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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.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum

Here, we develop a stochastic resolution of identity approach to the real-time second-order Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green's function [ Takeshita et al. J. Chem. Phys. 2019 , 151 , 044114 ]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(N e 5 ) down to O(N e 3 ) where N e is the number of electrons. Finally, this is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to N e ≈ 1000 electrons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads

Founded on a novel analytical formulation that led to a rigorous yet compact path-integral representation of the time-domain elastodynamic half-space Green's function, a unified analysis of the possible occurrence of different singular wavefront behaviour in the response under arbitrary impulsive internal or surface point loads at arbitrary source-receiver locations is presented. With the decomposition of the general solution into distinct initiating and reflected wave group integrals that share a common factored format and simple contour definitions, the mathematical framework is shown to allow a straightforward identification of the specific conditions and the particular wave groups that are responsible for the singular wavefront phenomena without resorting to advanced analytic function theories or asymptotic methods. Analytic characterizations of the nature, strength and direction of all intrinsic singular wavefront behaviours of the three-dimensional Green's function in three canonical cases of source-receiver configurations are given in a dual integral-closed form format to facilitate their theoretical understanding as well as computational applications. Graphical illustrations of their variation with the source-receiver configuration and the medium's Poisson's ratio together with relevant comparison and clarifications of some classical treatments are included.

Green’s functions↗
NASA NTRS2007

Simple and Efficient Numerical Evaluation of Near-Hypersingular Integrals

Recently, significant progress has been made in the handling of singular and nearly-singular potential integrals that commonly arise in the Boundary Element Method (BEM). To facilitate object-oriented programming and handling of higher order basis functions, cancellation techniques are favored over techniques involving singularity subtraction. However, gradients of the Newton-type potentials, which produce hypersingular kernels, are also frequently required in BEM formulations. As is the case with the potentials, treatment of the near-hypersingular integrals has proven more challenging than treating the limiting case in which the observation point approaches the surface. Historically, numerical evaluation of these near-hypersingularities has often involved a two-step procedure: a singularity subtraction to reduce the order of the singularity, followed by a boundary contour integral evaluation of the extracted part. Since this evaluation necessarily links basis function, Green s function, and the integration domain (element shape), the approach ill fits object-oriented programming concepts. Thus, there is a need for cancellation-type techniques for efficient numerical evaluation of the gradient of the potential. Progress in the development of efficient cancellation-type procedures for the gradient potentials was recently presented. To the extent possible, a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. However, since the gradient kernel involves singularities of different orders, we also require that the transformation leaves remaining terms that are analytic. The terms "normal" and "tangential" are used herein with reference to the source element. Also, since computational formulations often involve the numerical evaluation of both potentials and their gradients, it is highly desirable that a single integration procedure efficiently handles both.

Fink, Patrick W.↗
DOE OSTI2014

A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Near-field radiative heat transfer between irregularly shaped dielectric particles modeled with the discrete system Green's function method

Near-field radiative heat transfer (NFRHT) between irregularly shaped dielectric particles made of SiO 2 and morphology characterized by Gaussian random spheres is studied. Particles are modeled using the discrete system Green's function (DSGF) approach, which is a volume integral numerical method based on fluctuational electrodynamics. This method is applicable to finite, three-dimensional objects, and all system interactions are defined independent of thermal excitation by a generalized system Green's function. The DSGF method is deemed suitable to model NFRHT between irregularly shaped particles after verification against the analytical solution for chains of two and three SiO 2 spheres. The NFRHT results reveal that geometric irregularity in particles leads to a reduction of the total conductance from that of comparable perfect spheres at vacuum separation distances smaller than the particle size, a regime in which NFRHT is a surface phenomenon. At vacuum separation distances larger than the particle size, NFRHT becomes a volumetric process, and the total conductance between irregularly shaped particles converges to that of comparable perfect spheres. Spectral analysis reveals, however, that particle irregularity leads to damping and broadening of resonances at all separation distances, thereby highlighting the importance of the DSGF method for spectral engineering in the near field. The reduced spectral coherence when particle size is larger than the vacuum separation distance is attributed to coupling of surface phonon-polaritons within the randomly generated, distorted particle features. For particle size smaller than the vacuum separation distance, resonance broadening and damping are linked with the multiple localized surface phonon modes supported by the composite spherical harmonic morphologies of the Gaussian random spheres. In conclusion, this paper has direct implications for thermal management of packed particle systems, with applications in radiative property control, electronics, energy conversion, and nanomanufacturing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Mitigating Green's function Monte Carlo signal-to-noise problems using contour deformations

