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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
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 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↗
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.↗
NASA NTRS1988

The mean density and two-point correlation function for the CfA redshift survey slices

The effect of large-scale inhomogeneities on the determination of the mean number density and the two-point spatial correlation function were investigated for two complete slices of the extension of the Center for Astrophysics (CfA) redshift survey (de Lapparent et al., 1986). It was found that the mean galaxy number density for the two strips is uncertain by 25 percent, more so than previously estimated. The large uncertainty in the mean density introduces substantial uncertainty in the determination of the two-point correlation function, particularly at large scale; thus, for the 12-deg slice of the CfA redshift survey, the amplitude of the correlation function at intermediate scales is uncertain by a factor of 2. The large uncertainties in the correlation functions might reflect the lack of a fair sample.

De Lapparent, Valerie↗
DOE OSTI2023

Large-time correlation functions in bosonic lattice field theories

Large-time correlation functions have a pivotal role in extracting particle masses from Euclidean lattice field theory calculations, however little is known about the statistical properties of these quantities. In this work, the asymptotic form of the distributions of the correlation functions at vanishing momentum is determined for bosonic interacting lattice field theories with a unique gapped vacuum. It is demonstrated that the deviations from the asymptotic form at large Euclidean times can be utilized to determine the spectrum of the theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1998

A Kinematically Consistent Two-Point Correlation Function

A simple kinematically consistent expression for the longitudinal two-point correlation function related to both the integral length scale and the Taylor microscale is obtained. On the inner scale, in a region of width inversely proportional to the turbulent Reynolds number, the function has the appropriate curvature at the origin. The expression for two-point correlation is related to the nonlinear cascade rate, or dissipation epsilon, a quantity that is carried as part of a typical single-point turbulence closure simulation. Constructing an expression for the two-point correlation whose curvature at the origin is the Taylor microscale incorporates one of the fundamental quantities characterizing turbulence, epsilon, into a model for the two-point correlation function. The integral of the function also gives, as is required, an outer integral length scale of the turbulence independent of viscosity. The proposed expression is obtained by kinematic arguments; the intention is to produce a practically applicable expression in terms of simple elementary functions that allow an analytical evaluation, by asymptotic methods, of diverse functionals relevant to single-point turbulence closures. Using the expression devised an example of the asymptotic method by which functionals of the two-point correlation can be evaluated is given.

Ristorcelli, J. R.↗
DOE OSTI2021

Cumulants and correlation functions of net-proton, proton, and antiproton multiplicity distributions in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider

Here, we report a systematic measurement of cumulants, C n , for net-proton, proton, and antiproton multiplicity distributions, and correlation functions, κ n , for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The C n and κ n are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, y, and transverse momentum, p T . The data were taken during the first phase of the Beam Energy Scan (BES) program (2010–2017) at the BNL Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity (|y| < 0.5) and transverse momentum 0.4 < p T < 2.0 GeV/c, using the STAR detector at RHIC. We observe a nonmonotonic energy dependence ($\sqrt{s_{NN}}$ = 7.7–62.4 GeV) of the net-proton C 4 /C 2 with the significance of 3.1σ for the 0–5% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with $\sqrt{s_{NN}}$. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, κ 2 , of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, κ 4 , of protons plays a role in determining the energy dependence of proton C 4 /C 1 below 19.6 GeV, which cannot be understood by the effect of baryon number conservation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Angular Correlation Function Estimators Accounting for Contamination from Probabilistic Distance Measurements

With the advent of surveys containing millions to billions of galaxies, it is imperative to develop analysis techniques that utilize the available statistical power. In galaxy clustering, even small sample contamination arising from distance uncertainties can lead to large artifacts, which the standard estimator for two-point correlation functions does not account for. We first introduce a formalism, termed decontamination, that corrects for sample contamination by utilizing the observed cross-correlations in the contaminated samples; this corrects any correlation function estimator for contamination. Using this formalism, we present a new estimator that uses the standard estimator to measure correlation functions in the contaminated samples but then corrects for contamination. We also introduce a weighted estimator that assigns each galaxy a weight in each redshift bin based on its probability of being in that bin. We demonstrate that these estimators effectively recover the true correlation functions and their covariance matrices. Our estimators can correct for sample contamination caused by misclassification between object types as well as photometric redshifts; they should be particularly helpful for studies of galaxy evolution and baryonic acoustic oscillations, where forward modeling the clustering signal using the contaminated redshift distribution is undesirable.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1983

The spatial correlation function of rich clusters of galaxies

A series of objective statistical estimators is applied to directly study the three-dimensional distribution of rich clusters, using a recently completed redshift sample of 104 Abell clusters out to distance class four and galactic latitude of 30 deg or more. The sample and the relevant positional and redshift selection effects are discussed, and the two-point angular correlation function and nearest-neighbor distribution of clusters in the sample are determined, as well as in the larger D = 5+6 sample and in several subsamples of different richness classes and latitude zones. The redshift correlation function of clusters for various angular separations on the sky is examined as a test for the reality of the observed angular correlations. The two-point spatial correlation function of clusters in the sample is determined, and the consistency among the three observed correlation functions is tested. A model that describes all the observed correlations is presented.

