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Results for “Green's function methods”

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 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

The Prediction and Analysis of Jet Flows and Scattered Turbulent Mixing Noise About Flight Vehicle Airframes

Jet flows interacting with nearby surfaces exhibit a complex behavior in which acoustic and aerodynamic characteristics are altered. The physical understanding and prediction of these characteristics are essential to designing future low noise aircraft. A new approach is created for predicting scattered jet mixing noise that utilizes an acoustic analogy and steady Reynolds-averaged Navier-Stokes solutions. A tailored Green's function accounts for the propagation of mixing noise about the air-frame and is calculated numerically using a newly developed ray tracing method. The steady aerodynamic statistics, associated unsteady sound source, and acoustic intensity are examined as jet conditions are varied about a large at plate. A non-dimensional number is proposed to estimate the effect of the aerodynamic noise source relative to jet operating condition and airframe position. The steady Reynolds-averaged Navier-Stokes solutions, acoustic analogy, tailored Green's function, non- dimensional number, and predicted noise are validated with a wide variety of measurements. The combination of the developed theory, ray tracing method, and careful implementation in a stand-alone computer program result in an approach that is more first principles oriented than alternatives, computationally efficient, and captures the relevant physics of fluid-structure interaction.

Miller, Steven A.↗
DOE OSTI2022

Ab initio self-consistent many-body theory of polarons at all couplings

We present a theoretical framework to describe polarons from first principles within a many-body Green’s function formalism. Starting from a general electron-phonon Hamiltonian, we derive a self-consistent Dyson equation in which the phonon-mediated self-energy is composed by two distinct terms. One term is the Fan-Migdal self-energy and describes dynamic electron-phonon processes, the other term is a contribution to the self-energy originating from the static displacements of the atomic nuclei in the polaronic ground state. The lowest-order approximation to the present theory yields the standard many-body perturbation theory approach to electron-phonon interactions in the limit of large polarons, and the ab initio polaron equations introduced in the limit of small polarons. Here, a practical recipe to implement the present unifying formalism in first-principles calculations is outlined. We apply our method to the Fröhlich model, and obtain remarkably accurate polaron energies at all couplings, in line with Feynman’s polaron theory and diagrammatic Monte Carlo calculations. We also recover the well-known results of Fröhlich and Pekar at weak and strong coupling, respectively. The present approach enables predictive many-body calculations of polarons in real materials at all couplings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

We introduce a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing . The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we establish a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work indicate a more efficient scaling of computational cost with molecular size as compared to other methods.

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

Dual-function lignin monomers enable high-performance graphene electrodes via interface confinement and proton transfer enhancement

Graphene oxide (GO)-based energy storage faces dual bottlenecks: unsustainable reduction methods and sluggish proton transfer kinetics. Here, we introduce a groundbreaking green strategy using lignin-derived vanillyl alcohol (VA) as a dual-function monomer to simultaneously address these challenges. By thermally annealing GO/VA films at mild temperatures (<100 °C), VA triggers an interface-confined reduction of GO while self-polymerizing into redox-active oligomers (P-VA) that intercalate between graphene layers. This dual role-reducing agent and proton highway enables a 3D conductive network with minimized graphene restacking, abundant redox sites, and rapid H + transport pathways. Density Functional Theory (DFT) reveals how P-VA optimizes proton dynamics, while the resulting rGO-P-VA4-T90 electrode achieves a record volumetric capacitance of 311.1F/cm 3 (777.8F/cm 2 ) and retains 87.8 % capacity after 10,000 cycles. Flexible solid-state supercapacitors deliver 94.2 μWh/cm 2 energy density at 63.8 μW/cm 2 , rivaling state-of-the-art devices. Furthermore, this work redefines sustainable graphene engineering, merging biomass valorization with high-performance energy storage in a scalable, eco-friendly paradigm.

