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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Asymptotic form of the longitudinal correlation function for isotropic homogeneous turbulence

An asymptotic form is derived for the longitudinal correlation function for isotropic homogeneous turbulence in an incompressible fluid governed by the Navier-Stokes equation. The result is obtained from an analysis of the algebraic-differential structure of the two-point correlation tensor contained in the complex-valued Fourier transform of the probability measure over the turbulence ensemble, which reveals that the Hopf characteristic functional (the complex-valued Fourier transform of the probability measure) satisfies the Fourier interference inequality. Consequences of the expression obtained, in which the correlation function is a positive definite function of the inverse cube of the spatial coordinate as it approaches infinity, are shown to include the nonexistence of the Loitsianskii invariant, and the solution is shown to be consistent with empirical formulas.

Rosen, G.↗
NASA NTRS1991

The three-point correlation function for Abell clusters - Observations and simulations

Results are reported of a 3D study tracing the three-point correlation function of Abell clusters and of a comparison of this with the biased cold dark matter (CDM) simulations of Park (1990). For the observations, the maximum likelihood fits are Z11 = 0.85 and Q111 = 0.1, in excellent agreement with the result of the 2D study of Toth et al. (1989). For Park's simulation, maximum likelihood fits of Q11 = 0.9 and Q111 = 0.0 are found, which is in excellent agreement with the observational result. It is concluded that the standard biased CDM gravitational instability model reproduces the observed form of the three-point correlation functions for Abell clusters remarkably well. The number of triples as a function of the sides of triangles for Abell clusters, and the number of triples as a function of the sides of triangles for clusters in Park's simulation are illustrated on graphs.

Gott, J. R., III↗
DOE OSTI2023

The two-point correlation function covariance with fewer mocks

We present FITCOV an approach for accurate estimation of the covariance of two-point correlation functions that requires fewer mocks than the standard mock-based covariance. This can be achieved by dividing a set of mocks into jackknife regions and fitting the correction term first introduced in Mohammad & Percival (2022), such that the mean of the jackknife covariances corresponds to the one from the mocks. This extends the model beyond the shot-noise limited regime, allowing it to be used for denser samples of galaxies. We test the performance of our fitted jackknife approach, both in terms of accuracy and precision, using lognormal mocks with varying densities and approximate EZmocks mimicking the Dark Energy Spectroscopic Instrument LRG and ELG samples in the redshift range of z = [0.8, 1.1]. We find that the Mohammad–Percival correction produces a bias in the two-point correlation function covariance matrix that grows with number density and that our fitted jackknife approach does not. We also study the effect of the covariance on the uncertainty of cosmological parameters by performing a full-shape analysis. We demonstrate that our fitted jackknife approach based on 25 mocks can recover unbiased and as precise cosmological parameters as the ones obtained from a covariance matrix based on 1000 or 1500 mocks, while the Mohammad–Percival correction produces uncertainties that are twice as large.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1980

Collisional redistribution of radiation. II - The effects of degeneracy on the equations of motion for the density matrix. III - The equation of motion for the correlation function and the scattered spectrum

The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.

Burnett, K.↗
NASA NTRS1988

On the universality of the two-point galaxy correlation function

The behavior of the two-point galaxy correlation function in volume-limited subsamples of three complete redshift surveys is investigated. The correlation length is shown to scale approximately as the square root of the distance limit in both the CfA and Southern Sky catalogs, but to be independent of the distance limit in the IRAS sample. This effect is found to be due to factors such as the large positive density fluctuations in the foreground of the optically selected catalogs biasing the correlation length estimate downward, and the brightest galaxies appearing to be more strongly clustered than the mean.

Davis, Marc↗
NASA NTRS1991

Hexagonal and nematic phases of chains. I - Correlation functions. II - Phase transitions

The statistical mechanics of a system of semiflexible chains, which can represent polymer liquid crystals, long-chain biomolecules, stiff wormlike micelles, or columns of discotic liquid crystals, are examined. A continuum theory is used to calculate static correlation functions in the hexagonal and nematic phases. Two correlation functions are considered: (1) the structure factor which describes fluctuations in the density; and (2) the director fluctuation spectrum, which describes fluctuations in the local optical axis. In addition, a model is developed for the phase transitions of a system of infinitely long, semiflexible chains which interact through a steric, excluded-volume repulsion. The model yields generic phase diagrams in terms of pressure or density vs. persistence length or temperature.

