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DOE OSTI2017

Publisher Correction: Imaging the square of the correlated two-electron wave function of a hydrogen molecule

The tool box for imaging molecules is well-equipped today. Some of the techniques visualize the mean geometrical structure, others image the single electron density or single electron orbitals. Molecules, however, are many-body systems for which the correlation between the constituents is often decisive and the spatial and the momentum distribution of one electron depend on the positions and momenta of the other electrons and the nuclei. Such correlations have escaped direct observation by imaging techniques so far. We implement an imaging scheme which visualizes correlations between electrons by coincident detection of the electronic and nuclear fragments after high energy photofragmentation. We use this technique to examine parts of the H 2 two-electron wave function in which electron-electron correlation beyond the mean-field level is prominent and we visualize the dependence of the correlated two-electron wave function on the internuclear distance. High energy photoelectrons are shown to be a powerful tool for molecular imaging and our study paves the way for future time resolved imaging of electron correlations at free electron lasers and laser based X-ray sources. (The original version of this Article contained an error in the fifth sentence of the first paragraph of the 'Application on H 2 ' section of the Results, which incorrectly read 'The role of electron correlation is quite apparent in this presentation: Fig. 1a is empty for the uncorrelated Hartree-Fock wave function, since projection of the latter wave function onto the 2pσ u orbital is exactly zero, while this is not the case for the fully correlated wave function (Fig. 1d); also, Fig. 1b, c for the uncorrelated description are identical, while Fig. 1e, f for the correlated case are significantly different.' The correct version replaces 'Fig. 1e, f' with 'Fig. 2e and f'. This has been corrected in both the PDF and HTML versions of the Article.)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Importance of charge self-consistency in first-principles description of strongly correlated systems

First-principles approaches have been successful in solving many-body Hamiltonians for real materials to an extent when correlations are weak or moderate. As the electronic correlations become stronger often embedding methods based on first-principles approaches are used to better treat the correlations by solving a suitably chosen many-body Hamiltonian with a higher level theory. The success of such embedding theories, often referred to as second-principles, is commonly measured by the quality of self-energy Σ which is either a function of energy or momentum or both. However, Σ should, in principle, also modify the electronic eigenfunctions and thus change the real space charge distribution. While such practices are not prevalent, some works that use embedding techniques do take into account these effects. In such cases, choice of partitioning, of the parameters defining the correlated Hamiltonian, of double-counting corrections, and the adequacy of low-level Hamiltonian hosting the correlated subspace hinder a systematic and unambiguous understanding of such effects. Further, for a large variety of correlated systems, strong correlations are largely confined to the charge sector. Then an adequate nonlocal low-order theory is important, and the high-order local correlations embedding contributes become redundant. Here we study the impact of charge self-consistency within two example cases, TiSe 2 and CrBr 3 , and show how real space charge re-distribution due to correlation effects taken into account within a first-principles Green’s function-based many-body perturbative approach is key in driving qualitative changes to the final electronic structure of these materials.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Geometrical picture of the electron–electron correlation at the large- D limit

In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrödinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation. Both, the mean field, and the exact solutions at the large-D limit have distinct geometries. Thus, the difference might be used to describe the correlation effect. Moreover, correlations can be also described and quantified by the entanglement between the electrons, which is a strong correlation without a classical analog. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics and bounded by the area law for local gapped Hamiltonians of interacting many-body systems. This study opens up the possibility of presenting a geometrical picture of the electron–electron correlations and might give a bound on the correlation energy. Furthermore, the results at the large-D limit and at D = 3 indicate the feasibility of using the geometrical picture to get a bound on the electron–electron correlations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Correlation between the gas-phase metallicity and ionization parameter in extragalactic H II regions

