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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Upstreamness and downstreamness in input–output analysis from local and aggregate information

Abstract Ranking sectors and countries within global value chains is of paramount importance to estimate risks and forecast growth in large economies. However, this task is often non-trivial due to the lack of complete and accurate information on the flows of money and goods between sectors and countries, which are encoded in input–output (I–O) tables. In this work, we show that an accurate estimation of the role played by sectors and countries in supply chain networks can be achieved without full knowledge of the I–O tables, but only relying on local and aggregate information, e.g., the total intermediate demand per sector. Our method, based on a rank-1 approximation to the I–O table, shows consistently good performance in reconstructing rankings (i.e., upstreamness and downstreamness measures for countries and sectors) when tested on empirical data from the world input–output database. Moreover, we connect the accuracy of our approximate framework with the spectral properties of the I–O tables, which ordinarily exhibit relatively large spectral gaps. Our approach provides a fast and analytically tractable framework to rank constituents of a complex economy without the need of matrix inversions and the knowledge of finer intersectorial details.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Dark Energy Survey year 3 results: covariance modelling and its impact on parameter estimation and quality of fit

ABSTRACT We describe and test the fiducial covariance matrix model for the combined two-point function analysis of the Dark Energy Survey Year 3 (DES-Y3) data set. Using a variety of new ansatzes for covariance modelling and testing, we validate the assumptions and approximations of this model. These include the assumption of Gaussian likelihood, the trispectrum contribution to the covariance, the impact of evaluating the model at a wrong set of parameters, the impact of masking and survey geometry, deviations from Poissonian shot noise, galaxy weighting schemes, and other sub-dominant effects. We find that our covariance model is robust and that its approximations have little impact on goodness of fit and parameter estimation. The largest impact on best-fitting figure-of-merit arises from the so-called fsky approximation for dealing with finite survey area, which on average increases the χ2 between maximum posterior model and measurement by $3.7{{\ \rm per\ cent}}$ (Δχ2 ≈ 18.9). Standard methods to go beyond this approximation fail for DES-Y3, but we derive an approximate scheme to deal with these features. For parameter estimation, our ignorance of the exact parameters at which to evaluate our covariance model causes the dominant effect. We find that it increases the scatter of maximum posterior values for Ωm and σ8 by about $3{{\ \rm per\ cent}}$ and for the dark energy equation-of-state parameter by about $5{{\ \rm per\ cent}}$.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The two-point correlation function covariance with fewer mocks

We present FITCOV an approach for accurate estimation of the covariance of two-point correlation functions that requires fewer mocks than the standard mock-based covariance. This can be achieved by dividing a set of mocks into jackknife regions and fitting the correction term first introduced in Mohammad & Percival (2022), such that the mean of the jackknife covariances corresponds to the one from the mocks. This extends the model beyond the shot-noise limited regime, allowing it to be used for denser samples of galaxies. We test the performance of our fitted jackknife approach, both in terms of accuracy and precision, using lognormal mocks with varying densities and approximate EZmocks mimicking the Dark Energy Spectroscopic Instrument LRG and ELG samples in the redshift range of z = [0.8, 1.1]. We find that the Mohammad–Percival correction produces a bias in the two-point correlation function covariance matrix that grows with number density and that our fitted jackknife approach does not. We also study the effect of the covariance on the uncertainty of cosmological parameters by performing a full-shape analysis. We demonstrate that our fitted jackknife approach based on 25 mocks can recover unbiased and as precise cosmological parameters as the ones obtained from a covariance matrix based on 1000 or 1500 mocks, while the Mohammad–Percival correction produces uncertainties that are twice as large.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Applications of the modified Hulthén-Kohn method for bound and scattering states

We adapt the Hulthén–Kohn method suggested by Efros [Phys. Rev. C 99, 034620 (2019)] for calculating various observables in the continuum and discrete spectrum using two-body interactions in single- and coupled channel systems. We explore the convergence of phase shifts and wave functions as well as the location of S-matrix poles which enables obtaining both resonance and bound state parameters. We find that employing a harmonic oscillator basis, together with an interaction smoothing scheme introduced by Gyarmati et al. [Nucl. Phys. A 326, 119 (1979)], and adopting approximate bound-state solutions for the short-range components of basis wave functions lead to good convergence even with restricted oscillator quanta accessible for modern no-core shell model codes. The adapted Efros method will facilitate ab initio many-body nuclear structure applications.

