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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 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 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↗
DOE OSTI2022

The effect of quasar redshift errors on Lyman-α forest correlation functions

ABSTRACT Using synthetic Lyman-α forests from the Dark Energy Spectroscopic Instrument (DESI) survey, we present a study of the impact of errors in the estimation of quasar redshift on the Lyman-α correlation functions. Estimates of quasar redshift have large uncertainties of a few hundred km s−1 due to the broadness of the emission lines and the intrinsic shifts from other emission lines. We inject Gaussian random redshift errors into the mock quasar catalogues, and measure the auto-correlation and the Lyman-α-quasar cross-correlation functions. We find a smearing of the BAO feature in the radial direction, but changes in the peak position are negligible. However, we see a significant unphysical correlation for small separations transverse to the line of sight which increases with the amplitude of the redshift errors. We interpret this contamination as a result of the broadening of emission lines in the measured mean continuum, caused by quasar redshift errors, combined with the unrealistically strong clustering of the simulated quasars on small scales.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1989

Correlation Functions Aid Analyses Of Spectra

New uses found for correlation functions in analyses of spectra. In approach combining elements of both pattern-recognition and traditional spectral-analysis techniques, spectral lines identified in data appear useless at first glance because they are dominated by noise. New approach particularly useful in measurement of concentrations of rare species of molecules in atmosphere.

Beer, Reinhard↗
DOE OSTI2022

Exact constraints and appropriate norms in machine-learned exchange-correlation functionals

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human-designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently, efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to de-orbitalize the strongly constrained and appropriately normed (SCAN) functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding the use of the orbital-dependent kinetic energy density. The performance and transferability of the machine-learned functional are demonstrated for molecular and periodic systems.

Artificial neural networks↗
NASA NTRS1985

Cosmological density fluctuations and large-scale structure From N-point correlation functions to the probability distribution

Knowledge of N-point correlation functions for all N allows one to invert and obtain the probability distribution of mass fluctuations in a fixed volume. The hierarchical sequence of higher order is applied to correlations with dimensionless amplitudes suggested by the BBGKY equations. The resulting distribution is significantly non-Gaussian, even for quite small mean square fluctuations. The qualitative and to some degree quantitative results are to a large degree independent of the exact sequence of amplitudes. An ensemble of such models compared with N-body simulations fails in detail to account for the low-density frequency distribution.

Fry, J. N.↗
DOE OSTI2023

First test of the consistency relation for the large-scale structure using the anisotropic three-point correlation function of BOSS DR12 galaxies

ABSTRACT We present, for the first time, an observational test of the consistency relation for the large-scale structure (LSS) of the Universe through a joint analysis of the anisotropic two- and three-point correlation functions (2PCF and 3PCF) of galaxies. We parameterize the breakdown of the LSS consistency relation in the squeezed limit by Es, which represents the ratio of the coefficients of the shift terms in the second-order density and velocity fluctuations. Es ≠ 1 is a sufficient condition under which the LSS consistency relation is violated. A novel aspect of this work is that we constrain Es by obtaining information about the non-linear velocity field from the quadrupole component of the 3PCF without taking the squeezed limit. Using the galaxy catalogues in the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, we obtain $E_{\rm s} = -0.92_{-3.26}^{+3.13}$, indicating that there is no violation of the LSS consistency relation in our analysis within the statistical errors. Our parameterization is general enough that our constraint can be applied to a wide range of theories, such as multicomponent fluids, modified gravity theories, and their associated galaxy bias effects. Our analysis opens a new observational window to test the fundamental physics using the anisotropic higher-order correlation functions of galaxy clustering.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2012

Reporting Recommended Patch Density from Vehicle Panel Vibration Convergence Studies using both DAF and TBL Fits of the Spatial Correlation Function

Using the patch method to represent the continuous spatial correlation function of a phased pressure field over a structural surface is an approximation. The approximation approaches the continuous function as patches become smaller. Plotting comparisons of the approximation vs the continuous function may provide insight revealing: (1) For what patch size/density should the approximation be very good? (2) What the approximation looks like when it begins to break down? (3) What the approximation looks like when the patch size is grossly too large. Following these observations with a convergence study using one FEM may allow us to see the importance of patch density. We may develop insights that help us to predict sufficient patch density to provide adequate convergence for the intended purpose frequency range of interest

Smith, Andrew M.↗