The variations of the metallicity and ionization parameter in H II regions are usually thought to be the dominant factors that produce the variations we see in the observed emission line spectra. There is an increasing amount of evidence that these two quantities are physically correlated, although the exact form of this correlation is debatable in the literature. Simulated emission line spectra from photoionized clouds provide important clues about the physical conditions of H II regions and are frequently used for deriving metallicities and ionization parameters. Through a systematic investigation on the assumptions and methodology used in applying photoionization models, we find that the derived correlation has a strong dependence on the choice of model parameters. On the one hand, models that give consistent predictions over multiple emission-line ratios yield a positive correlation between the metallicity and ionization parameter for the general population of H II regions or star-forming galaxies. On the other hand, models that are inconsistent with the data locus in high-dimensional line ratio space yield discrepant correlations when different subsets of line ratios are used in the derivation. The correlation between the metallicity and ionization parameter has a secondary dependence on the surface density of the star formation rate (SFR), with the higher SFR regions showing a higher ionization parameter but weaker correlations. The existence of the positive correlation contradicts the analytical wind-driven bubble model for H II regions. We explore assumptions in both dynamical models and photoionization models, and conclude that there is a potential bias associated with the geometry. However, this is still insufficient to explain the correlation. Mechanisms that suppress the dynamical influence of stellar winds in realistic H II regions might be the key to solving this puzzle, though more sophisticated combinations of dynamical models and photoionization models to test are required.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Variability of interconnected wind plants: correlation length and its dependence on variability time scale

The variability in wind-generated electricity complicates the integration of this electricity into the electrical grid. This challenge steepens as the percentage of renewably-generated electricity on the grid grows, but variability can be reduced by exploiting geographic diversity: correlations between wind farms decrease as the separation between wind farms increases. However, how far is far enough to reduce variability? Grid management requires balancing production on various timescales, and so consideration of correlations reflective of those timescales can guide the appropriate spatial scales of geographic diversity grid integration. To answer 'how far is far enough,' we investigate the universal behavior of geographic diversity by exploring wind-speed correlations using three extensive datasets spanning continents, durations and time resolution. First, one year of five-minute wind power generation data from 29 wind farms span 1270 km across Southeastern Australia (Australian Energy Market Operator). Second, 45 years of hourly 10 m wind-speeds from 117 stations span 5000 km across Canada (National Climate Data Archive of Environment Canada). Finally, four years of five-minute wind-speeds from 14 meteorological towers span 350 km of the Northwestern US (Bonneville Power Administration). After removing diurnal cycles and seasonal trends from all datasets, we investigate dependence of correlation length on time scale by digitally high-pass filtering the data on 0.25–2000 h timescales and calculating correlations between sites for each high-pass filter cut-off. Correlations fall to zero with increasing station separation distance, but the characteristic correlation length varies with the high-pass filter applied: the higher the cut-off frequency, the smaller the station separation required to achieve de-correlation. Remarkable similarities between these three datasets reveal behavior that, if universal, could be particularly useful for grid management. For high-pass filter time constants shorter than about τ = 38 h, all datasets exhibit a correlation length $\xi $ that falls at least as fast as ${{\tau }^{-1}}$ . Since the inter-site separation needed for statistical independence falls for shorter time scales, higher-rate fluctuations can be effectively smoothed by aggregating wind plants over areas smaller than otherwise estimated.

17 WIND ENERGY↗

DOE OSTI2022

Projections of two-particle correlations onto transverse rapidity in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV at STAR

Two-particle correlation measurements projected onto two-dimensional, transverse rapidity coordinates (y T1 ,y T2 ), allow access to dynamical properties of the QCD medium produced in relativistic heavy-ion collisions that angular correlation measurements are not sensitive to. Here, we report non-identified charged-particle correlations for Au + Au minimum-bias collisions at $\sqrt{s_{NN}}$ = 200 GeV taken by the STAR experiment at the Relativistic Heavy-Ion Collider (RHIC). Correlations are presented as 2D functions of transverse rapidity for like-sign, unlike-sign and all charged-particle pairs, as well as for particle pairs whose relative azimuthal angles lie on the near-side, the away-side, or at all relative azimuth. The correlations are constructed using charged particles with transverse momentum p T ≥ 0.15 GeV/c, pseudorapidity from –1 to 1, and azimuthal angles from –π to π. The significant correlation structures that are observed evolve smoothly with collision centrality. The major correlation features include a saddle shape plus a broad peak with maximum near y T ≈ 3, corresponding to p T ≈ 1.5 GeV/c. The broad peak is observed in both like- and unlike-sign charge combinations and in near- and away-side relative azimuthal angles. The all-charge, all-azimuth correlation measurements are compared with the theoretical predictions of HIJING and EPOS. The results indicate that the correlations for peripheral to mid-central collisions can be approximately described as a superposition of nucleon + nucleon collisions with minimal effects from the QCD medium. Strong medium effects are indicated in mid- to most-central collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2016