Nuclear reactions↗
DOE OSTI2025

Construction of approximate invariants for non-integrable Hamiltonian systems

We present a method to construct high-order polynomial approximate invariants (AI) for non integrable Hamiltonian dynamical systems, and apply it to a modern ring-based particle accelerator. Taking advantage of a special property of one-turn transformation maps in the form of a square matrix, AIs can be constructed order-by-order iteratively. Evaluating AI with simulation data, we observe that AI’s fluctuation is actually a measure of chaos. Through minimizing the fluctuations, the stable region of long-term motions, i.e., the dynamic aperture of the accelerator, could be enlarged.

43 PARTICLE ACCELERATORS↗
NASA NTRS1975

Analysis of the dynamic response of a supersonic inlet to flow-field perturbations upstream of the normal shock

A linearized mathematical analysis is presented for determining the response of normal shock position and subsonic duct pressures to flow-field perturbations upstream of the normal shock in mixed-compression supersonic inlets. The inlet duct cross-sectional area variation is approximated by constant-area sections; this approximation results in one-dimensional wave equations. A movable normal shock separates the supersonic and subsonic flow regions, and a choked exit is assumed for the inlet exit condition. The analysis leads to a closed-form matrix solution for the shock position and pressure transfer functions. Analytical frequency response results are compared with experimental data and a method of characteristics solution.

Cole, G. L.↗
NASA NTRS1990

Application of the Schwinger multichannel formulation to electron-impact excitation of the b 3Sigma(+) state of CO

The Chi 1Sigma - b 3Sigma(+) transition of CO is described using the Schwinger multichannel method in the two-state approximation, in an energy range from threshold to 20 eV. The resonance structure is analyzed by performing a partial-wave decomposition and the resonance positions are established based on the typical discontinuous behavior in the K-matrix elements as well as the pi radian change in the partial-wave eigenphases. The resonance behavior is related to the concept of core-excited resonances and the 'grandparent' model of resonances. The results are related to the formation of the negative ion by carrying out bound-state calculations on the (5 sigma)(3 s sigma)-squared core-excited Rydberg state of CO(-), and the position is found to agree well with the low-energy resonance positions.

Weatherford, Charles A.↗
NASA NTRS1997

Vertical Transport Processes for Inert and Scavenged Species: TRACE-A Measurements

The TRACE-A mission of the NASA DC-8 aircraft made a large-scale survey of the tropical and subtropical atmosphere in September and October of 1992. Both In-situ measurements of CO (G. Sachsen NASA Langley) and aerosol size (J. Browell group, NASA Langley) provide excellent data sets with which to constrain vertical transport by planetary boundary layer mixing and deep-cloud cumulus convection. Lidar profiles of aerosol-induced scattering and ozone (also by Bremen) are somewhat require more subtle interpretation as tracers, but the vertical information on layering largely compensates for these complexities. The reason this DC-8 dataset is so useful is that very large areas of biomass burning over Africa and South America provide surface sources of appropriate sizes with which to characterize vertical and horizontal motions; the major limitation of our source description is that biomass burning patterns move considerably every few days, and daily burning inventories are a matter of concurrent, intensive research. We use the Penn State / NCAR MM5 model in an assimilation mode on the synoptic and intercontinental scale, and assess the success it shows in vertical transport descriptions. We find that the general level of emissions suggested by the climatological approach (Will. Has, U. of Montana) appears to be approximately correct, possibly a bit low, for this October, 1992, time period. Vertical transport in planetary boundary layer mixing to 5.5 kin was observed and reproduced in our simulations. Furthermore we find evidence that Blackader "transilient" or matrix-transport scheme is needed, but may require some adaptation in our tracer model: CO seems to exhibit very high values at the top of the planetary boundary layer, a process that stretches the eddy-diffusion parameterization. We will report on progress in improving the deep convective transport of carbon monoxide: the Grail scheme as we used it at 100 kin resolution did not transport enough material to the upper troposphere. We expect to be able to attribute this to either parameterization reasons (inadequacy of this parameterization at the large 100km scale) or other reasons. Nevertheless, the qualitative nature of deep transport by clouds shows up well in the simulations. As for scavengable species, the simulations predict tens of micrograms per standard cubic meter of smoke aerosol in the boundary layer. In a straightforward illustration of our simple bulk-mass scavenging parameterization, to one or two micrograms per standard cubic meter of smoke aerosol in the free troposphere just above the source regions: very high concentrations for the free troposphere. We expect to report on comparisons of these predictions to a variety of observations.

