On P- and S-functions and related classes of n-dimensional nonlinear mappings
Analysis of n-dimensional nonlinear mappings representative of P and S functions
More, J. J.↗
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Rapid Identification of Synthetic Routes to Functional Metastable Phases Using X-ray Probed Laser Anneal Mapping (XPLAM) Time-Temperature Quench Maps
Many material systems have known or predicted functional phases that are metastable at standard temperature and pressure. While substantial advances have been made in the high-throughput and combinatorial synthesis of materials with a range of stoichiometries, investigation of thermal processing remains largely the domain of iterative uniform anneals or static gradients. Here we develop X-ray probed laser anneal mapping (XPLAM), a high throughput technique coupling spatially resolved X-ray diffraction with microsecond to millisecond laser gradient anneals to produce temperature–dwell–transformation (TDT) diagrams of the phase as a function of quench time and temperature. In addition to showing regimes where specific metastable phases form preferentially, TDT diagrams provide insight into the submillisecond kinetics of solid–solid phase transitions. This is a unique tool for mapping reaction pathways for metastable phases. As a first demonstration of XPLAM, we study Bi2O3, which has a rich set of polytypes, including the d-phase with an exceptionally high oxygen ion conductivity. We demonstrate the first annealing-driven synthesis of room temperature d-Bi2O3. We expect XPLAM to prove a powerful technique for rapid identification of synthetic routes to metastable phases and to generate the exhaustive data sets required for machine learning-guided exploration of materials processing.
36 MATERIALS SCIENCE↗
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↗
Bifurcation diagram and the discriminant of a spectral curve of integrable systems on Lie algebras
A bifurcation diagram is a stratified (in general, nonclosed) set and is one of the efficient tools of studying the topology of the Liouville foliation. In the framework of the present paper, the coincidence of the closure of a bifurcation diagram {Sigma}-bar of the moment map defined by functions obtained by the method of argument shift with the closure of the discriminant D-bar{sub z} of a spectral curve is proved for the Lie algebras sl(n+1), sp(2n), so(2n+1), and g{sub 2}. Moreover, it is proved that these sets are distinct for the Lie algebra so(2n). Bibliography: 22 titles.
97 MATHEMATICS AND COMPUTING↗
Asymmetric neighborhood functions accelerate ordering process of self-organizing maps
A self-organizing map (SOM) algorithm can generate a topographic map from a high-dimensional stimulus space to a low-dimensional array of units. Because a topographic map preserves neighborhood relationships between the stimuli, the SOM can be applied to certain types of information processing such as data visualization. During the learning process, however, topological defects frequently emerge in the map. The presence of defects tends to drastically slow down the formation of a globally ordered topographic map. To remove such topological defects, it has been reported that an asymmetric neighborhood function is effective, but only in the simple case of mapping one-dimensional stimuli to a chain of units. In this paper, we demonstrate that even when high-dimensional stimuli are used, the asymmetric neighborhood function is effective for both artificial and real-world data. Our results suggest that applying the asymmetric neighborhood function to the SOM algorithm improves the reliability of the algorithm. In addition, it enables processing of complicated, high-dimensional data by using this algorithm.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Nonanalytic function generation routines for 16-bit microprocessors
Interpolation techniques for three types (univariate, bivariate, and map) of nonanalytic functions are described. These interpolation techniques are then implemented in scaled fraction arithmetic on a representative 16 bit microprocessor. A FORTRAN program is described that facilitates the scaling, documentation, and organization of data for use by these routines. Listings of all these programs are included in an appendix.