Near-side azimuthal and pseudorapidity correlations using neutral strange baryons and mesons in d + Au , Cu + Cu, and Au + Au collisions at s N N = 200 GeV

Here we present measurements of the near side of triggered di-hadron correlations using neutral strange baryons ( $Λ,\overline{Λ}$) and mesons (K$0\atop{S}$ ) at intermediate transverse momentum (3 < pT< 6 GeV/c) to look for possible flavor and baryon-meson dependence. This study is performed in d+Au, Cu+Cu, and Au+Au collisions at $\sqrt{s}$$_{NN}$ = 200 GeV measured by the STAR experiment at RHIC. The near-side di-hadron correlation contains two structures, a peak which is narrow in azimuth and pseudorapidity consistent with correlations from jet fragmentation, and a correlation in azimuth which is broad in pseudorapidity. The particle composition of the jet-like correlation is determined using identified associated particles. The dependence of the conditional yield of the jet-like correlation on the trigger particle momentum, associated particle momentum, and centrality for correlations with unidentified trigger particles are presented. The neutral strange particle composition in jet-like correlations with unidentified charged particle triggers is not well described by PYTHIA. However, the yield of unidentified particles in jet-like correlations with neutral strange particle triggers is described reasonably well by the same model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

SU-E-T-72: A Retrospective Correlation Analysis On Dose-Volume Control Points and Treatment Outcomes

Purpose: To quantify correlation between dose-volume control points and treatment outcomes. Specifically, two outcomes are analyzed: occurrence of radiation induced dysphagia and target complications. The results inform the treatment planning process when competing dose-volume criteria requires relaxations. Methods: 32 patients, treated with whole-field sequential intensity modulated radiation therapy during 2009–2010 period, are considered for this study. Acute dysphagia that is categorized into 3 grades is observed on all patients. 3 patients are observed in grade 1, 17 patients in grade 2, and 12 patients in grade 3. Ordinal logistic regression is employed to establish correlations between grades of dysphagia and dose to cervico-thoracic esophagus. Particularly, minimum (Dmin), mean (Dmean), and maximum (Dmax) dose control points are analyzed. Additionally, target complication, which includes local-regional recurrence and/or distant metastasis, is observed on 4 patients. Binary logistic regression is used to quantify correlation between target complication and four dose control points. Namely, ICRU recommended dose control points, D2, D50, D95, and D98 are analyzed. Results: For correlation with dysphagia, Dmin on cervico-thoracic esophagus is statistically significant (p-value = 0.005). Additionally, Dmean on cervico-thoracic esophagus is also significant in association with dysphagia (p-value = 0.012). However, no correlation was observed between Dmax and dysphagia (p-value = 0.263). For target complications, D50 on the target is a statistically significant dose control point (p-value = 0.032). No correlations were observed between treatment complications and D2 (p-value = 0.866), D95 (p-value = 0.750), and D98 (p-value = 0.710) on the target. Conclusion: Significant correlations are observed between radiation induced dysphagia and Dmean (and Dmin) to cervico-thoracic esophagus. Additionally, correlation between target complications and median dose to target (D50) is observed. Quantification of these correlations can inform treatment planners when any competing objectives requires relaxation of target D50 or Dmean (or Dmin) to cervico-thoracic esophagus.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Correlations between maximum mass of neutron stars and the nuclear matter properties and the constraints from PSR J0740+6620 and GW190814