Chatfield, Robert B.↗
NASA NTRS2004

Telescoping Mechanics: A New Paradigm for Composite Behavior Simulation

This report reviews the application of telescoping mechanics to composites using recursive laminate theory. The elemental scale is the fiber-matrix slice, the behavior of which propagates to laminate. The results from using applications for typical, hybrid, and smart composites and composite-enhanced reinforced concrete structures illustrate the versatility and generality of telescoping scale mechanics. Comparisons with approximate, single-cell, and two- and three-dimensional finite-element methods demonstrate the accuracy and computational effectiveness of telescoping scale mechanics for predicting complex composite behavior.

Chamis, C. C.↗
NASA NTRS2004

Failure of Non-Circular Composite Cylinders

In this study, a progressive failure analysis is used to investigate leakage in internally pressurized non-circular composite cylinders. This type of approach accounts for the localized loss of stiffness when material failure occurs at some location in a structure by degrading the local material elastic properties by a certain factor. The manner in which this degradation of material properties takes place depends on the failure modes, which are determined by the application of a failure criterion. The finite-element code STAGS, which has the capability to perform progressive failure analysis using different degradation schemes and failure criteria, is utilized to analyze laboratory scale, graphite-epoxy, elliptical cylinders with quasi-isotropic, circumferentially-stiff, and axially-stiff material orthotropies. The results are divided into two parts. The first part shows that leakage, which is assumed to develop if there is material failure in every layer at some axial and circumferential location within the cylinder, does not occur without failure of fibers. Moreover before fibers begin to fail, only matrix tensile failures, or matrix cracking, takes place, and at least one layer in all three cylinders studied remain uncracked, preventing the formation of a leakage path. That determination is corroborated by the use of different degradation schemes and various failure criteria. Among the degradation schemes investigated are the degradation of different engineering properties, the use of various degradation factors, the recursive or non-recursive degradation of the engineering properties, and the degradation of material properties using different computational approaches. The failure criteria used in the analysis include the noninteractive maximum stress criterion and the interactive Hashin and Tsai-Wu criteria. The second part of the results shows that leakage occurs due to a combination of matrix tensile and compressive, fiber tensile and compressive, and inplane shear failure modes in all three cylinders. Leakage develops after a relatively low amount of fiber damage, at about the same pressure for three material orthotropies, and at approximately the same location.

Hyer, M. W.↗
NASA NTRS2013

Improved Subcell Model for the Prediction of Braided Composite Response

In this work, the modeling of triaxially braided composites was explored through a semi-analytical discretization. Four unique subcells, each approximated by a "mosaic" stacking of unidirectional composite plies, were modeled through the use of layered-shell elements within the explicit finite element code LS-DYNA. Two subcell discretizations were investigated: a model explicitly capturing pure matrix regions, and a novel model which absorbed pure matrix pockets into neighboring tow plies. The in-plane stiffness properties of both models, computed using bottom-up micromechanics, correlated well to experimental data. The absorbed matrix model, however, was found to best capture out-of- plane flexural properties by comparing numerical simulations of the out-of-plane displacements from single-ply tension tests to experimental full field data. This strong correlation of out-of-plane characteristics supports the current modeling approach as a viable candidate for future work involving impact simulations.

