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All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Elementary solutions of coupled model equations in the kinetic theory of gases

The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.

Kriese, J. T.↗
DOE OSTI2014

Restoration of the covariant gauge α in the initial field of gravity in de Sitter spacetime

The gravitational field generated by a mass term and the initial surface through covariant retarded Green's function for linearized gravity in de Sitter spacetime was studied recently [4, 5] with the covariant gauges set to β = 2/3 and α = 5/3. In this paper we extend the work to restore the gauge parameter α in the field coming from the initial data using the method of shifting the parameter. The α terms in the initial field cancels exactly with the one coming from the source term. Consequently, the correct field configuration, with two equal mass points moving in its geodesic, one located at the North pole and another one located at the South pole, is reproduced in the whole manifold of de Sitter spacetime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Localization of phonons in mass-disordered alloys: A typical medium dynamical cluster approach

The effect of disorder on lattice vibrational modes has been a topic of interest for several decades. In this article, we employ a Green's function based approach, namely, the dynamical cluster approximation (DCA), to investigate phonons in mass-disordered systems. Detailed benchmarks with previous exact calculations are used to validate the method in a wide parameter space. An extension of the method, namely, the typical medium DCA (TMDCA), is used to study Anderson localization of phonons in three dimensions. We show that, for binary isotopic disorder, lighter impurities induce localized modes beyond the bandwidth of the host system, while heavier impurities lead to a partial localization of the low-frequency acoustic modes. For a uniform (box) distribution of masses, the physical spectrum is shown to develop long tails comprising mostly localized modes. The mobility edge separating extended and localized modes, obtained through the TMDCA, agrees well with results from the transfer matrix method. A reentrance behavior of the mobility edge with increasing disorder is found that is similar to, but somewhat more pronounced than, the behavior in disordered electronic systems. Our work establishes a computational approach, which recovers the thermodynamic limit, is versatile and computationally inexpensive, to investigate lattice vibrations in disordered lattice systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
DOE OSTI2022

Visualization of defect induced in-gap states in monolayer MoS 2

Atomic-scale intrinsic defects play a key role in controlling functional electronic properties of two-dimensional (2D) materials. Here, we present a low-temperature scanning–tunneling microscopy and spectroscopy investigation of a common point-defect in monolayer molybdenum disulfide (MoS 2 ). We employ a sample preparation method in which the film surface is never exposed to air so that the native dangling bonds surrounding the defects in the film are preserved. Molybdenum vacancies are identified by their three characteristic in-gap resonances by combining scanning–tunneling measurements with parallel Green’s function-based theoretical modeling. The relative energy shifts between the various in-gap states allow us to identify a relative charge difference between two of the observed vacancies. The role of the substrate on the band structure of the defective MoS 2 monolayer is unveiled. Our study highlights the effects of the substrate on the in-gap states of common defects found in MoS 2 providing a pathway in designing and optimizing 2D materials for electronic applications.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Advanced electromagnetic methods for aerospace vehicles

The Advanced Helicopter Electromagnetics (AHE) Industrial Associates Program has continuously progressed with its research effort focused on subjects identified and recommended by the Advisory Task Force of the program. The research activities in this reporting period have been steered toward practical helicopter electromagnetic problems, such as HF antenna problems and antenna efficiencies, recommended by the AHE members at the annual conference held at Arizona State University on 28-29 Oct. 1992 and the last biannual meeting held at the Boeing Helicopter on 19-20 May 1993. The main topics addressed include the following: Composite Materials and Antenna Technology. The research work on each topic is closely tied with the AHE Consortium members' interests. Significant progress in each subject is reported. Special attention in the area of Composite Materials has been given to the following: modeling of material discontinuity and their effects on towel-bar antenna patterns; guidelines for composite material modeling by using the Green's function approach in the NEC code; measurements of towel-bar antennas grounded with a partially material-coated plate; development of 3-D volume mesh generator for modeling thick and volumetric dielectrics by using FD-TD method; FDTD modeling of horn antennas with composite E-plane walls; and antenna efficiency analysis for a horn antenna loaded with composite dielectric materials.

