaxy power arises from scale-dependent bias: a bias with rapid scale dependence leads to a dramatic decrease of the the hierarchical amplitudes Q(sub J) at large scales, r is greater than or approximately R(sub p). Current observational constraints on the three-point amplitudes Q(sub 3) and S(sub 3) can place limits on the bias parameter(s) and appear to disfavor, but not yet rule out, the hypothesis that scale-dependent bias is responsible for the extra power observed on large scales.

Frieman, Joshua A.↗
NASA NTRS1994

Microwave background fluctuations due to the Sunyaev-Zel'dovich effects in pancakes

We calculate distortions in the microwave background radiation from the Sunyaev-Zel'dovich effect, produced by hot gas in large (approximately 100 Mpc) pancakes. The large-scale distribution of the pancakes is taken to be that of a Voronoi foam. Fluctuations for this scenario are estimated to be on the order of delta T/T is approximately 10(exp -5). Using computer simulations, we produce several 32 deg x 32 deg images with 0.25 deg resolution. These images show characteristic linear features produced when a pancake is viewed nearly edge-on. By calculating the two-point and the degenerate three-point correlation functions, we are able to statistically detect such non-Gaussian features even in the presence of a relatively large amount of Gaussian noise. The degenerate three-point correlation function is found to be particularly useful since it is insensitive to correlated Gaussian noise. We also smooth our data over a 7 deg Full Width at Half Maximum (FWHM) Gaussian window to simulate the Cosmic Background Explorer Satellite (COBE) observations. We find that under such low-resolution conditions, the features are highly suppressed.

Subbarao, M. U.↗
DOE OSTI2019

Is an interacting ground state (pure state) v-representable density also non-interacting ground state v-representable by a Slater determinant? In the absence of degeneracy, yes!

It is shown that in the absence of degeneracy a density,$n,(r)$, describing the probability of finding a particle in a small volume at position, r, that is known to be pure-state v-representable in terms of the ground state of an interacting system of particles evolving under an external potential,$v,(r)$, is also pure state v-representable in terms of a single Slater determinant describing the ground state of a system of non-interacting particles under a potential, $v_s(r)$ . This establishes the validity of the Kohn–Sham formalism of density functional theory. An explicit form of $v_s(r)$ is derived. We also derive the exact form of the correlation functional and the corresponding potential, $\mu_c(r)$, that lead to the exact density and energy of an interacting system's ground state. In addition, we demonstrate the existence of a one-to-one mapping between the ground-state densities of non-degenerate interacting and non-interacting systems. Finally, we show that practical implementations of the Kohn–Sham formalism can generate neither the exact density nor energy of an interacting system's ground state, a feature that is particularly true in the case of the so-called exact exchange, in which the correlation functional and potential are set equal to zero.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Forward-backward multiplicity correlations in pp, p+Pb and Pb+Pb collisions with the ATLAS detector

Two-particle pseudorapidity correlations are measured in √s NN = 2.76 TeV Pb+Pb, √s NN = 5.02 TeV p +Pb and √s = 13 TeV pp collisions [ATLAS Collaboration, ATLAS-CONF-2015-051; ATLAS-CONF-2015-020]. Correlation function is measured using charged particles in the pseudorapidity range |η|<2.4 with transverse momentum p T >0.2 GeV, and it is measured as a function of event multiplicity, defined by number of charged particles with |η|<2.5 and p T >0.4 GeV. The correlation function is decomposed into a short-range component (SRC) and a long-range component (LRC). The SRC differs significantly between the opposite-charge pairs and same-charge pairs, and between the three collision systems at similar multiplicity. The LRC is described approximately by 1 + n1n2 in all collision systems over the full multiplicity range. The values of are consistent between the opposite-charge and same-charge pairs, and are similar for the three collision systems at similar multiplicity. The values of and the magnitude of the SRC both follow a power-law dependence on the event multiplicity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1994

Limits on three-point correlations in the COBE DMR first-year anisotropy maps

We compute the three-point temperature correlation function of the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) first-year sky maps to search for non-Gaussian temperature fluctuations. The level of fluctuations seen in the computed correlation function are too large to be attributable solely to instrument noise. However the fluctuations are consistent with the level expected to result from a superposition of istrument noise and sky signal arising from a Gaussian power-law model of initial fluctuations, with a quadrupole normalized amplitude of 17 micro K and a power-law spectral index n = 1. We place limits on the amplitude of intrinsic three-point correlations with a variety of predicted functional forms.