The Green's function Monte Carlo (GFMC) method provides accurate solutions to the nuclear many-body problem and predicts properties of light nuclei starting from realistic two- and three-body interactions. Controlling the GFMC fermion sign problem is crucial, as the signal-to-noise ratio decreases exponentially with imaginary time, requiring significant computing resources. Inspired by similar scenarios in lattice quantum field theory and spin systems, in this work, we employ integration contour deformations to improve the GFMC signal-to-noise ratio. Machine learning techniques are used to select optimal contours with minimal variance from parametrized families of deformations. As a proof of principle, we consider the deuteron binding energies and Euclidean density response functions. Here, we only observe mild signal-to-noise improvement for the binding energy case. On the other hand, we achieve an order of magnitude reduction of the variance for Euclidean density response functions, paving the way for computing electron- and neutrino-nucleus cross sections of larger nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1986

Radiative transfer in multilayered random medium with laminar structure - Green's function approach

For a multilayered random medium with a laminar structure a Green's function approach is introduced to obtain the emitted intensity due to an arbitrary point source. It is then shown that the approach is applicable to both active and passive remote sensing. In active remote sensing, the computed radar backscattering cross section for the multilayered medium includes the effects of both volume multiple scattering and surface multiple scattering at the layer boundaries. In passive remote sensing, the brightness temperature is obtained for arbitrary temperature profiles in the layers. As an illustration the brightness temperature and reflectivity are calculated for a bounded layer and compared with results in the literature.

Karam, M. A.↗
DOE OSTI2023

Mitigating Green's function Monte Carlo signal-to-noise problems using contour deformations

The Green's function Monte Carlo (GFMC) method provides accurate solutions to the nuclear many-body problem and predicts properties of light nuclei starting from realistic two- and three-body interactions. Controlling the GFMC fermion-sign problem is crucial, as the signal-to-noise ratio decreases exponentially with Euclidean time, requiring significant computing resources. Inspired by similar scenarios in lattice quantum field theory and spin systems, in this work, we employ integration contour deformations to improve the GFMC signal-to-noise ratio. Machine learning techniques are used to select optimal contours with minimal variance from parameterized families of deformations. As a proof of principle, we consider the deuteron binding energies and Euclidean density response functions. We only observe mild signal-to-noise improvement for the binding energy case. On the other hand, we achieve an order of magnitude reduction of the variance for Euclidean density response functions, paving the way for computing electron- and neutrino-nucleus cross-sections of larger nuclei.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

The spectral green's function nodal method for multigroup slab-geometry fixed-source S{sub N} problems with anisotropic scattering

A generalization of the spectral Green's function (SGF) method is developed for multigroup, fixed-source, slab-geometry discrete ordinates (S{sub N}) problems with anisotropic scattering. The offered SGF method with the one-node block inversion (NBI) iterative scheme converges numerical solutions that are completely free from spatial truncation errors for multigroup slab-geometry S{sub N} problems with scattering anisotropy of order L, provided L < N. As a coarse-mesh numerical method, the SGF method generates numerical solutions that generally do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. Therefore, presented here is a technique for the spatial reconstruction of the coarse-mesh solution generated by the multigroup SGF method. Numerical results are given to illustrate the method's accuracy. (authors)

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Tseng, K.↗
NASA NTRS1977

A Green's function formulation for a nonlinear potential flow solution applicable to transonic flow

Routine determination of inviscid subsonic flow fields about wing-body-tail configurations employing a Green's function approach for numerical solution of the perturbation velocity potential equation is successfully extended into the high subsonic subcritical flow regime and into the shock-free supersonic flow regime. A modified Green's function formulation, valid throughout a range of Mach numbers including transonic, that takes an explicit accounting of the intrinsic nonlinearity in the parent governing partial differential equations is developed. Some considerations pertinent to flow field predictions in the transonic flow regime are discussed.