The correlations between the maximum mass of neutron stars (NSs) with the properties of nuclear matter at saturation density ρ 0 , i.e., the incompressibility K 0 , the symmetry energy E sym (ρ 0 ), and its slope L(ρ 0 ), the isoscalar effective mass m$^{*}_{s0}$, and the parameter f I , have been investigated using several sets of Skyrme interactions based on the momentum-dependent (MD) Skyrme interactions SAMi-J27 (soft), SAMi-J31 (stiff), and SAMi-J35 (super-stiff), as well as the momentum-independent (MI) Skyrme interaction SkT5. Only one physical quantity is varied at a time for a given set of Skyrme interactions. It is found that the maximum mass of NSs has (1) a strong positive linear correlation with K 0 for stiff and super-stiff equation of state (EOS) and no correlation with K 0 for soft EOS; (2) a negative logarithm correlation with the symmetry energy E sym (ρ 0 ) for all the EOSs; (3) a positive logarithm correlation with the slope L(ρ 0 ) for all the EOSs; (4) a positive logarithm correlation with the parameter f I for MD EOS; (5) a negative power-law correlation with m$^{*}_{s0}$ for MD EOS. Based on these established correlations, the constraints to the nuclear matter properties from the mass of PSR J0740+6620 and GW190814 are investigated. Furthermore, we find that while rotation enhances the maximum mass of NSs, it does not effect the underlying correlations between the maximum mass and the aforementioned nuclear matter parameters.

Zhou, M. [Shaanxi Normal University, Xi’an (China)↗

DOE OSTI2020

Probing Electron Correlations in 1D Electronic Materials Using Single Quantum Channels (Final Technical Report)

This research focuses on the investigation of strong electron correlations in quasi-one-dimensional oxide nanostructures. The archetypical system consisting of heterostructures formed from an ultrathin layer of LaAlO 3 and TiO 2 -terminated SrTiO 3 offers a unique laboratory for probing strong correlations due to intrinsic richness of the physical system and its ability to be modulated at extreme nanoscale dimensions. Under suitable conditions, SrTiO 3 is known to exhibit a variety of important properties associated with strong electronic correlations, especially superconductivity, magnetism. Understanding the nature of these electronic correlations at fundamental scales, and in reduced spatial dimensions, will provide the scientific basis for new energy technologies, information technologies, and materials. The research program is motivated by recent discoveries and technical advances in the PIs' lab, specifically, (1) pioneering work to create conductive nanostructures to be created in LaAlO 3 /SrTiO 3 heterointerfaces with 2 nm spatial resolution, (2) the discovery of a novel correlated electronic phases in which electrons pair without forming a superconductor, and (3) the demonstrated ability to form high-quality quantum point contacts (QPCs) and achieve ballistic electron transport over micrometer-scales in LaAlO 3 /SrTiO 3 nanowires. The program has three major components. First, we have press forward to develop a full microscopic understanding of the mechanism for electron pairing in LaAlO 3 /SrTiO 3 nanostructures. Understanding the “glue” that leads to pairing and superconductivity in a doped semiconductor will help to form a scientific basis for the correlated oxide nanoelectronics platform being developed. Second, we have used their ability to create well-defined quantum channels in nanowires allows to allow novel “scattering” experiments to be performed that probe fundamentally new quasiparticle excitations using an unprecedented combination of experimental methodologies. Experiments already underway with artificially defined superlattices (5 nm period) demonstrate the feasibility of this approach. Third, we have investigated 1D correlations in proximally coupled nanowires, which are predicted exhibit Majorana-like zero modes in the absence of superconductivity or spin-orbit coupling. These studies provide insight not only into new and emergent phenomena in the rich class of complex oxides, but also fundamental mechanisms of superconductivity and magnetism. Thematically, the research aims to combine some of the most important and interesting challenges in the physics of semiconductor nanostructures and correlated electronic materials. The increased understanding of electron correlations can pave the way to the development of new materials with outstanding or novel properties, which could be relevant for energy-related technologies such as low-power high performance computing, quantum computation, or the development of novel materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Conservative Release Fraction Correlation for Spray Releases

