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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

The double-soft limit in cosmological correlation functions and graviton exchange effects

The graviton exchange effect on cosmological correlation functions is examined by employing the double-soft limit technique. A new relation among correlation functions that contain the effects due to graviton exchange diagrams in addition to those due to scalar-exchange and scalar-contact-interaction, is derived by using the background field method and independently by the method of Ward identities associated with dilatation symmetry. We compare these three terms, putting small values for the slow-roll parameters and (1− n {sub s} ) ≈ 0.042, where n {sub s} is the scalar spectral index. It is argued that the graviton exchange effects are more dominant than the other two and could be observed in the trispectrum in the double-soft limit. Our observation strengthens the previous work by Seery, Sloth and Vernizzi, in which it has been argued that the graviton exchange dominates in the counter-collinear limit for single field slow-roll inflation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A perturbative approach to the redshift space correlation function: beyond the Standard Model

We extend our previous redshift space power spectrum code to the redshift space correlation function. Here we focus on the Gaussian Streaming Model (GSM). Again, the code accommodates a wide range of modified gravity and dark energy models. For the non-linear real space correlation function used in the GSM we use the Fourier transform of the RegPT 1-loop matter power spectrum. We compare predictions of the GSM for a Vainshtein screened and Chameleon screened model as well as GR. These predictions are compared to the Fourier transform of the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model which is fit to N-body data. We find very good agreement between the Fourier transform of the TNS model and the GSM predictions, with ≤ 6% deviations in the first two correlation function multipoles for all models for redshift space separations in 50Mpc h ≤ s ≤ 180Mpc/ h . Excellent agreement is found in the differences between the modified gravity and GR multipole predictions for both approaches to the redshift space correlation function, highlighting their matched ability in picking up deviations from GR. We elucidate the timeliness of such non-standard templates at the dawn of stage-IV surveys and discuss necessary preparations and extensions needed for upcoming high quality data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Development of Colle-Salvetti type electron-nucleus correlation functional for MC-DFT

A Colle-Salvetti type electron-nucleus correlation functional for multicomponent density-functional theory is proposed. We demonstrate that our correlation functional quantitatively reproduces the quantum nuclear effects of protons; the mean absolute deviation value is 2.8 millihartrees for the optimized structure of hydrogen-containing molecules. We also show other practical calculations with our new electron-deuteron and electron-triton correlation functionals. Since this functional is derived without any unphysical assumption, the strategy taken in this development will be a promising recipe to make new functionals for the potentials of other particles’ interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

The discrete correlation function: A new method for analyzing unevenly sampled variability data

A method of measuring correlation functions without interpolating in the temporal domain, the discrete correlation function, is introduced. It provides an assumption-free representation of the correlation measured in the data, and allows meaningful error estimates. This method does not produce spurious correlations at zero lag due to correlated errors. It is shown that physical interpretation of active galactic nuclei cross-correlation functions requires knowledge of the input function's fluctuation power spectrum, involves model-dependence in the form of symmetry assumptions, and must take into account intrinsic scale bias. This technique was used to find a correlation in published IUE data for NGC 4151, which indicates that the broad C IV feature emanates from a shell 15 to 75 light-days in radius, assuming spherical symmetry.

Edelson, R. A.↗
NASA NTRS1989

Two-point correlation function of cosmic-string loops

The two-point correlations of cosmic-string loops are studied with numerical simulations of the evolution of a cosmic-string network in an expanding universe. It is found that the initial positions of loops that are chopped off the network have a correlation function that is quite similar to the highest estimates of the Abell-cluster correlation function, but these correlations are rapidly washed out by the motion of the loops. The implications for the cosmic-string galaxy-formation scenario are briefly discussed.

Bennett, David P.↗
DOE OSTI2017

Localizing Holes as Polarons and Predicting Band Gaps, Defect Levels, and Delithiation Energies of Solid-State Materials with a Local Exchange-Correlation Functional

