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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

An analysis of the AVE-SESAME I period using statistical structure and correlation functions

Structure and correlation functions are used to describe atmospheric variability during the 10-11 April day of AVE-SESAME 1979 that coincided with the Red River Valley tornado outbreak. The special mesoscale rawinsonde data are employed in calculations involving temperature, geopotential height, horizontal wind speed and mixing ratio. Functional analyses are performed in both the lower and upper troposphere for the composite 24 h experiment period and at individual 3 h observation times. Results show that mesoscale features are prominent during the composite period. Fields of mixing ratio and horizontal wind speed exhibit the greatest amounts of small-scale variance, whereas temperature and geopotential height contain the least. Results for the nine individual times show that small-scale variance is greatest during the convective outbreak. The functions also are used to estimate random errors in the rawinsonde data. Finally, sensitivity analyses are presented to quantify confidence limits of the structure functions.

Fuelberg, H. E.↗
DOE OSTI2021

Information content of higher order galaxy correlation functions

The shapes of galaxy N-point correlation functions can be used as standard rulers to constrain the distance–redshift relationship. The cosmological density fields traced by late-time galaxy formation are initially nearly Gaussian, and hence, all the cosmological information can be extracted from their two-point correlation function. Subsequent non-linear evolution under gravity, as well as halo and then galaxy formation, generates higher order correlation functions. Since the mapping of the initial to the final density field is, on large scales, invertible, it is often claimed that the information content of the initial field’s power spectrum is equal to that of all the higher order functions of the final, non-linear field. This claim implies that reconstruction of the initial density field from the non-linear field renders analysis of higher order correlation functions of the latter superfluous. We show that this claim is false when the N-point functions are used as standard rulers. Constraints available from joint analysis of the two and three-point correlation functions can, in some cases, exceed those offered by the initial power spectrum. We provide a mathematical justification for this claim and demonstrate it using a large suite of N-body simulations. In particular, we show that for the z = 0 real-space matter field in the limit of vanishing shot-noise, taking modes up to k max = 0.2 h Mpc −1 , using the bispectrum alone offers a factor of 2 reduction in the variance on the cosmic distance scale relative to that available from the linear power spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2006

Spatial Correlation Function of the Chandra Selected Active Galactic Nuclei

We present the spatial correlation function analysis of non-stellar X-ray point sources in the Chandra Large Area Synoptic X-ray Survey of Lockman Hole Northwest (CLASXS). Our 9 ACIS-I fields cover a contiguous solid angle of 0.4 deg(exp 2) and reach a depth of 3 x 10(exp -15) erg/square cm/s in the 2-8 keV band. We supplement our analysis with data from the Chandra Deep Field North (CDFN). The addition of this field allows better probe of the correlation function at small scales. A total of 233 and 252 sources with spectroscopic information are used in the study of the CLASXS and CDFN fields respectively. We calculate both redshift-space and projected correlation functions in co-moving coordinates, averaged over the redshift range of 0.1 < z < 3.0, for both CLASXS and CDFN fields for a standard cosmology with Omega(sub Lambda) = 0.73,Omega(sub M) = 0.27, and h = 0.71 (H(sub 0) = 100h km/s Mpc(exp -1). The correlation function for the CLASXS field over scales of 3 Mpc< s < 200 Mpc can be modeled as a power-law of the form xi(s) = (S/SO)(exp - gamma), with gamma = 1.6(sup +0.4 sub -0.3) and S(sub o) = 8.0(sup +.14 sub -1.5) Mpc. The redshift-space correlation function for CDFN on scales of 1 Mpc< s < 100 Mpc is found to have a similar correlation length so = 8.55(sup +0.74 sub -0.74) Mpc, but a shallower slope (gamma = 1.3 +/- 0.1). The real-space correlation functions derived from the projected correlation functions, are found to be tau(sub 0 = 8.1(sup +1.2 sub -2.2) Mpc, and gamma = 2.1 +/- 0.5 for the CLASXS field, and tau(sub 0) = 5.8(sup +.1.0 sub -1.5) Mpc, gamma = 1.38(sup +0.12 sub -0.14 for the CDFN field. By comparing the real- and redshift-space correlation functions in the combined CLASXS and CDFN samples, we are able to estimate the redshift distortion parameter Beta = 0.4 +/- 0.2 at an effective redshift z = 0.94. We compare the correlation functions for hard and soft spectra sources in the CLASXS field and find no significant difference between the two groups. We have also found that the correlation between X-ray luminosity and clustering amplitude is weak, which, however, is fully consistent with the expectation using the simplest relations between X-ray luminosity, black hole mass, and dark halo mass. We study the evolution of the AGN clustering by dividing the samples into 4 redshift bins over 0.1 Mpc< z <3.0 Mpc. We find a very mild evolution in the clustering amplitude, which show the same evolution trend found in optically selected quasars in the 2dF survey. We estimate the evolution of the bias, and find that the bias increases rapidly with redshift (b(z = 0.45) = 0.95 +/- 0.15 and b(z = 2.07) = 3.03 +/- 0.83): The typical mass of the dark matter halo derived from the bias estimates show little change with redshift. The average halo mass is found to be log (M(sub halo)/M(sun))approximates 12.1. Subject headings: cosmology: observations - large-scale structure of the universe - x-rays: diffuse background - galaxies: nuclei