Bahcall, N. A.↗
DOE OSTI2022

Efficient computation of N -point correlation functions in D dimensions

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have $\mathscr O$(n N ) complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity $\mathscr O$(n 2 ) or $\mathscr O$(n g log n g ) if evaluated using a Fast Fourier Transform on a grid of size n g . Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the (D – 1) sphere and are intrinsically related to angular momentum operators. Concatenation of (N – 1) such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Omega from the anisotropy of the redshift correlation function in the IRAS 2 Jansky survey

Peculiar velocities distort the correlation function of galaxies in redshift space. In the linear regime, the distortion has a characteristic quadrupole plus hexadecapole form, with amplitude depending on the cosmological density parameter Omega. I report here measurements of the anisotropy of the correlation function in the IRAS 2 Jy redshift survey. The inferred value of Omega is Omega = 0.5 + 0.5 or - 0.25.

Hamilton, A. J. S.↗
NASA NTRS2014

Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 − S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

infrared radiation↗
NASA NTRS2012

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

correlation function↗
DOE OSTI2023

Exponential vs Gaussian Correlation Functions in the Characterization of Block Copolymer Grain Structure by Depolarized Light Scattering

Block copolymer (BCP) grain structure affects the mechanical, optical, and electrical properties of BCP materials, making the accurate characterization of this grain structure an important goal. In this study, improved BCP grain parameters were obtained by employing an exponentially decaying correlation function within the ellipsoidal grain model, instead of the Gaussian correlation function that was used in previous work. The exponential correlation function provides a better fit to the experimental depolarized light scattering data, which outweighs the disadvantage that it requires numerical integration to obtain the model scattered intensity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

Direct measurement of correlation functions in a lattice Lorentz gas

Simulations of a two-dimensional ballistic Lorentz gas on a lattice are reported. A moment-propagation technique allows direct measurements of the velocity correlation function and its moments with low relative errors for all times. The predicted 1/t-sq algebraic tails in the velocity correlation function are observed at all studied scatterer densities, unlike what has been reported for continuous systems. In the square lattice a fast oscillation is observed, consistent with the existence of staggered density modes. For the second-rank tensor correlation function, an extremely slow approach to the expected 1/t exp 3 tail is found.

Binder, P.-M.↗
NASA NTRS1988

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

A method for measuring correlation functions without interpolating in the temporal domain is proposed which provides an assumption-free representation of the correlation measured in the data and allows meaningful error estimates. Physical interpretation of the cross-correlation function of two series believed to be related by a convolution is shown to require knowledge of the input function's fluctuation power spectrum. Application of the method to two systems reveals no correlation for the optical data of Akn 120, but a strong correlation for the UV data of NGC 4151, placing bounds of between 1.2 and 20 light days on the size of the line-emitting region.

Edelson, R. A.↗
NASA NTRS1986

The Shane-Wirtanen counts - Plate correction factors and correlation functions

It has recently been argued that the break in the galaxy correlation function observed in the Lick counts of Shane and Wirtanen may be an artifact of plate variations in limiting magnitude. This has stimulated us to generalize our analysis of the effect of errors in the plate depths to include a possible systematic term, and to develop tests for the random and systematic errors. The tests show that neither can have appreciably affected the distinctive feature found in the galaxy two-point correlation function for the Lick sample.

Groth, Edward J.↗
DOE OSTI2020

Automated label flows for excited states of correlation functions in lattice gauge theory

Extracting excited states from lattice gauge theory correlation functions can be achieved through $χ^2$ minimization fits or algebraic approaches such as the variational method and Prony's method. Performing any kind of error analysis often leads to overlapping confidence regions of model parameters, even when the spectrum is not particularly dense. To correctly estimate errors, one must beware of mislabeling the states. In this work, we provide an algorithm that we call automated label flows which consistently and systematically identifies a deterministic labeling of states. This is a black-box approach in the sense that it gives a sensible set of labels without user guidance. Further, as an example, we pair one black box method with another, analyzing a lattice correlation function from real data using automated label flows in the context of Prony's method.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