Baker, A. J.↗
DOE OSTI2016

Using Green's Functions to Compute 3 Dimensional Neutron Flux Maps - 16016

The knowledge of the radionuclide content of radioactive waste is of utmost importance for safety and waste management reasons. Numerical simulations are used by EDF-DP2D to anticipate dismantling and radioactive waste management. The main numerical activation schemes include the computing of a 3 dimensional neutron flux map, obtained on the basis of a neutron propagation calculation. The codes used solve the transport equation called the Boltzmann equation without simplification. The Monte Carlo method is used to solve the Boltzmann equation. Random series of numbers are used to simulate the lives of millions of neutrons. The codes follow each neutron individually, from its birth to its disappearance by leakage, absorption, or fission, and then the neutron flux map is calculated at the nominal power rating conditions. The main drawback of the Monte Carlo codes is the large computing time needed to converge within acceptable statistical criteria. This extended time period is incompatible with the multiple fuel managements used by EDF to operate its NPPs because it is necessary to make a Monte Carlo calculation for each fuel loading pattern. The solution developed by EDF-DP2D is to use the importance factors of Green's Functions to simplify the computing of the 3 dimensional neutron flux maps. Physicists talk about Green's Functions where mathematicians talk about elementary solutions of linear equations with constant coefficients. With an activation scheme based on the Green's Functions approach the 3D neutron flux is obtained on the basis of the convolution of the normalized source contributions (i.e. normalized response matrices) with the neutrons emitted by the fuel assemblies. The response matrices to unitary sources are computed with the Monte Carlo code MCNP for different tallies of interest and the neutron sources emitted by the fuel are computed with a core code for different fuel loading patterns. The principal interest of this approach is the calculation of the response matrices to unitary sources that can be used for all power distributions, thus limiting the Monte Carlo computing time. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2014

Brownian dynamics without Green's functions

We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions “on the fly.” Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning

Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff–Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ where N t is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Monte Carlo Explicitly Correlated Second-Order Many-Body Green’s Function Calculations of Semiconductor Band Gaps

A systematically converging series of ab initio, post-density-functional, size-consistent, electron-correlated approximations is desired for predictive computing of felectronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green's function theory based on Gaussian-type-orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green's function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis-set-incompleteness errors by the explicit-correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular-orbital energy (HOMO-LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO-LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 eV and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. As a result, the experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 eV and 2.42 eV, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Study of electromagnetic wave scattering from an inhomogeneous plasma layer using Green's function volume integral equation method

Gigahertz electromagnetic wave scattering from an inhomogeneous collisional plasma layer with bell-like and Epstein electron density distributions is studied by the Green's function volume integral equation method to find the reflectance, transmittance, and absorbance coefficients of this inhomogeneous plasma. Also, the effects of the frequency of the electromagnetic wave, plasma parameters, such as collision frequency, electron density, and plasma thickness, and the effects of the profile of the electron density on the electromagnetic wave scattering from this plasma slab are investigated. According to the results, when the electron density, collision frequency, and plasma thickness are increased, collisional absorbance is enhanced, and as a result, the absorbance bandwidth of plasma is broadened. Moreover, this broadening is more evident for plasma with bell-like electron density profile. Also, the bandwidth of the frequency and the range of pressure in which plasma behaves as a good reflector are determined in this article. According to the results, the bandwidth of the frequency is decreased for thicker plasma with bell-like profile, while it does not vary for a different plasma thickness with Epstein profile. Moreover, the range of the pressure is decreased for bell-like profile in comparison with Epstein profile. Furthermore, due to the sharp inhomogeneity of the Epstein profile, the coefficients of plasma that are uniform for plasma with bell-like profile are changed for plasma with Epstein profile, and some perturbations are seen.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Real-space Green's function approach for intrinsic losses in x-ray spectra

Intrinsic inelastic losses in x-ray spectra originate from excitations in an interacting electron system due to a suddenly created core-hole. These losses characterize the features observed in x-ray photoemission spectra (XPS), as well as many-body effects such as satellites and edge-singularities in x-ray absorption spectra (XAS). However, they are usually neglected in practical calculations. As shown by Langreth these losses can be treated within linear response in terms of a cumulant Green's function in momentum space. Here we present a complementary ab initio real-space Green's function generalization of the Langreth cumulant in terms of the dynamically screened core-hole interaction W c (ω) and the independent particle response function. Here we find that the cumulant kernel β⁡(ω) is analogous to XAS, but with the transition operator replaced by the core-hole potential with monopole selection rules. The behavior reflects the analytic structure of the loss function, with peaks near the zeros of the dielectric function, consistent with delocalized quasiboson excitations. The approach simplifies when W c (ω) is localized and spherically symmetric. In conclusion, illustrative results and comparisons are presented for the electron gas, sodium, and some early transition metal compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