Yang, Y.↗
DOE OSTI2017

Two-point correlation functions in inhomogeneous and anisotropic cosmologies

Two-point correlation functions are ubiquitous tools of modern cosmology, appearing in disparate topics ranging from cosmological inflation to late-time astrophysics. When the background spacetime is maximally symmetric, invariance arguments can be used to fix the functional dependence of this function as the invariant distance between any two points. In this paper we introduce a novel formalism which fixes this functional dependence directly from the isometries of the background metric, thus allowing one to quickly assess the overall features of Gaussian correlators without resorting to the full machinery of perturbation theory. As an application we construct the CMB temperature correlation function in one inhomogeneous (namely, an off-center LTB model) and two spatially flat and anisotropic (Bianchi) universes, and derive their covariance matrices in the limit of almost Friedmannian symmetry. We show how the method can be extended to arbitrary N -point correlation functions and illustrate its use by constructing three-point correlation functions in some simple geometries.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Mapping the current–current correlation function near a quantum critical point

The current–current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson’s localization length can be computed entirely from this correlation function. Based on the critical behavior of these two physical quantities near the plateau–insulator or plateau–plateau transitions in the integer quantum Hall effect, we derive an asymptotic formula for the current–current correlation function, which enables us to make several theoretical predictions about its generic behavior. For the disordered Hofstadter model, we employ numerical simulations to map the current–current correlation function, obtain its asymptotic form near a critical point and confirm the theoretical predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Empirical investigation of nuclear correlation function distributions in lattice QCD

Two-point correlation functions of systems with baryon number 𝐵 ∈ {1,2,3,4} are investigated using lattice quantum chromodynamics (QCD). In particular, the empirical distributions of importance-sampling Monte-Carlo samples of these correlation functions are examined as a function of the spacetime separation between the two points and the baryon number. While the exact forms of these distributions are not known for QCD, recent work has determined asymptotic expressions for analogous correlation function distributions in simpler theories such as scalar field theory and the disordered phase of the 𝑂⁡(𝑁) model. The theoretical 𝑂⁡(𝑁) model distributions are found to provide an accurate description of the empirical QCD distributions at zero momentum over a wide range of temporal separations for each baryon number when assessed with a range of different statistical tests. In particular, the behavior of the baryon number 𝐵 QCD correlation function at large temporal separation is well reproduced by the 𝑂⁡(𝑁 ∼ 2/𝐵) model distribution.