Washington River Protection Solutions, LLC (WRPS) is planning to conduct repairs in the Liquid Effluent Retention Facility (LERF), and prior to conducting this work they will re-evaluate the hazard category designation for LERF. As part of this evaluation, WRPS needs estimates of the release fraction of potential accidental sprays, because a spray release is a potential bounding accident. Pacific Northwest National Laboratory previously developed a conservative correlation for the cumulative generation rate (volume per time) of aerosol droplets less than or equal to specific sizes from spray releases as a function of the spray pressure, orifice area, and droplet diameter. To obtain release fraction estimates from the conservative generation rate correlation, the correlation needs to be recast by dividing the aerosol generation rate by the flow rate of a spray. In the current study, a conservative release fraction correlation was developed from the conservative aerosol generation rate correlation developed previously by dividing the generation rate correlation by the flow rate of a spray using an orifice flow rate equation and then this correlation was adjusted to be conservative. Test data were also extrapolated to a lower pressure than the lowest pressure tested (100 psig) for the spray data used for developing the previous conservative generation rate correlation. The new conservative release fraction correlation was then used to predict release fractions of respirable droplets (droplets = 10 µm) for four specific pipes that are part of LERF.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Review and Analysis of Heat Transfer Correlations For Horizontal Pseudocritical CO 2 Heat Exchanger Applications

There is significant interest in the development of supercritical carbon dioxide (sCO 2 ) power cycles because of the potential for smaller and more energy efficient systems than a steam Rankine cycle. Heat exchanger designs typically use empirical correlations, but the applicability of these correlations near the CO 2 critical point is a potential issue. Though numerous correlations have been proposed in the literature, there are some disagreements when it comes to the accuracy. The current work recognizes the role of thermophysical properties, and its impacts on the heat transfer correlations and cycle efficiency. Heat transfer correlations proposed for horizontal flow inside circular pipes were analyzed with the help of numerical simulations. Steady state RANS simulations were performed using SST k-w turbulence model to evaluate the Nusselt number empirical correlations. It was found that the most of correlations (except Yoon) produced a Nusselt number that differed significantly with the one predicted numerically. Some of the correlations were developed for pure forced convection regime and as mentioned in Lin et al. do not account for mixed convection or free convection effects. Based on the limited observation, it appears that Yoon et al. predictions match well with the numerically predicted Nusselt Numbers. However, further analysis is required understand the applicability of various correlations and is contingent on accurate measurements or predictions of wall temperature profiles in the axial and the circumferential directions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS1995

Pressure correlations at a fluid/structure interface

The structure of pressure-pressure correlations at the interface of an incompressible steady-state turbulent flow with a rigid boundary was investigated. For the sake of completeness, the absolute value of the correlation between two random varying functions is herein defined as a number greater than or equal to zero and less than or equal to unity which is a measure of that fraction of one of the functions that 'follows' the second function (or vice versa). It was found that the soughtafter correlations can be determined by consideration of the high Re Navier-Stokes equation, but that the complexity of boundary layer turbulence, in particular the inhomogeneity perpendicular to the boundary and the anisotropy due to convective flow gradients, makes the structure of said correlations extremely difficult to assess. One of the earlier researchers in this field described the quantity under present consideration as 'a quantity which is beyond assessment.' Nonetheless, it was found that under some rather simplifying assumptions the determination of the required structure necessitates the formulation of the related structure of second order two-point correlations of turbulent velocity gradients, as well as third order two-point correlations of velocity gradients. The presence of these latter gradients is due to the nonlinearity in the turbulence ('turbulence self-interaction'). Both of these correlations are scaled, although not similarly, by factors dependent upon the magnitude of the convective flow, which can be modeled using a log law approximation. Fourth order correlations, although present, can be ignored, since they constitute 'higher order terms.' In a slightly more complex situation, it was found that convective flow gradients also have to be incorporated. At the moment, no definitive algebraic information peculiar to pressure-pressure correlations is available in the most highly idealized cases.