Cater, Christopher R.↗
DOE OSTI2021

The response field and the saddle points of quantum mechanical path integrals

Highlights: • Moyal quantum mechanics and Marinov’s path integral. • Classical and semiclassical limits of Marinov’s path integral. • Oscillating functional integrals. • Instantons of the Marinov’s path integral. In quantum statistical mechanics, Moyal’s equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal’s equation is given by Marinov’s path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov’s integral, plays for pure states even. The discussion focuses on how the integral’s semiclassical approximation relates to its strictly classical limit; unlike for Feynman type path integrals, the latter is well defined in the Marinov case. The topics covered include a random force representation of Marinov’s integral based upon the concept of “Airy averaging”, a related discussion of positivity-violating Wigner functions describing tunneling processes, and the role of the response field in maintaining quantum coherence and enabling interference phenomena. The double slit experiment for electrons and the Bohm–Aharonov effect are analyzed as illustrative examples. Furthermore, a surprising relationship between the instantons of the Marinov path integral over an analytically continued (“Wick rotated”) response field, and the complex instantons of Feynman-type integrals is found. The latter play a prominent role in recent work towards a Picard–Lefschetz theory applicable to oscillatory path integrals and the resurgence program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2003

HRTEM and EFTEM Observations of Matrix in the Oxidized CV3 Chondrite ALH 84028: Implications for the Origins of Matrix Olivines

The determination of the nature, distribution, and origin of organic material in carbonaceous chondrites is fundamental to understanding early solar nebular conditions and the origin of life. Using a variety of extraction techniques, followed by detailed chemical analysis, an extensive suite of organic compounds has been identified in carbonaceous chondrites. These data have provided key information on the diversity and isotopic composition of the organic component in chondrites. However, one disadvantage of extraction techniques is that all information regarding the spatial distribution of the organics on a fine scale is lost. This is especially important for the insoluble macromolecular carbon, which constitutes approximately 70% of the carbon in carbonaceous chondrites such as Murchison. The distribution and mineralogical associations may provide important constraints on the possible origins of the carbonaceous material. Our previous studies of the CV3 chondrites Allende and Vigarano have demonstrated that energy filtered transmission electron microscopy (EFTEM), combined with high resolution TEM (HRTEM) are powerful tools for the in situ characterization of insoluble organic matter in carbonaceous chondrites. In this study, we have used SEM and TEM techniques to characterize the matrix mineralogy of the CV3 chondrite ALH 84028 and examine the distribution and mineralogical associations of carbon. We are especially interested in establishing whether the occurrence of poorly graphitized carbon (PGC), observed in Allende matrix olivines, is common to all oxidized CV3 chondrites or is a unique feature of Allende.

Abreu, Neyda M.↗
DOE OSTI2025

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential for specialized applications in segmented inverse beta decay (IBD) neutrino detectors, astronomy, machine learning, and more. Although this method may easily extend to 3D scalar fields, our focus here is on 2D real-valued fields as it directly applies to directionality. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Data Analysis, Statistics and Probability (physics↗
NASA NTRS2000

Directionally Solidified NiAl-Based Alloys Studied for Improved Elevated-Temperature Strength and Room-Temperature Fracture Toughness