Soeder, J. F.↗
Structures and magnetic properties of Co-Zr-B magnets studied by first-principles calculations
The structures and magnetic properties of Co-Zr-B alloys near the composition of Co{sub 5}Zr with B at. % ≤6% were studied using adaptive genetic algorithm and first-principles calculations. The energy and magnetic moment contour maps as a function of chemical composition were constructed for the Co-Zr-B magnet alloys through extensive structure searches and calculations. We found that Co-Zr-B system exhibits the same structure motif as the “Co{sub 11}Zr{sub 2}” polymorphs, and such motif plays a key role in achieving strong magnetic anisotropy. Boron atoms were found to be able to substitute cobalt atoms or occupy the “interruption” sites. First-principles calculations showed that the magnetocrystalline anisotropy energies of the boron-doped alloys are close to that of the high-temperature rhombohedral Co{sub 5}Zr phase and larger than that of the low-temperature Co{sub 5.25}Zr phase. Our calculations provide useful guidelines for further experimental optimization of the magnetic performances of these alloys.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Integrating very-high-resolution UAS data and airborne imaging spectroscopy to map the fractional composition of Arctic plant functional types in Western Alaska
Widespread changes in vegetation cover and composition are driving strong impacts on Arctic ecosystem functioning and global climate feedbacks. An accurate characterization of tundra vegetation composition is required to understand how the Arctic will respond to future climate change. However, quantifying tundra vegetation composition over large areas is challenging as commonly-used satellite observations are too coarse, spatially and spectrally, to differentiate low-lying tundra vegetation types. Recent airborne and spaceborne imaging spectroscopy platforms provide better data to characterize vegetation composition. Yet, our ability to characterize vegetation composition with imaging spectroscopy remains largely unexplored in the Arctic, particularly due to a lack of ground observations needed to train and test classification models. To address this problem, we collected very-high-resolution (VHR, ~5 cm) unoccupied aerial system (UAS) imagery at three low-Arctic tundra sites located on the Seward Peninsula, western Alaska. In this paper, we examine the feasibility of integrating imagery from the UAS and the hyperspectral Airborne Visible/Infrared Imaging Spectrometer, Next Generation (AVIRIS-NG) airborne instrument to map the fractional composition of 12 key Arctic plant functional types (PFTs). To this end, we first mapped the 12 PFTs from our VHR UAS imagery using random forest classification. We then used these UAS-derived PFT maps as ground truth to develop partial least squares regression (PLSR) models to predict the fractional cover (FCover) of each PFT from AVIRIS-NG imagery. Further, we evaluated the performance of our PLSR models using reserved UAS samples, as well as by mapping PFT FCover and dominant PFT for large tundra landscapes. Our results show that 1) Arctic PFTs can be effectively mapped using VHR UAS imagery, with overall accuracy between 86% and 92%, 2) when the UAS mapped PFTs were used to inform PLSR scaling models, the FCover of the 12 PFTs could be effectively estimated from AVIRIS-NG imagery with a mean absolute error (MAE) <0.13, and 3) our PLSR models outperformed traditional, fully constrained least-squares (FCLS) linear mixture analysis and produced high-quality, spatially contiguous PFT FCover and PFT maps that captured vegetation spatial patterns with similar accuracy to those developed from UAS imagery. The developed PLSR models have the potential to be broadly applied for quantifying vegetation composition with AVIRIS-NG images to help monitor tundra vegetation dynamics and improve process-based modeling of tundra ecosystems.
54 ENVIRONMENTAL SCIENCES↗
THE GINI COEFFICIENT AS A MORPHOLOGICAL MEASUREMENT OF STRONGLY LENSED GALAXIES IN THE IMAGE PLANE
Characterization of the morphology of strongly lensed galaxies is challenging because images of such galaxies are typically highly distorted. Lens modeling and source plane reconstruction is one approach that can provide reasonably undistorted images from which morphological measurements can be made, though at the expense of a highly spatially variable telescope point-spread function (PSF) when mapped back to the source plane. Unfortunately, modeling the lensing mass is a time- and resource-intensive process, and in many cases there are too few constraints to precisely model the lensing mass. If, however, useful morphological measurements could be made in the image plane rather than the source plane, it would bypass this issue and obviate the need for a source reconstruction process for some applications. We examine the use of the Gini coefficient as one such measurement. Because it depends on the cumulative distribution of the light of a galaxy, but not the relative spatial positions, the fact that surface brightness is conserved by lensing means that the Gini coefficient may be well preserved by strong gravitational lensing. Through simulations, we test the extent to which the Gini coefficient is conserved, including by effects due to PSF convolution and pixelization, to determine whether it is invariant enough under lensing to be used as a measurement of galaxy morphology that can be made in the image plane.
