Pair-correlation functions and correlation energies of a quantum electron gas.
Pair correlation functions and energies of quantum electron gas in thermal equilibrium
Broyles, A. A.↗
SEARCH · Engineering Papers
Results for “pair correlation function”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Nanoscale Phase Identification Using Two-Dimensional Pair Correlation Functions: A Case Study on Hafnium Oxide
Accurate identification of local phases in nanocrystalline materials is essential for understanding their functional properties, but it remains a significant challenge for polymorphic materials to locally differentiate them at nanoscale. This challenge is further compounded in polycrystalline materials with randomly oriented grains and the coexistence of multiple phases. In this report, we present a methodology for phase and orientation identification at the nanoscale by leveraging vector pair correlation functions extracted from atomically resolved scanning transmission electron microscopy (STEM) images. We demonstrate the accuracy of the methodology on both simulated and experimental data from HfO 2 -based films, a material that exhibits multiple coexisting phases in films with thicknesses ranging from 5 to 20 nm. While demonstrated on HfO 2 films, the methodology can be extended to other polymorphic nanocrystalline systems with complex phase coexistence.
36 MATERIALS SCIENCE↗
Variational derivation of equation for generalized pair correlation function
The wavefunction of a system is explicitly written down in a fully anti-symmetric way between a fermion pair and a medium, and the equations for each one of them are derived from the variation of total energy for bound systems and by forming appropriate scalar products for continuum states. High-energy particles, such as protons, electrons, and nuclei impinging upon spacecraft, produce secondary radiations. In order to protect the internal environment of spacecraft from these radiations, their intensities are determined in many instances theoretically, and an appropriate program has been developed in the High Energy Science Branch. The purpose of this research is to investigate the problem of indistinguishability of an incident projectile with one of the same in a target.
Malik, F. Bary↗
Dust Particle Pair Correlation Functions and the Nonlinear Effect of Interaction Potentials
Explore the source record for details and available documents.
Jie Kong↗
Stochastic Transport Theory for Investigating the Three-Dimensional Canopy Structure from Space Measurements
Radiation reflected from vegetation canopies exhibits high spatial variation. Satellite-borne sensors measure the mean intensities emanating from heterogeneous vegetated pixels. The theory of radiative transfer in stochastic media provides the most logical linkage between satellite observations and the three-dimensional canopy structure through a closed system of simple equations which contains the mean intensity and higher statistical moments directly as its unknowns. Although this theory has been a highly active research field in recent years, its potential for satellite remote sensing of vegetated surfaces has not been fully realized because of the lack of models of a canopy pair-correlation function that the stochastic radiative transfer equations require. The pair correlation function is defined as the probability of finding simultaneously phytoelements at two points. This paper presents analytical and Monte Carlo generated pair correlation functions. Theoretical and numerical analyses show that the spatial correlation between phytoelements is primarily responsible for the effects of the three-dimensional canopy structure on canopy reflective and absorptive properties. The pair correlation function, therefore, is the most natural and physically meaningful measure of the canopy structure over a wide range of scales. The stochastic radiative transfer equations naturally admit this measure and thus provide a powerful means to investigate the three-dimensional canopy structure from space. Canopy reflectances predicted by the stochastic equations are assessed by comparisons with the PARABOLA measurements from coniferous and broadleaf forest stands in the BOREAS Southern Study Areas. The pair correlation functions are derived from data on tree structural parameters collected during field campaigns conducted at these sites. The simulated canopy reflectances compare well with the PARABOLA data.
Huang, Dong↗
Correlation functions for pairs and groups of galaxies
There are many studies on the correlation functions of galaxies, of clusters of galaxies, even of superclusters (e.g., Groth and Peebles 1977; Davies and Peebles 1983; Kalinkov and Kuneva 1985, 1986; Bahcall 1988 and references therein) but not so many on pairs and groups of galaxies. Results of the calculations of two-point correlation fuctions for some catalogs of pairs and groups of galaxies are given. It is assumed that the distances to pairs and groups of galaxies are given by their mean redshifts according to R = sigma (sup n, sub i-1) V sub i/nH (sub 0), where n is the number of galaxies in the system and H sub 0 = 100 km s(exp -1) Mpc(exp -1).