Balanis, Constantine A.↗
DOE OSTI2020

DFTB+, a software package for efficient approximate density functional theory based atomistic simulations

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green’s functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

Testing thermal conductivity models with equilibrium molecular dynamics simulations of the one-component plasma

Equilibrium molecular dynamics simulations are used to calculate the thermal conductivity of the onecomponent plasma via the Green-Kubo formalism over a broad range of Coulomb coupling strength, 0.1 ≤ Γ ≤180. These simulations address previous discrepancies between computations using equilibrium versus nonequilibrium methods. Analysis of heat flux autocorrelation functions show that very long (6×10 5 $ω^{-1}_{p}$) time series are needed to reduce the noise level to allow ≲2% accuracy. The simulations provide accurate data for Γ ≲ 1. Furthermore, this enables a test of the traditional Landau-Spitzer theory, which is found to agree with the simulations for Γ ≲ 0.3. It also enables tests of theories to address moderate and strong Coulomb coupling. Two are found to provide accurate extensions to the moderate coupling regime of Γ ≲ 10, but none are accurate in the Γ ≳ 10 regime where potential energy transport and coupling between mass flow and stress dominate thermal conduction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Moment tensor analysis of very shallow sources

An issue for moment tensor (MT) inversion of shallow seismic sources is that some components of the Green’s functions have vanishing amplitudes at the free surface, which can result in bias in the MT solution. The effects of the free surface on the stability of the MT method become important as we continue to investigate and improve the capabilities of regional full MT inversion for source–type identification and discrimination. It is important to understand free–surface effects on discriminating shallow explosive sources for nuclear monitoring purposes. It may also be important in natural systems that have very shallow seismicity, such as volcanic and geothermal systems. We examine the effects of the free surface on the MT via synthetic testing and apply the MT–based discrimination method to three quarry blasts from the HUMMING ALBATROSS experiment. These shallow chemical explosions at ~10 m depth and recorded up to several kilometers distance represent rather severe source–station geometry in terms of free–surface effects. We show that the method is capable of recovering a predominantly explosive source mechanism, and the combined waveform and first–motion method enables the unique discrimination of these events. Furthermore, recovering the design yield using seismic moment estimates from MT inversion remains challenging, but we can begin to put error bounds on our moment estimates using the network sensitivity solution technique.

58 GEOSCIENCES↗
NASA NTRS1986

Use of speckle for determining the response characteristics of Doppler imaging radars

An optical model is developed for imaging optical radars such as the SAR on Seasat and the Shuttle Imaging Radar (SIR-B) by analyzing the Doppler shift of individual speckles in the image. The signal received at the spacecraft is treated in terms of a Fresnel-Kirchhoff integration over all backscattered radiation within a Huygen aperture at the earth. Account is taken of the movement of the spacecraft along the orbital path between emission and reception. The individual points are described by integration of the point source amplitude with a Green's function scattering kernel. Doppler data at each point furnishes the coordinates for visual representations. A Rayleigh-Poisson model of the surface scattering characteristics is used with Monte Carlo methods to generate simulations of Doppler radar speckle that compare well with Seasat SAR data SIR-B data.

Tilley, D. G.↗
NASA NTRS1991

Polarimetric passive remote sensing of periodic surfaces

The concept of polarimetry in active remote sensing is extended to passive remote sensing. The potential use of the third and fourth Stokes parameters U and V, which play an important role in polarimetric active remote sensing, is demonstrated for passive remote sensing. It is shown that, by the use of the reciprocity principle, the polarimetric parameters of passive remote sensing can be obtained through the solution of the associated direct scattering problem. These ideas are applied to study polarimetric passive remote sensing of periodic surfaces. The solution of the direct scattering problem is obtained by an integral equation formulation which involves evaluation of periodic Green's functions and normal derivative of those on the surface. Rapid evaluation of the slowly convergent series associated with these functions is observed to be critical for the feasibility of the method. New formulas, which are rapidly convergent, are derived for the calculation of these series. The study has shown that the brightness temperature of the Stokes parameter U can be significant in passive remote sensing. Values as high as 50 K are observed for certain configurations.