Lattice field theory↗
NASA NTRS1993

Omega from the anisotropy of the redshift correlation function

Peculiar velocities distort the correlation function of galaxies observed in redshift space. In the large scale, linear regime, the distortion takes a characteristic quadrupole plus hexadecapole form, with the amplitude of the distortion depending on the cosmological density parameter omega. Preliminary measurements are reported here of the harmonics of the correlation function in the CfA, SSRS, and IRAS 2 Jansky redshift surveys. The observed behavior of the harmonics agrees qualitatively with the predictions of linear theory on large scales in every survey. However, real anisotropy in the galaxy distribution induces large fluctuations in samples which do not yet probe a sufficiently fair volume of the Universe. In the CfA 14.5 sample in particular, the Great Wall induces a large negative quadrupole, which taken at face value implies an unrealistically large omega 20. The IRAS 2 Jy survey, which covers a substantially larger volume than the optical surveys and is less affected by fingers-of-god, yields a more reliable and believable value, omega = 0.5 sup +.5 sub -.25.

Hamilton, A. J. S.↗
DOE OSTI2017

Correlation function of the luminosity distances

We present the correlation function of the luminosity distances in a flat ΛCDM universe. Decomposing the luminosity distance fluctuation into the velocity, the gravitational potential, and the lensing contributions in linear perturbation theory, we study their individual contributions to the correlation function. The lensing contribution is important at large redshift ( z ∼> 0.5) but only for small angular separation (θ ∼< 3°), while the velocity contribution dominates over the other contributions at low redshift or at larger separation. However, the gravitational potential contribution is always subdominant at all scale, if the correct gauge-invariant expression is used. The correlation function of the luminosity distances depends significantly on the matter content, especially for the lensing contribution, thus providing a novel tool of estimating cosmological parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Euclidean correlation functions in quantum gravity

We calculate Euclidean correlation functions through next-to-leading order in the low-energy effective theory of gravity. We focus on correlation functions of curvature and volume operators, calculating these functions through one-loop order. We show that quantum fluctuations of the background spacetime must be taken into account in order to obtain gauge invariant expressions, and we point out a subtlety associated with the analytic continuation of the conformal mode. Our final expressions for the correlation functions involve only Newton’s constant and the source-sink separation, and they are a universal prediction of the low-energy effective theory. Thus, they serve as a useful point of comparison for nonperturbative lattice formulations of gravity.

Effective field theory↗
NASA NTRS2004

The Generalization of Mutual Information as the Information between a Set of Variables: The Information Correlation Function Hierarchy and the Information Structure of Multi-Agent Systems

The topic of this paper is a hierarchy of information-like functions, here named the information correlation functions, where each function of the hierarchy may be thought of as the information between the variables it depends upon. The information correlation functions are particularly suited to the description of the emergence of complex behaviors due to many- body or many-agent processes. They are particularly well suited to the quantification of the decomposition of the information carried among a set of variables or agents, and its subsets. In more graphical language, they provide the information theoretic basis for understanding the synergistic and non-synergistic components of a system, and as such should serve as a forceful toolkit for the analysis of the complexity structure of complex many agent systems. The information correlation functions are the natural generalization to an arbitrary number of sets of variables of the sequence starting with the entropy function (one set of variables) and the mutual information function (two sets). We start by describing the traditional measures of information (entropy) and mutual information.

Wolf, David R.↗
DOE OSTI2024

Correlation functions from tensor network influence functionals: The case of the spin-boson model

We investigate the application of matrix product state (MPS) representations of the influence functionals (IFs) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff–Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation, which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.

Chemistry↗
NASA NTRS1972

Estimation of correlation functions by stochastic approximation.

Consideration of the autocorrelation function of a zero-mean stationary random process. The techniques are applicable to processes with nonzero mean provided the mean is estimated first and subtracted. Two recursive techniques are proposed, both of which are based on the method of stochastic approximation and assume a functional form for the correlation function that depends on a number of parameters that are recursively estimated from successive records. One technique uses a standard point estimator of the correlation function to provide estimates of the parameters that minimize the mean-square error between the point estimates and the parametric function. The other technique provides estimates of the parameters that maximize a likelihood function relating the parameters of the function to the random process. Examples are presented.

