Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “GREEN 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.

At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Renormalized Singles Green’s Function for Quasi-Particle Calculations beyond the G 0 W 0 Approximation

Quasi-particle energies and band gaps in particular are critical for investigating novel materials. Commonly used density functional approximations (DFAs) systematically underestimate band gaps, and GW approximation is the established method of choice for good accuracy and reliability. However, G 0 W 0 has some undesired dependence on the DFA, while self-consistent GW (scGW) is expensive and not consistent in accuracy improvement. Here a simple and efficient G RS W 0 approach has been developed: a subspace diagonalization of the Hartree-Fock (HF) Hamiltonian with the DFA density matrix provides the new reference Green's function GRS that incorporates the effect of all single excitation contributions to the self-energy, thereby essentially eliminating the starting-point dependence. Calculations for molecules and large band gap solids demonstrate the significant improvement over G 0 W 0 and greatly reduced dependence on the initial DFA. GRS W0 approach also improve results for other bulks over G 0 W 0 but to a lesser extent, which could be due to the limitations in current implementation for bulks. The results demonstrate that to achieve good accuracy, it is not necessary to use hybrid DFA, which is expensive for bulks. Lastly, this work should be greatly significant in making GW a more robust approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Microscopic optical potentials from a Green's function approach

Optical potentials are a standard tool in the study of nuclear reactions, as they describe the interaction between a target nucleus and a projectile. The use of phenomenological optical potentials built using experimental data on stable isotopes is widespread. Although successful in their dedicated domain, it is unclear whether these phenomenological potentials can provide reliable predictions for unstable isotopes. To address this problem, optical potentials based on microscopic nuclear structure input calculations prove to be crucial and are an important current line of research. In this work we present an explicit implementation of the Feshbach formalism for the systematic derivation of optical potentials using input from nuclear structure models. Numerical tools for the derivation of Green's functions associated with nonlocal potentials are presented. In conclusion, the new optical potential, based on the valence shell model, is applied to the calculations of 𝑛 + 24 Mg elastic scattering and yields a close agreement with the experimental data.

Direct reactions↗
DOE OSTI2019

Evaluating and Improving the USGS 3D Seismic Velocity Model in the San Francisco East Bay by Integrating Earthquake Ground-Motion Simulations and Noise-Derived Empirical Green's Functions

Simulations of scenario earthquake ground motions play an increasingly important role in improving seismic hazard assessment. In the San Francisco Bay Area (SFBA) the USGS has developed a 3D geologic/seismic model. Simulations of large magnitude (M) 7 Hayward Fault scenario earthquakes show dramatic differences in peak ground motions across the fault, arising from wavespeed differences, which highlights the need to evaluate the model. Our comparison of observed and simulated waveforms from M 4 SFBA earthquakes reveals bias in the travel times of direct S-waves for paths crossing the East Bay Hills, east of Hayward Fault, suggests that the shear wavespeeds in the upper crust of the USGS 3D model are too low, resulting in large delay times of S-wave arrivals at the East Bay Hills. We also retrieved noise-derived Green's functions (NGFs) and examined the path-specific bias in the USGS 3D model. We systematically compared synthetic waveforms with the 3D velocity model and observed NGFs. Our result shows that the time lags between the synthetic and observed data ranging from 2-5 seconds for the ray paths propagating the East Bay Hills. This result also suggests that the SFBA 3D model generates arrivals that are too slow. Additionally, we evaluate the Rayleigh-wave ellipticity to evaluate the subsurface velocity beneath seismic stations. A lateral variation in Rayleigh-wave ellipticity across the Hayward fault is observed, which will contribute to refine the SFBA 3D velocity model.

58 GEOSCIENCES↗
NASA NTRS2001

A Study of Green's Function Methods Applied to Space Radiation Protection

The purpose of this research was to study the propagation of galactic ions through various materials. Galactic light ions result from the break up of heavy ion particles and their propagation through materials is modeled using the one-dimensional Boltzmann equation. When ions enter materials there can occur (i) the interaction of ions with orbital electrons which causes ionization within the material and (ii) ions collide with atoms causing production of secondary particles which penetrate deeper within the material. These processes are modeled by a continuum model. The basic idea is to place a control volume within the material and examine the change in ion flux across this control volume. In this way on can derive the basic equations for the transport of light and heavy ions in matter. Green's function perturbation methods can then be employed to solve the resulting equations using energy dependent nuclear cross sections.