Here, we assess the performance of seven exchange–correlation functionals (some with and some without a Hubbard U correction) for their ability (i) to predict band gaps of silicon, diamond, and Li-ion battery cathode materials, (ii) to localize hole polarons and predict delithiation energies in Li-ion battery cathode materials, and (iii) to predict transition levels of charge carriers of doped silicon and diamond. Both local and hybrid exchange–correlation functionals were tested. The local functionals tend to underestimate band gaps and delocalize polarons. The hybrid functionals very often give a good description of both properties, but they may not be practical for calculations involving large unit cells, large ensembles, or dynamics, and therefore a local functional with a Hubbard U correction is often used (giving the method called DFT+U), where the value of a parameter U is adjusted according to the system and the property being investigated. Keeping in mind the importance of computational cost and the undesirability of having to adjust an empirical parameter for each system or property of interest, we recently developed a local functional, namely HLE17, to try to accurately predict band gaps and excitation energies, and we validated it using mostly main-group solids and molecules. Here we test the performance of HLE17 for its ability to predict band gaps and localize polarons in other solid-state materials, and we compare its performance to that of popular local functionals (PBE, PBEsol, and TPSS), a range-separated hybrid functional with screened exchange (HSE06), and DFT+U. We find that HLE17 predicts more accurate band gaps than other local functionals and can localize holes as polarons, which other local functionals usually fail to do, and for a number of cases it is comparable in performance quality to Hubbard-corrected functionals without the need for system-specific parametrization and to hybrid functionals without the high cost. Because HLE17 does not predict accurate lattice constants, we use the single-point method of quantum chemistry, where the geometry is optimized with one functional and the band gap is calculated with HLE17, or we perform calculations with the lattice constants obtained by TPSS and both the fractional intracell coordinates and the electronic structure obtained by HLE17 (a new method denoted HLE17\\TPSS). In particular, we performed calculations by HLE17//TPSS, HLE17//HSE06, HLE17//DFT+U, and HLE17\\TPSS, and these methods usually agree well with each other and give values similar to experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1989

The Shane Wirtanen counts - Observability of the galaxy correlation function

An explicit test of the ability of the galaxy two-point correlation function to be recovered from the Lick counts of galaxies (Shane and Wirtanen, 1967) is reported. High-fidelity simulations are created, starting with the distribution of galaxies in space. These distributions are projected onto a set of simulated Lick plates which are reduced to a uniform limiting magnitude with the method of Seldner et al. (1977). The simulated catalogs are then analyzed with the methods of Groth and Peebles (1977). The resulting correlation functions are found to reproduce accurately the correlation functions that were built in during the first step of the simulations.

Brown, Michael E.↗
DOE OSTI2019

Correlation functions on the Half-BPS Wilson loop: perturbation and hexagonalization

We compute correlation functions of protected primaries on the 1/2-BPS Wilson loop in N=4 super Yang-Mills theory at weak coupling. We first perform direct perturbative computation at one loop in the planar limit and present explicit formulae for general two-, three- and four-point functions. The results for two- and three-point functions as well as four-point functions in special kinematics are in perfect agreement with the localization computation performed in arXiv:1802.05201 . We then analyze the results in view of the integrability-based approach called “hexagonalization”, which was introduced previously to study the correlation functions in the absence of the Wilson loop. In this approach, one decomposes the correlator into fundamental building blocks called “hexagons”, and glues them back together by summing over the intermediate states. Through the comparison, we conjecture that the correlation functions on the Wilson loop can be computed by contracting hexagons with boundary states, where each boundary state represents a segment of the Wilson loop. As a byproduct, we make predictions for the large-charge asymptotics of the structure constants on the Wilson loop. Along the way, we refine the conjecture for the integrability-based approach to the general non-BPS structure constants on the Wilson loop, proposed originally in arXiv:1706.02989 .

1/N Expansion↗
DOE OSTI2024

Multiparticle integral and differential correlation functions

This paper formalizes the use of integral and differential cumulants for measurements of multiparticle event-by-event transverse momentum fluctuations, rapidity fluctuations, as well as net-charge fluctuations. This enables the introduction of multiparticle balance functions, defined based on differential correlation functions (factorial cumulants), that suppress two- and three-prong resonance decays effects and enable measurements of underlying long-range correlations obeying quantum number conservation constraints. These multiparticle balance functions satisfy simple sum rules determined by quantum number conservation. It is additionally shown that these multiparticle balance functions arise as an intrinsic component of high-order net-charge cumulants. This implies that the magnitude of these cumulants, measured in a specific experimental acceptance, is strictly constrained by charge conservation and primarily determined by the rapidity and momentum width of these balance functions. The paper also presents techniques to reduce the computation time of differential correlation functions up to order n = 10 based on the methods of moments. Published by the American Physical Society 2024

Physics↗
NASA NTRS1981

Correlation function studies for snow and ice

The random medium model is used to characterize snow and ice fields in the interpretation of active and passive microwave remote sensing data. A correlation function is used to describe the random permittivity fluctuations with the associated mean and variance and correlation lengths; and several samples are investigated to determine typical correlation functions for snow and ice. It is shown that correlation functions are extracted directly from appropriate ground truth data, and an exponential correlation function is observed for snow and ice with lengths corresponding to the actual size of ice particles or air bubbles. Thus, given that a medium has spatially stationary statistics and a small medium, the random medium model can interpret remote sensing data where theoretical parameters correspond to actual physical parameters of the terrain.