Efforts are underway to replace superalloys used in the hot sections of gas turbine engines with materials possessing better mechanical and physical properties. Alloys based on the intermetallic NiAl have demonstrated potential; however, they generally suffer from low fracture resistance (toughness) at room temperature and from poor strength at elevated temperatures. Directional solidification of NiAl alloyed with both Cr and Mo has yielded materials with useful toughness and elevated-temperature strength values. The intermetallic alloy NiAl has been proposed as an advanced material to extend the maximum operational temperature of gas turbine engines by several hundred degrees centigrade. This intermetallic alloy displays a lower density (approximately 30-percent less) and a higher thermal conductivity (4 to 8 times greater) than conventional superalloys as well as good high-temperature oxidation resistance. Unfortunately, unalloyed NiAl has poor elevated temperature strength (approximately 50 MPa at 1027 C) and low room-temperature fracture toughness (about 5 MPa). Directionally solidified NiAl eutectic alloys are known to possess a combination of high elevated-temperature strength and good room-temperature fracture toughness. Research has demonstrated that a NiAl matrix containing a uniform distribution of very thin Cr plates alloyed with Mo possessed both increased fracture toughness and elevated-temperature creep strength. Although attractive properties were obtained, these alloys were formed at low growth rates (greater than 19 mm/hr), which are considered to be economically unviable. Hence, an investigation was warranted of the strength and toughness behavior of NiAl-(Cr,Mo) directionally solidified at faster growth rates. If the mechanical properties did not deteriorate with increased growth rates, directional solidification could offer an economical means to produce NiAl-based alloys commercially for gas turbine engines. An investigation at the NASA Glenn Research Center at Lewis Field was undertaken to study the effect of the directional solidification growth rate on the microstructure, room temperature fracture toughness, and strength at 1027 C of a Ni-33Al-31Cr-3Mo eutectic alloy. The directionally solidified rates varied between 7.6 and 508 millimeters per hour Essentially fault-free, alternating (Cr, Mo)/NiAl lamellar plate microstructures (left photograph) were formed during growth at and below 12.7 mm/hr, whereas cellular microstructures (right photograph) with the (Cr, Mo) phase in a radial spokelike pattern were developed at faster growth rates. The compressive strength at 1027 C continuously increased with increasing growth rate and did not indicate a maxima as was reported for directionally solidified Ni-33Al-34Cr. Surprisingly, samples with the lamellar plate microstructure (left photograph) possessed a room-temperature fracture toughness of approximately 12 MPa(sup square root of m), whereas all the alloys with a cellular microstructure had a toughness of about 17 MPa(sup square root of m). These results are significant since they clearly demonstrate that Ni-33Al-31Cr-3Mo can be directionally solidified at much faster growth rates without any observable deterioration in its mechanical properties. Thus, the potential to produce strong, tough NiAl-based eutectics at commercially acceptable growth rates exists. Additional testing and alloy optimization studies are underway.

Whittenberger, J. Daniel↗
DOE OSTI2022

Self-consistency in GWΓ formalism leading to quasiparticle-quasiparticle couplings

Within many-body perturbation theory, Hedin's formalism offers a systematic way to iteratively compute the self-energy Σ of any dynamically correlated interacting system, provided one can evaluate the interaction vertex Γ exactly. This is, however, impossible, in general, for it involves the functional derivative of Σ with respect to the Green's function. Here, we analyze the structure of this derivative, splitting it into four contributions and outlining the type of quasiparticle interactions that each of them generate. Moreover, we show how, in the implementation of self-consistency, the action of these contributions can be classified into two: A quantitative renormalization of previously included interaction terms and the inclusion of qualitatively distinct interaction terms through successive functional derivatives of Γ itself. Implementing this latter type of self-consistency can extend the validity of perturbative approximations based on Hedin's equations toward the high interaction limit, as we show in the example of the Hubbard dimer. Furthermore, our analysis also provides a unifying perspective on the perturbation theory landscape, showing how the T-matrix approach is completely contained in Hedin's formalism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations

In this work, we present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\mathcal{O}(N\log^2 N)$ computation and $\mathcal{O}(N)$ memory complexity when applied to an $N\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

Rapid methods for calculating radiation transport in the entry environment

A procedure is developed for the prediction of radiation transport events in the context of the entry heating environment. The equivalent-width and exponential approximations are employed to reduce the computational requirements of the governing equations. Novel features are introduced in the use of an Elsasser band model to estimate line overlapping events and in the formulation of the wall reflection events. A matrix of calculations is presented to allow an assessment of the trade-offs between accuracy and computational efforts. It is concluded that the equivalent width model allows significant savings in computational effort with only modest penalties in accuracy. Consequently, the model should be viewed as an attractive candidate for use in radiation-coupled flow field prediction procedures.

Nicolet, W. E.↗