Heinbockel, John H.↗
NASA NTRS1974

Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green's functions

The scalar, electromagnetic, and gravitational geodesic-synchrotron-radiation (GSR) spectra are determined for the case of a test particle moving on a highly relativistic circular orbit about a rotating (Kerr) black hole. It is found that the spectral shape depends only weakly on the value of the angular-momentum parameter (a/M) of the black hole, but the total radiated power drops unexpectedly for a value of at least 0.95 and vanishes as the value approaches unity. A spin-dependent factor (involving the inner product of the polarization of a radiated quantum with the source) is isolated to explain the dependence of the spectral shape on the spin of the radiated field. Although the scalar wave equation is solved by separation of variables, this procedure is avoided for the vector and tensor cases by postulating a sum-over-states expansion for the Green's function similar to that found to hold in the scalar case. The terms in this sum, significant for GSR, can then be evaluated in the geometric-optics approximation without requiring the use of vector or tensor spherical harmonics.

Chrzanowski, P. L.↗
DOE OSTI2015

Many-body Green’s function theory for electron-phonon interactions: The Kadanoff-Baym approach to spectral properties of the Holstein dimer

We present a Kadanoff-Baym formalism to study time-dependent phenomena for systems of interacting electrons and phonons in the framework of many-body perturbation theory. The formalism takes correctly into account effects of the initial preparation of an equilibrium state and allows for an explicit time-dependence of both the electronic and phononic degrees of freedom. The method is applied to investigate the charge neutral and non-neutral excitation spectra of a homogeneous, two-site, two-electron Holstein model. This is an extension of a previous study of the ground state properties in the Hartree (H), partially self-consistent Born (Gd) and fully self-consistent Born (GD) approximations published in Säkkinen et al. [J. Chem. Phys. 143, 234101 (2015)]. Here, the homogeneous ground state solution is shown to become unstable for a sufficiently strong interaction while a symmetry-broken ground state solution is shown to be stable in the Hartree approximation. Signatures of this instability are observed for the partially self-consistent Born approximation but are not found for the fully self-consistent Born approximation. By understanding the stability properties, we are able to study the linear response regime by calculating the density-density response function by time-propagation. This amounts to a solution of the Bethe-Salpeter equation with a sophisticated kernel. The results indicate that none of the approximations is able to describe the response function during or beyond the bipolaronic crossover for the parameters investigated. Overall, we provide an extensive discussion on when the approximations are valid and how they fail to describe the studied exact properties of the chosen model system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Rigorous Ab Initio Quantum Embedding for Quantum Chemistry Using Green’s Function Theory: Screened Interaction, Nonlocal Self-Energy Relaxation, Orbital Basis, and Chemical Accuracy

We present a detailed discussion of the self-energy embedding theory (SEET), which is a quantum embedding scheme allowing us to describe a chosen subsystem very accurately while keeping the description of the environment at a lower level. We apply SEET to molecular examples where our chosen subsystem is made out of a set of strongly correlated orbitals while the weakly correlated orbitals constitute an environment. Consequently, a highly accurate method is used to calculate the self-energy for the system, while a lower-level method is employed to find the self-energy for the environment. Such a self-energy separation is very general, and to make the SEET procedure applicable to multiple systems, a detailed and practical procedure for the evaluation of the system and environment self-energy is necessary. We list all of the intricacies for one of the possible procedures while focusing our discussion on many practical implementation aspects such as the choice of best orbital basis, impurity solver, and many steps necessary to reach chemical accuracy. Finally, on a set of carefully chosen molecular examples, we demonstrate that SEET, which is a controlled, systematically improvable Green’s function method, can be as accurate as established wave function quantum chemistry methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Local Hamiltonians for quantitative Green's function embedding methods