Hinshaw, G.↗
DOE OSTI2019

Nanoscale kinetics and dynamics during Ar + patterning of SiO 2

Broad-beam low-energy ion bombardment can lead to the spontaneous formation of nanoscale surface structures, but the dominant mechanisms driving evolution remain controversial. Using coherent x-ray scattering to examine the classic case of ion-beam rippling of SiO 2 surfaces, we study the relationship between the average kinetics of ripple formation and the underlying fluctuation dynamics. The early stage growth of fluctuations is well fit with a linear theory formalism employing a viscous relaxation term with full wave-number dependence. In this regime, the x-ray photon correlation spectroscopy two-time correlation function shows distinctive behavior with memory stretching back to the beginning of the bombardment. For a given length scale, correlation times do not grow significantly beyond the characteristic time associated with the early-stage ripple growth. In the late stages of patterning, when the average surface structure on a given length scale is no longer evolving, dynamical processes continue on the surface. Nonlinear processes dominate at long length scales, leading to compressed exponential decay of the speckle correlation functions, while at short length scales the dynamics appears to approach a linear behavior consistent with viscous flow relaxation. This behavior is found to be consistent with simulations of a recent nonlinear growth model. In addition, it is shown that the surface ripple velocity, an important parameter of the ion-driven surface evolution, can be measured with coherent x-ray scattering in conjunction with use of an inhomogeneous ion beam. The change in viewpoint exemplified by this study, from a focus on only average surface kinetics to one incorporating the underlying nanoscale dynamics, is rapidly becoming more widely applicable as new and upgraded x-ray sources with higher coherent flux come online.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Dark Energy Survey Year 1 Results: Cross-correlation between Dark Energy Survey Y1 galaxy weak lensing and South Pole Telescope + P l a n c k CMB weak lensing

We cross-correlate galaxy weak lensing measurements from the Dark Energy Survey (DES) year-one data with a cosmic microwave background (CMB) weak lensing map derived from South Pole Telescope (SPT) and Planck data, with an effective overlapping area of 1289-deg 2 . With the combined measurements from four source galaxy redshift bins, we obtain a detection significance of 5.8σ. We fit the amplitude of the correlation functions while fixing the cosmological parameters to a fiducial ΛCDM model, finding A =0.99±0.17. We also use the correlation function measurements to constrain shear calibration bias, obtaining constraints that are consistent with previous DES analyses. Lastly, when performing a cosmological analysis under the ΛCDM model, we obtain the marginalized constraints of Ω m = 0.261$^{+0.070}_{-0.051}$ and S 8≡σ 8 $\sqrt{Ω_m/0.3}$=0.660$^{+0.085}_{-0.100}$. These measurements are used in a companion work that presents cosmological constraints from the joint analysis of two-point functions among galaxies, galaxy shears, and CMB lensing using DES, SPT, and Planck data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Temporal Variation of the Rotation of the Solar Mean Magnetic Field

Based on continuous wavelet transformation analysis, the daily solar mean magnetic field (SMMF) from 1975 May 16 to 2014 July 31 is analyzed to reveal its rotational behavior. Both the recurrent plot in Bartels form and the continuous wavelet transformation analysis show the existence of rotational modulation in the variation of the daily SMMF. The dependence of the rotational cycle lengths on solar cycle phase is also studied, which indicates that the yearly mean rotational cycle lengths generally seem to be longer during the rising phase of solar cycles and shorter during the declining phase. The mean rotational cycle length for the rising phase of all of the solar cycles in the considered time is 28.28 ± 0.67 days, while for the declining phase it is 27.32 ± 0.64 days. The difference of the mean rotational cycle lengths between the rising phase and the declining phase is 0.96 days. The periodicity analysis, through the use of an auto-correlation function, indicates that the rotational cycle lengths have a significant period of about 10.1 years. Furthermore, the cross-correlation analysis indicates that there exists a phase difference between the rotational cycle lengths and solar activity.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1974

Design data for radars based on 13.9 GHz Skylab scattering coefficient measurements

The author has identified the following significant results. Measurements made at 13.9 GHz with the radar scatterometer on Skylab have been combined to produce median curves of the variation of scattering coefficient with angle of incidence out to 45 deg. Because of the large number of observations, and the large area averaged for each measured data point, these curves may be used as a new design base for radars. A reasonably good fit at larger angles is obtained using the theoretical expression based on an exponential height correlation function and also using Lambert's law. For angles under 10 deg, a different fit based on the exponential correlation function, and a fit based on geometric optics expressions are both reasonably valid.

Moore, R. K.↗