Trevino, George↗

NASA NTRS1999

The Impact of Anisotropic Error Correlation Modelling

Most data assimilation systems assume isotropic forecast error correlations, but results from two dimensional Kalman Filter experiments indicate that the correlations can be far from isotropic. In this paper we use a simple two-dimensional data assimilation system, which analyses trace chemical species such as ozone, to assess different approaches to modelling the error correlations. We compare assimilation results using isotropic correlations with results obtained using different approaches to modelling anisotropic correlations: first, using correlations based on the concentrations of the trace chemicals, and secondly using an advective correlation model. We show that these relatively cheap ways of modelling anisotropic correlations give objectively better results than using isotropic correlations. We discuss the possible extension of these approaches to a full 3-D meteorological data assimilation system.

Swinbank, R.↗

NASA NTRS1996

Quantifying the Correlation Between Eye-Movement and Perceptual Responses to Moving Plaids

To determine the extent to which the pursuit eye-movement and perceptual systems share a common neural motion-processing pathway, we simultaneously measure the psychophysical and eye-movement responses to drifting plaids in a direction-discrimination task. Correlation between the noise in the eye movements and percepts would suggest a shared neural substrate. Three observers were asked to track a plaid (Type I 90 deg; TF = 4 Hz, SF = 0.6 c/d; direction = -2, 0, or 2 deg), and to respond whether the motion was to the right or left of vertical. The eye-movement direction is computed from the initial 300 ms of saccade-free tracking (near open-loop). On each trial, we use the eye-movement direction to predict the perceptual response. We then compute the probability of successfully predicting the observer's response. We also use SOC analysis as an alternate measure of the correlation. We compare the data from both these analyses to the predictions of two models in which the eye movements and the percept are driven by either a common noisy signal (correlated model) or by two separate noisy signals (uncorrelated model). We also allow for the fact that our measured eye movements are degraded by eye-tracker noise. This noise causes our measured correlation to be lower than the actual biological correlation. The correlations in our data are higher than those predicted by the uncorrelated model, and are similar to the predictions of the correlated model. The proportion of perceptual responses correctly predicted by the eye movements were 0.66, 0.60, 0.73 for the -2, 0, 2 deg stimuli respectively (correlated model 0.65, 0.60, 0.70; uncorrelated model 0.58, 0.51, 0.60).The SOC proportions were 0.71, 0.64, 0.72 (correlated model 0.66, 0.64, 0.69; uncorrelated model 0.5, 0.5, 0.5). These results show that the oculomotor and perceptual system share a performance-limiting noise source and provide strong evidence that a common neural mechanism (perhaps MT or MST) drives both perception and smooth eye movements.

Beutter, Brent R.↗

NASA NTRS2003

On the Computation of Space-Time Correlations by Large-Eddy Simulation

Numerical comparisons in decaying isotropic turbulence suggest that there exist discrepancies in time correlations evaluated by DNS and LES using eddy-viscosity-type SGS models. This is consistent with the previous observations in forced isotropic turbulence. Therefore, forcing is not the main cause of the discrepancies. Comparisons among different SGS models in the LES also indicate that the model choice affects the time correlations in the LES. The multi-scale LES method using the dynamic Smagorinsky model on the small scale equation is the most accurate of the all models, the classic Smagorinsky model is the least accurate and the dynamic Smagorinsky model and spectral eddy viscosity model give intermediate results with small differences. The generalized sweeping hypothesis implies that time correlations in decaying isotropic turbulence are mainly determined by the instantaneous energy spectra and sweeping velocities. The analysis based on the sweeping hypothesis explains the discrepancies in our numerical simulations: the LES overpredicts the decorrelation time scales because the sweeping velocities are smaller than the DNS values, and underpredicts the magnitudes of time correlations because the energy spectrum levels are lower than the DNS ones. Since the sweeping velocity is determined by the energy spectra, one concludes that an accurate prediction of the instantaneous energy spectra guarantees the accuracy of time correlations. An analytical expression of sound power spectra based on Lighthill's theory and the quasi-normal closure assumption suggests that the sound power spectra are sensitive to errors in time correlations. Small errors in time correlations can cause significant errors in the sound power spectra, which exhibit a sizable drop at moderate to high frequencies accompanied by a shift of the peaks to lower frequencies. Based on the above analysis, two possible ways to improve the acoustic power spectrum predictions can be considered. The first is to construct better SGS models to improve the LES accuracy for time correlations. The second is to remedy the temporal statistics of the Lighthill stress tensor in order to "recover" the contribution from the unresolved scales in LES to time correlations.