Embedding calculations that find approximate solutions to the Schrödinger equation for large molecules and realistic solids are performed commonly in a three step procedure involving (i) construction of a model system with effective interactions approximating the low energy physics of the initial realistic system, (ii) mapping the model system onto an impurity Hamiltonian, and (iii) solving the impurity problem. We have developed a novel procedure for parametrizing the impurity Hamiltonian that avoids the mathematically uncontrolled step of constructing the low energy model system. Instead, the impurity Hamiltonian is immediately parametrized to recover the self-energy of the realistic system in the limit of high frequencies or short time. The effective interactions parametrizing the fictitious impurity Hamiltonian are local to the embedded regions, and include all the non-local interactions present in the original realistic Hamiltonian in an implicit way. We show that this impurity Hamiltonian can lead to excellent total energies and self-energies that approximate the quantities of the initial realistic system very well. Moreover, we show that as long as the effective impurity Hamiltonian parametrization is designed to recover the self-energy of the initial realistic system for high frequencies, we can expect a good total energy and self-energy. Lastly, we propose two practical ways of evaluating effective integrals for parametrizing impurity models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Deep Green: Structural and Functional Genomic Characterization of Conserved Unannotated Green Lineage Proteins

Our overall objective is to improve and increase functional and structural predictions for a growing number of plant proteins of unknown structure and function (the Deep Green proteins), and to make our predictive data useful and accessible to the larger research community. The project is divided into five major objectives which include 1) Assembly and curation of Deep Green candidate protein sets; 2) in silico structural and functional predictions and network analyses; 3) assembly and validation of reverse genetic resources in Chlamydomonas reinhardtii (Chlamydomonas); 4) high throughput functional genomics characterization and prioritization in Chlamydomonas; and 5) structural validation of selected candidates and functional validation in two important reference plant species, Arabidopsis thaliana (Arabidopsis) and Setaria viridis (Setaria).

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Many-body Green’s function theory for electron-phonon interactions: Ground state properties of the Holstein dimer

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

A GREEN'S FUNCTION APPROACH FOR DETERMINING DOSE RATES FOR SMALL GRAM QUANTITIES IN SHIPPING PACKAGINGS

The Small Gram Quantity (SGQ) concept is based on the understanding that small amounts of hazardous materials, in this case radioactive materials (RAM), are significantly less hazardous than large amounts of the same materials. This paper describes a methodology designed to estimate an SGQ for several neutron and gamma emitting isotopes that can be shipped in a package in compliance with 10 CFR Part 71 external radiation level limits regulations. The neutron and photon sources were calculated using both ORIGEN-S and RASTA. The response from a unit source in each neutron and photon group was calculated using MCNP5 with each unshielded and shielded container configuration. Effects of self-shielding on both neutron and photon response were evaluated by including either plutonium oxide or iron in the source region for the case with no shielded container. For the cases of actinides mixed with light elements, beryllium is the bounding light element. The added beryllium (10 to 90 percent of the actinide mass) in the cases studied represents between 9 and 47 percent concentration of the total mixture mass. For beryllium concentrations larger than 50 percent, the increase in the neutron source term and dose rate tend to increase at a much lower rate than at concentrations lower than 50%. The intimately mixed actinide-beryllium form used in these models is very conservative and thus the limits presented in this report are practical bounds on the mass that can be safely shipped. The calculated dose rate from one gram of each isotope was then used to determin the maximum amount of a single isotope that could be shipped in the Model 9977 Package (or packagings having the same or larger external dimensions as well as similar structural materials) and have the external radiation level within the regulatory dose limits at the surface of the package. The estimates of the mass limits presented would also serve as conservative limits for both the Models 9975 and 9978 packages. If a package contains a mixture of isotopes, the acceptability for shipment can be determined by a sum of fractions approach. It should be noted that the SGQ masses presented in this report represent limits that would comply with the external radiation limits under 10CFR Part 71. They do not necessarily bound lower limits that may be required to comply with other factors such as heat load of the package.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

