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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
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.↗
NASA NTRS1971

Causality of the nonequilibrium correlation functions.

It is shown that the correct lowest-order two-particle correlation function solution to the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy is given via a Green's function whose Fourier transform satisfies the analyticity requirements for causality. The Bogoliubov adiabatic approximation is shown to imply a solution which is acausal. Extension to the s-particle correlation function is discussed.

Murphy, F. X.↗
NASA NTRS1990

Recognition and characterization of hierarchical interstellar structure. I - Correlation function

The problem of the quantitative description of multiscale structure in interstellar cloud complexes and gravitational collapse calculations is considered, emphasizing the recognition and characterization of hierarchical fragmentation structure. The response of the two-point correlation function to a variety of analytical models for density structure is discussed for simple clustering of pointlike clouds to more complex models involving clouds with a distribution of sizes and densities and hierarchical substructure. By expressing the density distribution as the superposition of individual clouds, it is shown that the correlation function generates two types of terms: those involving each cloud's density convolved with itself and those involving pairs of different clouds. Major distortion of the correlation function are introduced by the presence of any image features with size scales a significant fraction of the image size.

Houlahan, Padraig↗
NASA NTRS1993

The two-point correlation function of randomly distributed Lyman alpha clouds

It is often assumed that Ly-alpha forest clouds are randomly distributed, intergalactic objects that are highly ionized by the UV background produced by quasars. If these assumptions are true, fluctuations in the UV background should produce a nonzero two point correlation function in the Ly-alpha forest. This effect, which is really just a generalization of the proximity effect, is more significant at high redshift (z is approximately 3-4) because the mean free path for UV photons is smaller there, and the fluctuations correspondingly larger. This effect was studied using both the semi-analytic techniques of Zuo's recent papers and Monte Carlo simulations. The correlation function is expected to have a small yet potentially measurable amplitude that is consistent with current upper limits. Furthermore, the signature of this effect is distinctive because the nonzero correlation function extends over the photon mean free path, which is larger than the expected scale of large-scale structure. Observations or upper limits on this effect could provide information about the source of the ionizing background at high redshifts and the nature of the Ly-alpha forest clouds.

Fardal, Mark A.↗
NASA NTRS1992

Correlation function ratios and the identification of space plasma instabilities

Wave-particle transport in a collisionless plasma is due to particle scattering by enhanced fluctuations associated with the growth of instabilities. In particular, relatively short wave-length kinetic instabilities are frequently invoked to explain many different types of plasma transport in space. Although there is an extensive theoretical and simulation literature describing the potential applications of many such instabilities, there are only a few cases of clear-cut identification of kinetic modes in space. The research described in this paper uses linear Vlasov dispersion theory to study correlation functions and dimensionless correlation function ratios for fluctuations or instabilities in three space plasma regimes. This research shows that both the compressibility and the parallel compressibility are likely to be useful in distinguishing modes in the magnetosheath as well as in the plasma sheet boundary layer and that helicity remains a useful identifier of electromagnetic ion/ion instabilities in the foreshock.

Gary, S. P.↗
DOE OSTI2024

Exact evaluation of large-charge correlation functions in nonrelativistic conformal field theory

The large-charge master field which generates all n -point correlation functions with an insertion of large charge Q in nonrelativistic conformal field theory is obtained. This field is used to compute Schrödinger-invariant n -point correlation functions of large-charge operators via a direct evaluation of the path integral. Conformal dimensions are found to agree with calculations based on the state-operator correspondence. The master field solution exhibits an emergent harmonic trap whose frequency is a function of the Euclidean time. The large-charge effective action with operator insertions describes a droplet of superfluid matter whose spatial size scales with the time separation of sources. The solution is used to compute Schrödinger symmetry breaking corrections in the large-charge effective field theory (EFT) due to a finite scattering length in the fundamental theory of fermions near unitarity. The scaling of these effects in the large-charge power counting scheme is established, and the size of the effects is quantified using input from quantum Monte Carlo simulations of the near-unitary gas, as well as from the large- N expansion at large charge. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Lattice-QCD Computable Quark Correlation Functions at Three-Loop Order and Extraction of Splitting Functions

We present the first complete next-to-next-to-next-to-leading-order calculation of the matching coefficients that link unpolarized flavor nonsinglet parton distribution functions with lattice QCD computable correlation functions. By using this high-order result, we notice a reduction in theoretical uncertainties compared to relying solely on previously known lower-order matching coefficients. Furthermore, based on this result we have extracted the three-loop unpolarized flavor nonsinglet splitting function, which is in agreement with the state-of-the-art result. Because of the simplicity of our method, it has the potential to advance the calculation of splitting functions to the desired four-loop order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1977

The correlation function for density perturbations in an expanding universe. I - Linear theory

The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.

Mcclelland, J.↗
NASA NTRS1993

Ways to improve your correlation functions

This paper describes a number of ways to improve on the standard method for measuring the two-point correlation function of large scale structure in the Universe. Issues addressed are: (1) the problem of the mean density, and how to solve it; (2) how to estimate the uncertainty in a measured correlation function; (3) minimum variance pair weighting; (4) unbiased estimation of the selection function when magnitudes are discrete; and (5) analytic computation of angular integrals in background pair counts.

Hamilton, A. J. S.↗
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↗
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.↗