Graphene oxide reduction↗
DOE OSTI2024

A computational approach to complex junctions and interfaces

Molecular- and nano- junctions, surfaces, interfaces, and interfacial processes have been the subjects of this DOE supported program for about 20 years. We have investigated electronic and magnetic structure, spin-dependent charge transport, and emerging phenomena at surfaces and interfaces in a number of physical systems ranging from nano-clusters, to nanowires, to two-dimensional (2D) crystals and their interactions, to bulk matter. Eighty-four refereed papers were published [1-84], with a majority effort from the group led by the PI, and over a hundred presentations were made at international conferences. We use first-principles methods in the framework of density functional theory in conjunction with nano-equilibrium Green function techniques, semi-empirical Boltzmann transport theory, tight-binding models, and the Hubbard model and many-body wavefunction approaches. In pursuing our scientific goals, we have also developed a number of computational algorithms and computational packages.

2D materials↗
NASA NTRS2000

3D Higher Order Modeling in the BEM/FEM Hybrid Formulation

Higher order divergence- and curl-conforming bases have been shown to provide significant benefits, in both convergence rate and accuracy, in the 2D hybrid finite element/boundary element formulation (P. Fink and D. Wilton, National Radio Science Meeting, Boulder, CO, Jan. 2000). A critical issue in achieving the potential for accuracy of the approach is the accurate evaluation of all matrix elements. These involve products of high order polynomials and, in some instances, singular Green's functions. In the 2D formulation, the use of a generalized Gaussian quadrature method was found to greatly facilitate the computation and to improve the accuracy of the boundary integral equation self-terms. In this paper, a 3D, hybrid electric field formulation employing higher order bases and higher order elements is presented. The improvements in convergence rate and accuracy, compared to those resulting from lower order modeling, are established. Techniques developed to facilitate the computation of the boundary integral self-terms are also shown to improve the accuracy of these terms. Finally, simple preconditioning techniques are used in conjunction with iterative solution procedures to solve the resulting linear system efficiently. In order to handle the boundary integral singularities in the 3D formulation, the parent element- either a triangle or rectangle-is subdivided into a set of sub-triangles with a common vertex at the singularity. The contribution to the integral from each of the sub-triangles is computed using the Duffy transformation to remove the singularity. This method is shown to greatly facilitate t'pe self-term computation when the bases are of higher order. In addition, the sub-triangles can be further divided to achieve near arbitrary accuracy in the self-term computation. An efficient method for subdividing the parent element is presented. The accuracy obtained using higher order bases is compared to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained using higher order bases are compared to those obtained with lower order bases for selected sample

Fink, P. W.↗
NASA NTRS1991

Analysis of a slot loaded microstrip disk antenna for circular polarisation

A method is presented to analyze a circular microstrip disk antenna loaded with a narrow, inclined slot at its center and fed by a coaxial probe. Making use of the exact dyadic Green's functions for a grounded dielectric slab due to electric and magnetic currents, Richmond's reaction integral equation in conjunction with the method of moments (Galerkin), a generalized h-parameter equivalent network for the loaded patch is obtained. An expression for the input impedance of a slot loaded microstrip patch is obtained from the equivalent parameters. The theoretical results are compared with the experiment.

Rao, Y. R.↗
NASA NTRS1985

Experimental methods for quenching structures in lunar-analog silicate melts: Variations as a function of quench media and composition

Compositions analogous to lunar green, organge, and brown glasses were synthesized under consistent conditions, then quenched into a variety of different media when the samples were removed from the furnace. Iron valence and coordination are a direct function of quench media used, spanning the range from brine/ice (most effective quench), water, butyl phthalate, silicone oil, liquid nitrogen, highly reducing CO-CO2 gas, to air (least efficient quench). In the green and brown glasses, Fe(3+) in four-fold and six-fold coordination is observed in the slowest-quenched samples; Fe(2+) coordination varies directly with quench efficiency. Less pronounced changes were observed in the Ti-rich orange glass. Therefore the remote-sensed spectrum of a glass-bearing regolith on the Moon may be influenced by the process by which the glass cooled, and extreme caution must be used when comparing spectra of synthetic glass analogs with real lunar glasses.