Selinger, Jonathan V.↗
NASA NTRS2011

Correlation Function Approach for Estimating Thermal Conductivity in Highly Porous Fibrous Materials

Heat transport in highly porous fiber networks is analyzed via two-point correlation functions. Fibers are assumed to be long and thin to allow a large number of crossing points per fiber. The network is characterized by three parameters: the fiber aspect ratio, the porosity and the anisotropy of the structure. We show that the effective thermal conductivity of the system can be estimated from knowledge of the porosity and the correlation lengths of the correlation functions obtained from a fiber structure image. As an application, the effects of the fiber aspect ratio and the network anisotropy on the thermal conductivity is studied.

Martinez-Garcia, Jorge↗
NASA NTRS1977

The correlation function for density perturbations in an expanding universe. II - Nonlinear theory

A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies

Mcclelland, J.↗
DOE OSTI2024

SmoQyDEAC.jl: A differential evolution package for the analytic continuation of imaginary time correlation functions

We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl package. It also provides detailed benchmarks of the package's output against the popular maximum entropy and stochastic analytic continuation methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

N-point correlation functions in the CfA and SSRS redshift distribution of galaxies

Using counts in cells, we estimate the volume-average N-point galaxy correlation functions for N = 2, 3, and 4, in redshift samples of the CfA and SSRS catalogs. Volume-limited samples of different sizes are used to study the uncertainties at different scales, the shot noise, and the problem with the boundaries. The hierarchical constants S3 and S4 agree well in all samples in CfA and SSRS, with average S3 = 194 +/- 0.07 and S4 = 4.56 +/- 0.53. We compare these results with estimates obtained from angular catalogs and recent analysis over IRAS samples. The amplitudes SJ seem larger in real space than in redshift space, although the values from the angular analysis correspond to smaller scales, where we might expect larger nonperturbative effects. It is also found that S3 and S4 are smaller for IRAS than for optical galaxies. This, together with the fact that IRAS galaxies have smaller amplitude for the above correlation functions, indicates that the density fluctuations of IRAS galaxies cannot be simply proportional to the density fluctuations of optical galaxies, i.e., biasing has to be nonlinear between them.

Gaztanaga, Enrique↗
NASA NTRS1986

Statistical properties and correlation functions for drift waves

The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.

Horton, W.↗
DOE OSTI2023

Higher-order cumulants and correlation functions of proton multiplicity distributions in s N N = 3 GeV Au + Au collisions at the RHIC STAR experiment

Here, we report a measurement of cumulants and correlation functions of event-by-event proton multiplicity distributions from fixed-target Au+Au collisions at $\sqrt{s_\text{NN}}$ = 3 GeV measured by the STAR experiment. Protons are identified within the rapidity (y) and transverse momentum ($p_T$) region –0:9 < $\textit{y}$ < 0 and 0:4 < pT < 2:0 GeV/c in the center-of-mass frame. A systematic analysis of the proton cumulants and correlation functions up to sixth-order as well as the corresponding ratios as a function of the collision centrality, $p_T$, and $\textit{y}$ are presented. The effect of pileup and initial volume fluctuations on these observables and the respective corrections are discussed in detail. The results are compared to calculations from the hadronic transport UrQMD model as well as a hydrodynamic model. In the most central 5% collisions, the value of proton cumulant ratio $C_4 = C_2$ is negative, drastically different from the values observed in Au+Au collisions at higher energies. Compared to model calculations including Lattice QCD, a hadronic transport model, and a hydrodynamic model, the strong suppression in the ratio of $C_4/C_2$ at 3 GeV Au+Au collisions indicates an energy regime dominated by hadronic interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Cosmic shear cosmology beyond two-point statistics: a combined peak count and correlation function analysis of DES-Y1