Vallese, F.↗
DOE OSTI2021

Theory and application of the vector pair correlation function for real-space crystallographic analysis of order/disorder correlations from STEM images

Deviations of local structure and chemistry from the average crystalline unit cell are increasingly recognized to have a significant influence on the properties of many technologically important materials. Here, we present the vector pair correlation function (vPCF) as a new real-space crystallographic analysis method, which can be applied to atomic-resolution scanning transmission electron microscopy (STEM) images to quantify and analyze structural order/disorder correlations. Our STEM-based vPCFs have several advantages over radial PCFs and/or 3D pair distribution functions from x-ray total scattering: vPCFs explicitly retain crystallographic orientation information, are spatially resolved, can be applied directly on a sublattice basis, and are suitable for any material that can be imaged with STEM. To show the utility of our approach, we measure partial vPCFs in Ba 5 SmSn 3 Nb 7 O 30 (BSSN), a tetragonal tungsten bronze (TTB) structured complex oxide. Many TTBs are known to be classical or relaxor ferroelectrics, and these properties have been correlated with the presence of superlattice ordering. BSSN, specifically, exhibits relaxor behavior and an incommensurate structural modulation. From the vPCF data, we observe that, of the cation sites, only the Ba (A2) sublattice is structurally modulated. We then infer the local modulation vector and reveal a marked anisotropy in its correlation length. Finally, short-range correlated polar displacements on the B2 cation sites are observed. This work introduces the vPCF as a powerful real-space crystallography technique, which enables direct, robust quantification of short-to-long range order on a sublattice-specific basis and is applicable to a wide range of complex material types.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Simulation studies of R 2 (Δη,Δφ) and P 2 (Δη,Δφ) correlation functions in pp collisions with the PYTHIA and HERWIG models

We report studies of charge-independent (CI) and charge-dependent (CD) two-particle differential-number correlation functions, R 2 (Δη,Δφ), and transverse momentum (p T ) correlation functions, P 2 (Δη,Δφ), of charged particles in √s = 2.76 TeV pp collisions with the PYTHIA and HERWIG models. Model predictions are presented for inclusive charged hadrons (h ± ), as well as pions (π ± ), kaons (K ± ), and (anti-)protons (p¯/p) in the ranges 0.2 < p T ≤ 2.0 GeV/c, 2.0 < p T ≤ 5.0 GeV/c, and 5.0 < p T ≤ 30.0 GeV/c, with full azimuthal coverage in the range |η| < 1.0. We compare the model predictions for the strength and shape of the R 2 and P 2 correlators as these pertain to recent measurements by the ALICE collaboration. The R 2 and P 2 correlation functions estimated with PYTHIA and HERWIG exhibit qualitatively similar near-side and away-side correlation structures but feature important differences. Here, our analysis indicates that comparative studies of R 2 and P 2 correlation functions would provide valuable insight towards the understanding of particle production in pp collisions, and by extension, should also be useful in studies of heavy-ion collisions. Comparison of the Δη dependence of R 2 and P 2 could contribute, in particular, to a better understanding and modeling of the angular ordering of particles produced by hadronization in jets, as well as a better description of jet fragmentation functions of identified species at low momentum fraction (z).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Effect of centrality bin width corrections on two-particle number and transverse momentum differential correlation functions

Two-particle number and transverse momentum differential correlation functions are powerful tools for unveiling the detailed dynamics and particle production mechanisms involved in relativistic heavy-ion collisions. Measurements of transverse momentum correlators P 2 and G 2 , in particular, provide added information not readily accessible with better known number correlation functions R 2 . However, it is found that the R 2 and G 2 correlators are somewhat sensitive to the details of the experimental procedure used to measure them. They exhibit, in particular, a dependence on the collision centrality bin width, which may have a rather detrimental impact on their physical interpretation. A technique to correct these correlators for collision centrality bin-width averaging is presented. The technique is based on the hypothesis that the shape of single- and pair-probability densities vary slower with collision centrality than the corresponding integrated yields. In conclusion, the technique is tested with Pb-Pb simulations based on the HIJING and ultrarelativistic quantum molecular dynamics models and shown to enable a precision better than 1% for particles in the kinematic range 0.2 ≤ p T ≤ 2.0 GeV/c.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Non-Gaussianity in the weak lensing correlation function likelihood – implications for cosmological parameter biases