He, Guo-Wei↗

NASA NTRS2007

Determination of Black Hole Mass in Cyg X-1 by Scaling of Spectral Index-QPO Frequency Correlation

It is well established that timing and spectral properties of Galactic Black Hole (BH) X-ray binaries (XRB) are strongly correlated. In particular, it has been shown that low frequency Quasi-Periodic Oscillation (QPO) nu(sub low) - photon index GAMMA correlation curves have a specific pattern. In a number of the sources studied the shape of the index-low frequency QPO correlations are self-similar with a position offset in the nu(sub low) - GAMMA plane determined by a BH mass M(sub BH). Specifically, Titarchuk & Fiorito (2004) gave strong theoretical and observational arguments that the QPO frequency values in this nu(sub low) - GAMMA correlation should be inversely proportional to M(sub BH). A simple translation of the correlation for a given source along frequency axis leads to the observed correlation for another source. As a result of this translation one can obtain a scaling factor which is simply a BH mass ratio for these particular sources. This property of the correlations offers a fundamentally new method for BH mass determination in XRBs. Here we use the observed QPO-index correlations observed in three BH sources: GRO J1655-40, GRS 1915+105 and Cyg X-1. The BH mass of (6.3 plus or minus 0.5) solar mass in GRO J1655-40 is obtained using optical observations. RXTE observations during the recent 2005 outburst yielded sufficient data to establish the correlation pattern during both rise and decay of the event. We use GRO J1655-40 as a standard reference source to measure the BH mass in Cyg X-1. We also revisit the GRS 1915+105 data as a further test of our scaling method. We obtain the BH mass in Cyg X-1 in the range 7.6-9.9.

Shaposhnikov, Nickolai↗

NASA NTRS2004

Ultralow-Power Digital Correlator for Microwave Polarimetry

A recently developed high-speed digital correlator is especially well suited for processing readings of a passive microwave polarimeter. This circuit computes the autocorrelations of, and the cross-correlations among, data in four digital input streams representing samples of in-phase (I) and quadrature (Q) components of two intermediate-frequency (IF) signals, denoted A and B, that are generated in heterodyne reception of two microwave signals. The IF signals arriving at the correlator input terminals have been digitized to three levels (-1,0,1) at a sampling rate up to 500 MHz. Two bits (representing sign and magnitude) are needed to represent the instantaneous datum in each input channel; hence, eight bits are needed to represent the four input signals during any given cycle of the sampling clock. The accumulation (integration) time for the correlation is programmable in increments of 2(exp 8) cycles of the sampling clock, up to a maximum of 2(exp 24) cycles. The basic functionality of the correlator is embodied in 16 correlation slices, each of which contains identical logic circuits and counters (see figure). The first stage of each correlation slice is a logic gate that computes one of the desired correlations (for example, the autocorrelation of the I component of A or the negative of the cross-correlation of the I component of A and the Q component of B). The sampling of the output of the logic gate output is controlled by the sampling-clock signal, and an 8-bit counter increments in every clock cycle when the logic gate generates output. The most significant bit of the 8-bit counter is sampled by a 16-bit counter with a clock signal at 2(exp 8) the frequency of the sampling clock. The 16-bit counter is incremented every time the 8-bit counter rolls over.

Piepmeier, Jeffrey R.↗