Dyar, M. D.↗
NASA NTRS1984

Experimental methods for quenching structures in lunar-analog silicate melts - Variations as a function of quench media and composition

Compositions analogous to lunar green, orange, and brown glasses were synthesized under consistent conditions, then quenched into a variety of different media when the samples were removed from the furnace. Iron valence and coordination are a direct function of quench media used, spanning the range from brine/ice (most effective quench), water, butyl phthalate, silicone oil, liquid nitrogen, highly reducing CO-CO2 gas, to air (least efficient quench). In the green and brown glasses, Fe(3+) in four-fold and six-fold coordination is observed in the slowest-quenched samples; Fe(2+) coordination varies directly with quench efficiency. Less pronounced changes were observed in the Ti-rich orange glass. Therefore the remote-sensed spectrum of a glass-bearing regolith on the moon may be influenced by the process by which the glass cooled, and extreme caution must be used when comparing spectra of synthetic glass analogs with real lunar glasses.

Dyar, M. D.↗
DOE OSTI2013

Propagators in polymer quantum mechanics

Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to represent some aspects of the loop quantization in a simpler context, and, on the other, it has been applied to each of the infinite mechanical modes of other systems. Indeed, this polymer approach was recently implemented for the free scalar field propagator. In this work we compute the polymer propagators of the free particle and a particle in a box; amusingly, just as in the non polymeric case, the one of the particle in a box may be computed also from that of the free particle using the method of images. We verify the propagators hereby obtained satisfy standard properties such as: consistency with initial conditions, composition and Green’s function character. Furthermore they are also shown to reduce to the usual Schrödinger propagators in the limit of small parameter μ{sub 0}, the length scale introduced in the polymer dynamics and which plays a role analog of that of Planck length in Quantum Gravity. -- Highlights: •Formulas for propagators of free and particle in a box in polymer quantum mechanics. •Initial conditions, composition and Green’s function character is checked. •Propagators reduce to corresponding Schrödinger ones in an appropriately defined limit. •Results show overall consistency of the polymer framework. •For the particle in a box results are also verified using formula from method of images.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

Nonperturbative methods in HZE ion transport

A nonperturbative analytic solution of the high charge and energy (HZE) Green's function is used to implement a computer code for laboratory ion beam transport. The code is established to operate on the Langley Research Center nuclear fragmentation model used in engineering applications. Computational procedures are established to generate linear energy transfer (LET) distributions for a specified ion beam and target for comparison with experimental measurements. The code is highly efficient and compares well with the perturbation approximations.

Wilson, John W.↗
DOE OSTI2015

Photoacoustic tomography based on the Green's function retrieval with ultrasound interferometry for sample partially behind an acoustically scattering layer

Acoustically inhomogeneous mediums with multiple scattering are often the nightmare of photoacoustic tomography. In order to break this limitation, a photoacoustic tomography scheme combining ultrasound interferometry and time reversal is proposed to achieve images in acoustically scattering medium. An ultrasound interferometry is developed to determine the unknown Green's function of strong scattering tissue. Using the determined Greens' function, a time-reversal process is carried out to restore images behind an acoustically inhomogeneous layer from the scattering photoacoustic signals. This method effectively decreases the false contrast, noise, and position deviation of images induced by the multiple scattering. Phantom experiment is carried out to validate the method. Therefore, the proposed method could have potential value in extending the biomedical applications of photoacoustic tomography in acoustically inhomogeneous tissue.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Spin relaxation rate for heavy quarks in weakly coupled QCD plasma

We compute the relaxation rate of the spin density of heavy quarks in a perturbative QCD plasma to leading-log order in the coupling constant g. The spin relaxation rate Γ s in spin hydrodynamics is shown to be Γ s ~ g 4 log(1/g)T(T/M) 2 in the heavy-quark limit T/M $\ll$ 1, which is smaller than the relaxation rate of other non- hydrodynamic modes by additional powers of T/M. We demonstrate three different methods to evaluate the spin relaxation rate: 1) the Green-Kubo formula in the spin hydrodynamic regime, 2) the spin density correlation function in the strict hydrodynamic limit, and 3) quantum kinetic theory of the spin distribution function in momentum space. We highlight the interesting differences between these methods, while they are ultimately connected to each other by the underlying Ward-Takahashi identity for the non-conserved spin density.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms

A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green’s function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green’s function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green’s function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green’s function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green’s function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams

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

Efficient separation and coprecipitation for simplified cathode recycling

Hydrometallurgical recycling of spent lithium-ion batteries is among the most promising recovery approaches. The current hydrometallurgical method for battery recycling faces challenges such as complex separation and precipitation processes, and environmental concerns from the use of caustic inorganic acid and hazardous hydrogen peroxide. Our proposed modified method, namely polyol-metallurgy, uses citric acid in ethylene glycol as dual-function green solution to overcome these obstacles. This bifunctional solution leaches valuable metal ions from cathode materials (e.g., LiCoO 2 ), and then acts as chelating agents to selectively precipitate cobalt through an esterification reaction, without the need for additional precipitation agents. The leaching efficiency of cobalt and lithium reaches 99.55% and 97.65%, respectively, and more than 96% of cobalt could be directly self-precipitated and recovered. Further, the unique characteristics of the dual-function solution also avoids impurities from Al foils and PVDF/carbon black films, enabling the simple separation process. Therefore, the process can be completed in one-pot system with efficient leaching, separation and coprecipitation, making it more efficient and feasible for operation than existing alternatives.

25 ENERGY STORAGE↗
DOE OSTI2023

A high order Cartesian grid, finite volume method for elliptic interface problems

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems with high-contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We include a generalized truncation error analysis based on cell-centered Taylor series expansions, which then define stencils in terms of local discrete solution data and geometric information. In the process, we develop a simple method based on Green's theorem for computing exact geometric moments directly from an implicit function definition of the embedded interface. This approach produces stencils with a simple bilinear representation, where spatially-varying coefficients and jump conditions can be easily included and finite volume conservation can be enforced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

An asymptotic-preserving semi-Lagrangian algorithm for the anisotropic heat transport equation with arbitrary magnetic fields

Here, we extend the recently proposed semi-Lagrangian algorithm for the extremely anisotropic heat transport equation [Chacón et al., J. Comput. Phys ., 272 (2014)] to deal with arbitrary magnetic field topologies. The original scheme (which showed remarkable numerical properties) was valid for the so-called tokamak-ordering regime, in which the magnetic field magnitude was not allowed to vary much along field lines. The proposed extension maintains the attractive features of the original scheme (including the analytical Green's function, which is critical for tractability) with minor modifications, while allowing for completely general magnetic fields. The accuracy and generality of the approach are demonstrated by numerical experiment with an analytical manufactured solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Three–Dimensional Acoustic Multipole Waveform Inversion at Yasur Volcano, Vanuatu

Acoustic waveform inversions can provide estimates of volume flow rate and erupted mass, enhancing the ability to estimate volcanic emissions. Previous studies have generally assumed a simple acoustic source (monopole); however, more complex and accurate source reconstructions are possible with a combination of equivalent sources (multipole). We deployed a high–density acoustic network around Yasur volcano, Vanuatu, including acoustic sensors on a tethered aerostat that was moved every ~15–60 min. Using this unique data set we invert for the acoustic multipole source mechanism using a grid search approach for 80 events to examine volume flow rates and dipole strengths. Our method utilizes finite–difference time–domain modeling to obtain the full 3–D Green's functions that account for topography. Inversion results are compared using a monopole–only, multipole (monopole and dipole), simulations that do not include topography, and those that use a subset of sensors. We find that the monopole source is a good approximation when topography is considered. However, initial compression amplitude is not fully captured by a monopole source so source directionality cannot be ruled out. The monopole solution is stable regardless of whether a monopole–only or multipole inversion is performed. Inversions for the dipole components produce estimates consistent with observed source directionality, though these inversions are somewhat unstable given station configurations of typical deployments. Furthermore, our results suggest that infrasound waveform inversion shows promise for realistic quantitative source estimates, but additional work is necessary to fully explore inversion stability, uncertainty, and robustness.

58 GEOSCIENCES↗