Habibi, A.↗
NASA NTRS1986

The cluster-cluster correlation function

The clustering properties of the Abell and Zwicky cluster catalogs are studied using the two-point angular and spatial correlation functions. The catalogs are divided into eight subsamples to determine the dependence of the correlation function on distance, richness, and the method of cluster identification. It is found that the Corona Borealis supercluster contributes significant power to the spatial correlation function to the Abell cluster sample with distance class of four or less. The distance-limited catalog of 152 Abell clusters, which is not greatly affected by a single system, has a spatial correlation function consistent with the power law Xi(r) = 300r exp -1.8. In both the distance class four or less and distance-limited samples the signal in the spatial correlation function is a power law detectable out to 60/h Mpc. The amplitude of Xi(r) for clusters of richness class two is about three times that for richness class one clusters. The two-point spatial correlation function is sensitive to the use of estimated redshifts.

Postman, M.↗
NASA NTRS1990

The two-point correlation function for groups of galaxies in the Center for Astrophysics redshift survey

The large-scale distribution of groups of galaxies selected from complete slices of the CfA redshift survey extension is examined. The survey is used to reexamine the contribution of group members to the galaxy correlation function. The relationship between the correlation function for groups and those calculated for rich clusters is discussed, and the results for groups are examined as an extension of the relation between correlation function amplitude and richness. The group correlation function indicates that groups and individual galaxies are equivalent tracers of the large-scale matter distribution. The distribution of group centers is equivalent to random sampling of the galaxy distribution. The amplitude of the correlation function for groups is consistent with an extrapolation of the amplitude-richness relation for clusters. The amplitude scaled by the mean intersystem separation is also consistent with results for richer clusters.

Ramella, Massimo↗
DOE OSTI2017

Cumulants and correlation functions versus the QCD phase diagram

Here, we discuss the relation of particle number cumulants and correlation functions. It is argued that measuring couplings of the genuine multiparticle correlation functions could provide cleaner information on possible nontrivial dynamics in heavy-ion collisions. We also extract integrated multiproton correlation functions from the presently available experimental data on proton cumulants. We find that the STAR data contain significant four-proton correlations, at least at the lower energies, with indication of changing dynamics in central collisions. We also find that these correlations are rather long ranged in rapidity. Finally, using the Ising model, we demonstrate how the signs of the multiproton correlation functions may be used to exclude certain regions of the phase diagram close to the critical point.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Statistics of baryon correlation functions in lattice QCD

A systematic analysis of the structure of single-baryon correlation functions calculated with lattice QCD is performed, with a particular focus on characterizing the structure of the noise associated with quantum fluctuations. The signal-to-noise problem in these correlation functions is shown, as long suspected, to result from a sign problem. The log-magnitude and complex phase are found to be approximately described by normal and wrapped normal distributions respectively. Properties of circular statistics are used to understand the emergence of a large time noise region where standard energy measurements are unreliable. Power-law tails in the distribution of baryon correlation functions, associated with stable distributions and “Lévy flights,” are found to play a central role in their time evolution. A new method of analyzing correlation functions is considered for which the signal-to-noise ratio of energy measurements is constant, rather than exponentially degrading, with increasing source-sink separation time. This new method includes an additional systematic uncertainty that can be removed by performing an extrapolation, and the signal-to-noise problem reemerges in the statistics of this extrapolation. It is demonstrated that this new method allows accurate results for the nucleon mass to be extracted from the large-time noise region inaccessible to standard methods. The observations presented here are expected to apply to quantum Monte Carlo calculations more generally. Similar methods to those introduced here may lead to practical improvements in analysis of noisier systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1986

Analysis/forecast experiments with a flow-dependent correlation function using FGGE data

The use of a flow-dependent correlation function to improve the accuracy of an optimum interpolation (OI) scheme is examined. The development of the correlation function for the OI analysis scheme used for numerical weather prediction is described. The scheme uses a multivariate surface analysis over the oceans to model the pressure-wind error cross-correlation and it has the ability to use an error correlation function that is flow- and geographically-dependent. A series of four-day data assimilation experiments, conducted from January 5-9, 1979, were used to investigate the effect of the different features of the OI scheme (error correlation) on forecast skill for the barotropic lows and highs. The skill of the OI was compared with that of a successive correlation method (SCM) of analysis. It is observed that the largest difference in the correlation statistics occurred in barotropic and baroclinic lows and highs. The comparison reveals that the OI forecasts were more accurate than the SCM forecasts.

Baker, W. E.↗