Veysoglu, Murat E.↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS1996

A Computer Program for the Computation of Running Gear Temperatures Using Green's Function

A new technique has been developed to study two dimensional heat transfer problems in gears. This technique consists of transforming the heat equation into a line integral equation with the use of Green's theorem. The equation is then expressed in terms of eigenfunctions that satisfy the Helmholtz equation, and their corresponding eigenvalues for an arbitrarily shaped region of interest. The eigenfunction are obtalned by solving an intergral equation. Once the eigenfunctions are found, the temperature is expanded in terms of the eigenfunctions with unknown time dependent coefficients that can be solved by using Runge Kutta methods. The time integration is extremely efficient. Therefore, any changes in the time dependent coefficients or source terms in the boundary conditions do not impose a great computational burden on the user. The method is demonstrated by applying it to a sample gear tooth. Temperature histories at representative surface locatons are given.

GREENS FUNCTIONS↗
DOE OSTI2018

A Systems Biology and Pond Culture-based Understanding and Improvement of Metabolic Processes Related to Productivity in Diverse Microalgal Classes for Viable Biofuel Production

The overarching goal of this project was to understand and manipulate fundamental molecular mechanisms involved in maximizing growth rate and lipid accumulation in diverse classes of microalgae under authentic diurnal conditions to enhance production capabilities for biofuels. The research was aimed at filling two critical knowledge gaps by addressing fundamental cellular issues that govern growth and fuel molecule accumulation in conjunction with realistic climate-simulated cultivation: 1) The insufficient understanding of the effect of metabolic topology on cellular carbon partitioning and its regulation with regards to productivity. 2) The understudied effect of the diurnal and cell cycles on cellular metabolism, resource allocation, and resource mobilization under simulated production conditions. To unravel broader as well as lineage-specific regulatory mechanisms that determine productivity, we compared green algae with diatoms. Complementing the systems approach with a pond-based cultivation method under authentic diurnal conditions, we anticipated an understanding of how the effect of diurnal and cell cycles affects growth and lipid productivity. Elucidation of the topology and regulation of relevant metabolic networks in proposed new model organisms was expected to enable improvements in functional capabilities and biosynthetic pathways. The major goals of the project were achieved by the following accomplishments. Genome assemblies and functional annotations for the green algae S. obliquus strain DOE0152Z and Coleastrella sp. strain DOE0202. Development of a metabolic map for the core carbon metabolism for S. obliquus. Analyzed the cellular topology for the core carbon network and proposed differences in core carbon metabolism for the Chlorophyceae versus the Trebouxiophyceae. Discovered the genes for enzymes involved in dicarboxylic acid metabolism and proposed the existence of C4-type metabolism for S. obliquus. Calculated the energy and reducing equivalencies for TAG and isoprenoid biosynthesis based on the core carbon network created in this project. Identified one newly created strain SOM-P004 (UV-Mutagenesis), which performed better at higher culture densities than wild type in LEAPS reactors under simulated environmental conditions. Results obtained within the course of this project were used in 2017 to apply for a Community Science Program (CSP) at the DOE Joint Genome Institute (JGI). The project (JGI Proposal Id: 503423) with the Title “Comparative genomics and germ plasm diversity in Acutodesmus, a green microalgal bioenergy feedstock candidate with potential for breeding and hybridization.” was selected for CSP 2018 for sequencing of up to 30 genomes of the alga A. obliquus (=S. obliquus). Our genome of the strain DOE0152Z serves as a reference for this new CSP project. Characterization of synchronized cultures of Cyclotella cryptica and the implications on productivity. Determination that some cellular pigments respond to light, but others to the cell cycle. Characterization of productivity of C. cryptica in PNNL ponds. Genome sequence and metabolic mapping of Marinichlorella kaistiae KAS603. Demonstration that some green algae store and utilize starch in the cytoplasm. Photorespiratory pathway clarified in T. pseudonana leading to a better understanding of carbon flux pathways in diatoms. Genome sequence determination, annotation, and comparison completed for C. cryptica, identifying potential metabolic differences that lead to high biomass and lipid accumulation ability for this species. Transcriptomic comparison of silicon (Si) and nitrogen (N) limited triacylglycerol accumulation in Cyclotella cryptica.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