Continuum limit of electrostatic gyrokinetic absolute equilibrium

Electrostatic gyrokinetic absolute equilibria with continuum velocity field are obtained through the partition function and through the Green function of the functional integral. The new results justify and explain the prescription for quantization/discretization or taking the continuum limit of velocity. The mistakes in the Appendix D of our earlier work [J.-Z. Zhu and G. W. Hammett, Phys. Plasmas 17, 122307 (2010)] are explained and corrected. If the lattice spacing for discretizing velocity is big enough, all the invariants could concentrate at the lowest Fourier modes in a negative-temperature state, which might indicate a possible variation of the dual cascade picture in 2D plasma turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Instanton dominance over $a_s$ at low momenta from lattice QCD simulations at $N_f=0$, $N_f=2+1$ and $N_f=2+1+1$

We report on an instanton-based analysis of the gluon Green functions in the Landau gauge for low momenta; in particular we use lattice results for αs in the symmetric momentum subtraction scheme (MOM) for large-volume lattice simulations. We have exploited quenched gauge field configurations, Nf = 0, with both Wilson and tree-level Symanzik improved actions, and unquenched ones with Nf = 2 + 1 and Nf = 2 + 1 + 1 dynamical flavors (domain wall and twisted-mass fermions, respectively).We show that the dominance of instanton correlations on the low-momenta gluon Green functions can be applied to the determination of phenomenological parameters of the instanton liquid and, eventually, to a determination of the lattice spacing.We furthermore apply the Gradient Flow to remove short-distance fluctuations. The Gradient Flow gets rid of the QCD scale, ΛQCD, and reveals that the instanton prediction extents to large momenta. For those gauge field configurations free of quantum fluctuations, the direct study of topological charge density shows the appearance of large-scale lumps that can be identified as instantons, giving access to a direct study of the instanton density and size distribution that is compatible with those extracted from the analysis of the Green functions.

Athenodorou, Andreas↗
DOE OSTI2014

Convergence of Feynman integrals in Coulomb gauge QCD

At 2-loop order, Feynman integrals in the Coulomb gauge are divergent over the internal energy variables. Nevertheless, it is known how to calculate the effective action, provided that the external gluon fields are all transverse. We show that, for the two-gluon Greens function as an example, the method can be extended to include longitudinal external fields. The longitudinal Greens functions appear in the BRST identities. As an intermediate step, we use a flow gauge, which interpolates between the Feynman and Coulomb gauges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Evolution of finite viscous disks with time-independent viscosity

We find Green functions for the accretion disk with fixed outer radius and time-independent viscosity. With the Green functions, a viscous evolution of the disk with any initial conditions can be described. Two types of inner boundary conditions are considered: the zero stress tensor and the zero accretion rate. The variable mass inflow at the outer radius can also be included. The well-known exponential decline of the accretion rate is a part of the solution with the inner zero stress tensor. The solution with the zero central accretion rate is applicable to disks around stars whose magnetosphere's boundary exceeds the corotation radius. Using the solution, the viscous evolution of disks in some binary systems can be studied. We apply the solution with zero inner stress tensor to outbursts of short-period X-ray transients during the time around the peak. It is found that for the Kramers’ regime of opacity and the initial surface density proportional to the radius, the rise time to the peak is t{sub rise}≈0.15 r{sub out}{sup 2}/ν{sub out} and the e-folding time of the decay is t{sub exp}≈0.45 r{sub out}{sup 2}/ν{sub out}. Comparison to non-stationary α-disks shows that both models with the same value of viscosity at the outer radius produce similar behavior on the viscous time-scale. For six bursts in X-ray novae, which exhibit fast-rise–exponential-decay and are fitted by the model, we find a way to restrict the turbulent parameter α.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Simulation of optical response functions in molecular junctions

Here, we discuss theoretical approaches to nonlinear optical spectroscopy of molecular junctions. Optical response functions are derived in a form convenient for the implementation of Green function techniques, and their expressions in terms of pseudoparticle nonequilibrium Green functions are proposed. The formulation allows to account for both intramolecular interactions and hybridization of molecular states with those of contacts. Within a generic model and utilizing two-dimensional optical spectroscopy as an example, the methodology is compared with exact simulations and is shown to work where the traditional Liouville space approach fails.

74 ATOMIC AND MOLECULAR PHYSICS↗