ABSTRACT We constrain cosmological parameters from a joint cosmic shear analysis of peak-counts and the two-point shear correlation functions, as measured from the Dark Energy Survey (DES-Y1). We find the structure growth parameter $S_8\equiv \sigma _8\sqrt{\Omega _{\rm m}/0.3} = 0.766^{+0.033}_{-0.038}$ which, at 4.8 per cent precision, provides one of the tightest constraints on S8 from the DES-Y1 weak lensing data. In our simulation-based method we determine the expected DES-Y1 peak-count signal for a range of cosmologies sampled in four w cold dark matter parameters (Ωm, σ8, h, w0). We also determine the joint covariance matrix with over 1000 realizations at our fiducial cosmology. With mock DES-Y1 data we calibrate the impact of photometric redshift and shear calibration uncertainty on the peak-count, marginalizing over these uncertainties in our cosmological analysis. Using dedicated training samples we show that our measurements are unaffected by mass resolution limits in the simulation, and that our constraints are robust against uncertainty in the effect of baryon feedback. Accurate modelling for the impact of intrinsic alignments on the tomographic peak-count remains a challenge, currently limiting our exploitation of cross-correlated peak counts between high and low redshift bins. We demonstrate that once calibrated, a fully tomographic joint peak-count and correlation functions analysis has the potential to reach a 3 per cent precision on S8 for DES-Y1. Our methodology can be adopted to model any statistic that is sensitive to the non-Gaussian information encoded in the shear field. In order to accelerate the development of these beyond-two-point cosmic shear studies, our simulations are made available to the community upon request.

Harnois-Déraps, Joachim↗
DOE OSTI2021

Baryon acoustic oscillations in the projected cross-correlation function between the eBOSS DR16 quasars and photometric galaxies from the DESI Legacy Imaging Surveys

ABSTRACT We search for the baryon acoustic oscillations in the projected cross-correlation function binned into transverse comoving radius between the SDSS-IV DR16 eBOSS quasars and a dense photometric sample of galaxies selected from the DESI Legacy Imaging Surveys. We estimate the density of the photometric sample of galaxies in this redshift range to be about 2900 deg−2, which is deeper than the official DESI emission line galaxy selection, and the density of the spectroscopic sample is about 20 deg−2. In order to mitigate the systematics related to the use of different imaging surveys close to the detection limit, we use a neural network approach that accounts for complex dependences between the imaging attributes and the observed galaxy density. We find that we are limited by the depth of the imaging surveys that affects the density and purity of the photometric sample and its overlap in redshift with the quasar sample, which thus affects the performance of the method. When cross-correlating the photometric galaxies with quasars in the range 0.6 ≤ z ≤ 1.2, the cross-correlation function can provide better constraints on the comoving angular distance DM (6 per cent precision) compared to the constraint on the spherically averaged distance DV (9 per cent precision) obtained from the autocorrelation. Although not yet competitive, this technique will benefit from the arrival of deeper photometric data from upcoming surveys that will enable it to go beyond the current limitations we have identified in this work.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Constraining primordial non-Gaussianity from the large scale structure two-point and three-point correlation functions

Surveys of cosmological large-scale structure (LSS) are sensitive to the presence of local primordial non-Gaussianity (PNG), and may be used to constrain models of inflation. Local PNG, characterized by f NL ⁠, the amplitude of the quadratic correction to the potential of a Gaussian random field, is traditionally measured from LSS two-point and three-point clustering via the power spectrum and bi-spectrum. We propose a framework to measure f NL using the configuration space two-point correlation function (2pcf) monopole and three-point correlation function (3pcf) monopole of survey tracers. Our model estimates the effect of the scale-dependent bias induced by the presence of PNG on the 2pcf and 3pcf from the clustering of simulated dark matter haloes. We describe how this effect may be scaled to an arbitrary tracer of the cosmological matter density. The 2pcf and 3pcf of this tracer are measured to constrain the value of f NL ⁠. In LSS surveys, the effect of imaging systematics on two-point statistics is often degenerate with the PNG signal. Our proposed model employs three-point statistics primarily to break this degeneracy. Using simulations of luminous red galaxies observed by the Dark Energy Spectroscopic Instrument (DESI), we demonstrate the accuracy and constraining power of our method. Our forecast indicates the ability to constrain f NL to a precision of σf NL ≈ 22 with one year of DESI survey data, as well as the ability to constrain the imaging systematic weights in situ.

early Universe↗