Single-cone finite difference scheme for the (2+1)D Dirac von Neumann equation

An explicit finite difference scheme is presented for the von Neumann equation for (2+1)D Dirac fermions. It is founded upon a staggered space–time grid which ensures a single-cone energy dispersion and performs the time-derivative in one sweep using a three-step leap-frog procedure. It enables a space–time-resolved numerical treatment of the mixed-state dynamics of Dirac fermions within the effective single-particle density matrix formalism. Energy-momentum dispersion, stability and convergence properties are derived. Elementary numerical tests to demonstrate stability properties use parameters which pertain to topological insulator surface states. A method for the simulation of charge injection from an electric contact is presented and tested numerically. Potential extensions of the scheme to a Dirac–Lindblad equation, real-space–time Green's function formulations, and higher-order finite-difference schemes are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Light-Nuclei Spectra from Chiral Dynamics

In recent years local chiral interactions have been derived and implemented in quantum Monte Carlo methods in order to test to what extent the chiral effective field theory framework impacts our knowledge of few- and many-body systems. Here in this Letter, we present Green’s function Monte Carlo calculations of light nuclei based on the family of local two-body interactions presented by our group in a previous paper in conjunction with chiral three-body interactions fitted to bound- and scattering-state observables in the three-nucleon sector. These interactions include Δ intermediate states in their two-pion-exchange components. We obtain predictions for the energy levels and level ordering of nuclei in the mass range A=4–12, accurate to ≤2% of the binding energy, in very satisfactory agreement with experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Coupled cluster Green function: Model involving single and double excitations

In this paper, we report on the development of a parallel implementation of the coupled-cluster (CC) Green function formulation (GFCC) employing single and double excitations in the cluster operator (GFCCSD). A key aspect of this work is the determination of the frequency dependent self-energy, Σ(ω). The detailed description of the underlying algorithm is provided, including approximations used that preserve the pole structure of the full GFCCSD method, thereby reducing the computational costs while maintaining an accurate character of methodology. Furthermore, for systems with strong local correlation, our formulation reveals a diagonally dominate block structure where as the non-local correlation increases, the block size increases proportionally. Here, to demonstrate the accuracy of our approach, several examples including calculations of ionization potentials for benchmark systems are presented and compared against experiment.

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

The role of cytosine methylation on charge transport through a DNA strand

Cytosine methylation has been found to play a crucial role in various biological processes, including a number of human diseases. The detection of this small modification remains challenging. In this work, we computationally explore the possibility of detecting methylated DNA strands through direct electrical conductance measurements. Using density functional theory and the Landauer-Büttiker method, we study the electronic properties and charge transport through an eight base-pair methylated DNA strand and its native counterpart. We first analyze the effect of cytosine methylation on the tight-binding parameters of two DNA strands and then model the transmission of the electrons and conductance through the strands both with and without decoherence. We find that the main difference of the tight-binding parameters between the native DNA and the methylated DNA lies in the on-site energies of (methylated) cytosine bases. The intra- and inter-strand hopping integrals between two nearest neighboring guanine base and (methylated) cytosine base also change with the addition of the methyl groups. Our calculations show that in the phase-coherent limit, the transmission of the methylated strand is close to the native strand when the energy is nearby the highest occupied molecular orbital level and larger than the native strand by 5 times in the bandgap. The trend in transmission also holds in the presence of the decoherence with the same rate. The lower conductance for the methylated strand in the experiment is suggested to be caused by the more stable structure due to the introduction of the methyl groups. We also study the role of the exchange-correlation functional and the effect of contact coupling by choosing coupling strengths ranging from weak to strong coupling limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