Kalinkov, M.↗
Thermophysical Properties of Liquid Tritium: A Path Integral Monte Carlo Study
Here, we present worm-algorithm, path integral Monte Carlo simulations of bulk liquid tritium. The simulations are benchmarked against empirically known thermophysical properties of liquid deuterium and liquid tritium. Results for the pair correlation function, chemical potential, isothermal compressibility, isochoric heat capacity, and single-particle momentum distributions are reported. Given the benchmark comparisons, our predictions of liquid tritium properties are expected to be accurate to within a few percent. Our simulations unambiguously demonstrate the significance of nuclear quantum effects to the properties of liquid tritium. In particular, under saturated vapor pressure, the average molecular kinetic energy of the liquid is found to be more than 60% higher than the value expected from the classical equipartition theorem.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Useful operator in plasma kinetic theory.
Operator used in derivation of plasma kinetic equation, expressing integral of pair correlation function for stable and unstable cases via Fourier transform
PLASMA DYNAMICS↗
Binary correlations in a stable homogeneous plasma.
Pair correlations function in stable homogeneous plasma
PLASMA STABILITY↗
Extensions to the classical calculation of the effect of mutual shadowing in diffuse reflection
The classical method for accounting for the mutual shadowing among closely packed particles in multiple scattering calculations is extended in the following ways. (1) By modeling the particle distribution by a Poisson process with a varying density parameter, a 'Van der Waals' type approximation allows extension to a greater fractional volume density, D. In this case it is only required that D squared be much less than 1 instead of D being much less than 1. (2) In the case that the particle distribution is not uniform the classical calculation may be weighted by the pair correlation function of the distribution. (3) The use of the Markov chain formalism for radiative transfer allows inclusion of the effect of shadowing for two orders of scattering. For conditions such as might apply in Saturn's rings, the inclusion of this effect makes less than a 0.1% difference in the calculated phase curves, compared to previous calculations which have included shadowing only in the first scattering. The latter are thus shown to be quite accurate.
Esposito, L. W.↗
An Interplay between Photons, Canopy Structure, and Recollision Probability: A Review of the Spectral Invariants Theory of 3D Canopy Radiative Transfer Processes
Earth observations collected by remote sensors provide unique information to our ever-growing knowledge of the terrestrial biosphere. Yet, retrieving information from remote sensing data requires sophisticated processing and demands a better understanding of the underlying physics. This paper reviews research efforts that lead to the developments of the stochastic radiative transfer equation (RTE) and the spectral invariants theory. The former simplifies the characteristics of canopy structures with a pair-correlation function so that the 3D information can be succinctly packed into a 1D equation. The latter indicates that the interactions between photons and canopy elements converge to certain invariant patterns quantifiable by a few wavelength independent parameters, which satisfy the law of energy conservation. By revealing the connections between plant structural characteristics and photon recollision probability, these developments significantly advance our understanding of the transportation of radiation within vegetation canopies. They enable a novel physically-based algorithm to simulate the “hot-spot” phenomenon of canopy bidirectional reflectance while conserving energy, a challenge known to the classic radiative transfer models. Therefore, these theoretical developments have a far-reaching influence in optical remote sensing of the biosphere.
vegetation remote sensing; stochastic radiative tr↗
Finite-range pairing in nuclear density functional theory
Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic pair densities and pairing fields are introduced. Many pairing functionals currently used can be traced back to zero-range nucleon-nucleon interactions. Unfortunately, such functionals are plagued by deficiencies that become apparent in large model spaces that contain unbound single-particle (continuum) states. In particular, the underlying computational schemes diverge as the single-particle space increases, and the results depend on how marginally occupied states are incorporated. These problems become more pronounced for pairing functionals that contain gradient-density dependence, such as in the Fayans functional. To remedy this, finite-range pairing functionals are introduced. In this study, this is done by folding the pair density with Gaussians. Here, we show that a folding radius of about 1 fm offers the best compromise between quality and stability, and substantially reduces the pathological behavior in different numerical applications.
Nuclear density functional theory↗
Theoretical Calculation of the Power Spectra of the Rolling and Yawing Moments on a Wing in Random Turbulence
The correlation functions and power spectra of the rolling and yawing moments on an airplane wing due to the three components of continuous random turbulence are calculated. The rolling moments to the longitudinal (horizontal) and normal (vertical) components depend on the spanwise distributions of instantaneous gust intensity, which are taken into account by using the inherent properties of symmetry of isotropic turbulence. The results consist of expressions for correlation functions or spectra of the rolling moment in terms of the point correlation functions of the two components of turbulence. Specific numerical calculations are made for a pair of correlation functions given by simple analytic expressions which fit available experimental data quite well. Calculations are made for four lift distributions. Comparison is made with the results of previous analyses which assumed random turbulence along the flight path and linear variations of gust velocity across the span.