ABSTRACT We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in 1D marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in 1D posteriors of Ωm and σ8 due to the non-Gaussian likelihood distributions of shear correlations functions using the mock data (100 deg2). We also present a systematic approach to constructing approximate multivariate likelihoods with 1D parametric functions by assuming independence or more flexible non-parametric multivariate methods after decorrelating the data points using principal component analysis (PCA). While the use of PCA does not modify the non-Gaussianity of the multivariate likelihood, we find empirically that the 1D marginal sampling distributions of the PCA components exhibit less skewness and kurtosis than the original shear correlation functions. Modelling the likelihood with marginal parametric functions based on the assumption of independence between PCA components thus gives a lower limit for the biases. We further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex non-Gaussian likelihood models would be even smaller for an LSST-like survey. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of ∼5.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Measurement of the dipole in the cross-correlation function of galaxies

It is usually assumed that in the linear regime the two-point correlation function of galaxies contains only a monopole, quadrupole and hexadecapole. Looking at cross-correlations between different populations of galaxies, this turns out not to be the case. In particular, the cross-correlations between a bright and a faint population of galaxies contain also a dipole. In this paper we present the first attempt to measure this dipole. We discuss the four types of effects that contribute to the dipole: relativistic distortions, evolution effect, wide-angle effect and large-angle effect. We show that the first three contributions are intrinsic anti-symmetric contributions that do not depend on the choice of angle used to measure the dipole. On the other hand the large-angle effect appears only if the angle chosen to extract the dipole breaks the symmetry of the problem. We show that the relativistic distortions, the evolution effect and the wide-angle effect are too small to be detected in the LOWz and CMASS sample of the BOSS survey. On the other hand with a specific combination of angles we are able to measure the large-angle effect with high significance. We emphasise that this large-angle dipole does not contain new physical information, since it is just a geometrical combination of the monopole and the quadrupole. However this measurement, which is in excellent agreement with theoretical predictions, validates our method for extracting the dipole from the two-point correlation function and it opens the way to the detection of relativistic effects in future surveys like e.g. DESI.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1977

The velocity correlation function in cosmic-ray diffusion theory

It is shown that Earl's (1973) eigenvalue sum for the cosmic-ray spatial diffusion coefficient parallel to the mean magnetic field is precisely equivalent to the time integral of the particle-velocity correlation function parallel to the mean field. A derivation due to Kubo (1957) is applied to cosmic-ray pitch-angle scattering, and it is proven that all nine components of the cosmic-ray diffusion tensor can be expressed as integrals over the velocity correlation function. A pitch-angle correlation function is derived, and the effect of long-wavelength turbulence on the velocity correlation function and spatial diffusion coefficients is examined. Application of the velocity-correlation method to a realistic case involving both pitch-angle scattering and appreciable fluctuation in the direction of the local field indicates that long-wavelength turbulence in the local field reduces the parallel diffusion coefficient and places an upper limit on the ratio of the perpendicular to parallel diffusion coefficients.

Forman, M. A.↗
DOE OSTI2015

Position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey Data Release 10 CMASS sample

We report on the first measurement of the three-point function with the position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 10 CMASS sample. This new observable measures the correlation between two-point functions of galaxy pairs within different subvolumes, ξ-circumflex (ř,ř{sub L}), where ř{sub L} is the location of a subvolume, and the corresponding mean overdensities, δ-bar (ř{sub L}). This correlation, which we call the 'integrated three-point function', iζ(r)≡(ξ-circumflex (ř,ř{sub L})δ-bar (ř{sub L})), measures a three-point function of two short- and one long-wavelength modes, and is generated by nonlinear gravitational evolution and possibly also by the physics of inflation. The iζ(r) measured from the BOSS data lies within the scatter of those from the mock galaxy catalogs in redshift space, yielding a ten-percent-level determination of the amplitude of iζ(r). The tree-level perturbation theory in redshift space predicts how this amplitude depends on the linear and quadratic nonlinear galaxy bias parameters (b{sub 1} and b{sub 2}), as well as on the amplitude and linear growth rate of matter fluctuations (σ{sub 8} and f). Combining iζ(r) with the constraints on b{sub 1σ{sub 8}} and fσ{sub 8} from the global two-point correlation function and that on σ{sub 8} from the weak lensing signal of BOSS galaxies, we measure b{sub 2}=0.41±0.41 (68% C.L.) assuming standard perturbation theory at the tree level and the local bias model.

79 ASTRONOMY AND ASTROPHYSICS↗