Eggleston, John M↗
Sub-baud coding
In a spread-spectrum communication system, a data sequence of +1's and -1's is expanded into a sequence of +x's (bottom bar) and -x's (bottom bar) where x (bottom bar) is a length n sequence of +1's and -1's. A sub-baud code is the assignment of a different such baud sequence to each of M users with the objective of reducing interference between users. It is shown that this interference can be described in terms of the even and odd correlation functions between pairs of sequences. A technique for deriving sub-baud codes from cyclic error-correcting codes is given, and a theorem proved which bounds the quality of the resultant code. A specific such cyclic code construction procedure is given which, for any M, yields a sub-baud code for which the mutual interference can be made arbitrarily small by choosing n sufficiently large.
Massey, J. L.↗
Theoretical studies of diatomic and triatomic systems containing the group IB atoms Cu, Ag, and Au
Selected portions of the ground state potential energy surfaces of the Cu3, Ag3, AgCu2, and AuCu2 trimers are studied at the single-reference singles plus doubles configuration interaction and couple pair functional levels correlating 33 electrons. The calculations use the effective core potentials of Hay and Wadt (1985) to replace the deep core levels. The Cu3 and Ag3 molecules are found to have 2B2 obtuse-angled ground states, with low-lying 2A1 acute-angled excited states. The AgCu2 and AuCu2 molecules have 2A1 acute-angled ground states. The Cu3 molecule has a smaller 3d population than Ag3, and Cu3 has a smaller s electron density in the open-shell orbital than does Ag3, in agreement with recent ESR experiments.
Walch, Stephen P.↗
Pruning the Lyman alpha forest of Q1331+170
A multitude of absorption lines seen shortward of QSO Ly-alpha emission, that cannot be traced to heavy element absorption systems, are assumed to be Ly-alpha lines arising in intervening clouds. Studies of these Ly-alpha clouds, typically done at 1 A or lower resolution, have shown N(H1) approximately equal to 10(exp 13) - 10(exp 17) sq cm and b approximately equal to 35 km/s. Sargent et al 1980, on the basis of a flat pair velocity correlation function (PVCF), argued that these clouds are intergalactic. But Crotts 1989 showed that the strong Ly-alpha lines are spatially clustered. High resolution studies of Webb 1987 and Rauch et al 1992 also report some evidence for weak clustering, but overall such high resolution studies have been rare. A study of the Ly-alpha forest of Q1331 + 170 over x(sub abs) = 1.60 - 2.19 based on 18 km/s resolution data at S/N approximately equal to 15, with metal-line deblending incorporated.
Kulkarni, Varsha P.↗
A theory and method for correlation analysis of nonstationary signals.
Cross correlation and autocorrelation functions of nonstationary signals based on optimal approximation of ensemble correlation function for one pair of signals
CROSS CORRELATION↗
Pairing tendencies in the doped Kitaev-Heisenberg model
Here, we study the impact of hole doping on the Kitaev-Heisenberg model on the honeycomb lattice. We investigate the pairing tendencies and correlation functions in the framework of a t - J - K model using density matrix renormalization group calculations on three-leg cylinders. In the case of the pure Kitaev model, which realizes a quantum spin-liquid phase at half-filling, we find that binding of two holes only occurs at low values of the hopping, where the holes are slow. We have theoretically verified that pair formation occurs in the limit of immobile holes, where the pure Kitaev model remains exactly solvable. When we instead fix the hopping at an intermediate, more realistic, value, and vary the Heisenberg and Kitaev interaction strengths, we find pairing tendencies only in the Néel phase. This is in contrast to prior mean-field calculations, highlighting the importance of accounting for the kinetic energy of dopants in generalized Kitaev models. Interestingly, we also find signatures of pair-density wave formation over the studied range of model parameters, namely, a periodic modulation of the charge density as well as the spin-spin and pair-pair correlations in real space. Moreover, we present a comparative study of the different correlations as a function of doping. We finally discuss the potential for experimentally observing the studied physics in quantum materials and heterostructures.
36 MATERIALS SCIENCE↗