79 ASTRONOMY AND ASTROPHYSICS↗
How Snow Aggregate Ellipsoid Shape and Orientation Variability Affects Fall Speed and Self-Aggregation Rates
Snow aggregate shapes and orientations have long been known to exhibit substantial variability. Despite this observed variability, most weather and climate prediction models use fixed power-law functions that deterministically map particle size to mass and fall speed. As such, integrated quantities like precipitation and self-aggregation rates currently ignore nonlinear effects resulting from variation in shape and orientation for aggregates of the same size. This study therefore develops an analytic framework that couples an empirically based bivariate distribution of ellipsoid shapes to classical hydrodynamic theory so as to capture an appropriate dispersion of masses, projected areas, and fall speeds for an assumed size distribution. For a fixed aggregate size, shape variations produce approximately ±0.13 m s -1 standard deviation of fall speed which increases the mass flux fall speed dispersion by more than 100% over traditional microphysics models. This increased fall speed dispersion results predominantly from shape-induced mass dispersion whereas orientation and drag dispersion play a lesser role. Shape variations can increase mass- and reflectivity-weighted fall speeds by up to 60% of traditional models whereas self-aggregation rates can increase by a factor of 100 for very small slope parameters. This implies that aggregate shape variations effectively forestall the theorized onset of fall speed distribution narrowing and subsequent quenching of the aggregation process. As a result, it is likely that secondary ice formation is necessary to prevent an ever decreasing slope parameter. The mathematical theory presented in this study is used to develop simple correction factors for snow forecast and climate models.
54 ENVIRONMENTAL SCIENCES↗
Matching Crystal Structures Atom-to-Atom
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions and developing models for interface and grain boundary structures. Here, we formulate the matching of crystals as an optimization problem where the goal is to find the alignment and the atom-to-atom map that minimize a given cost function such as the Euclidean distance between the atoms. We construct an algorithm that directly solves this problem for large finite portions of the crystals and retrieves the periodicity of the match subsequently. We demonstrate its capacity to describe transformation pathways between known polymorphs and to reproduce experimentally realized structures of semi-coherent interfaces. Additionally, from our findings, we define a rigorous metric for measuring distances between crystal structures that can be used to properly quantify their geometric (Euclidean) closeness.
36 MATERIALS SCIENCE↗
VLA observations of impulsive solar flares at 4.9 GHz
A series of snapshot synthesis maps constructed as a function of time provided a complete mapping of source structure in one dimension and absolute location in two dimensions of five impulsive solar microwave bursts observed during July 15-18, 1978. It was found that all five flares were dominated by a single 12-18 arcsec source located between the H-alpha kernels, near the magnetic neutral line. Spectral data from Sagamore Hill (1.4-35 GHz) show that the spectral turnover at low frequencies results from the absorption by the ambient active region; these results, together with the observed magnetic configuration, suggest a model which could explain the evolution in source structure at 4.9 GHz in terms of magnetic reconnection which starts below the optical depth of the ambient active region equal to 1.
Marsh, K. A.↗
A quantitative comparison of simultaneous BOLD fMRI and NIRS recordings during functional brain activation
Near-infrared spectroscopy (NIRS) has been used to noninvasively monitor adult human brain function in a wide variety of tasks. While rough spatial correspondences with maps generated from functional magnetic resonance imaging (fMRI) have been found in such experiments, the amplitude correspondences between the two recording modalities have not been fully characterized. To do so, we simultaneously acquired NIRS and blood-oxygenation level-dependent (BOLD) fMRI data and compared Delta(1/BOLD) (approximately R(2)(*)) to changes in oxyhemoglobin, deoxyhemoglobin, and total hemoglobin concentrations derived from the NIRS data from subjects performing a simple motor task. We expected the correlation with deoxyhemoglobin to be strongest, due to the causal relation between changes in deoxyhemoglobin concentrations and BOLD signal. Instead we found highly variable correlations, suggesting the need to account for individual subject differences in our NIRS calculations. We argue that the variability resulted from systematic errors associated with each of the signals, including: (1) partial volume errors due to focal concentration changes, (2) wavelength dependence of this partial volume effect, (3) tissue model errors, and (4) possible spatial incongruence between oxy- and deoxyhemoglobin concentration changes. After such effects were accounted for, strong correlations were found between fMRI changes and all optical measures, with oxyhemoglobin providing the strongest correlation. Importantly, this finding held even when including scalp, skull, and inactive brain tissue in the average BOLD signal. This may reflect, at least in part, the superior contrast-to-noise ratio for oxyhemoglobin relative to deoxyhemoglobin (from optical measurements), rather than physiology related to BOLD signal interpretation.
Non-NASA Center↗
Force Matching Approaches to Extend Density Functional Theory to Large Time and Length Scales
We present methods for the creation of semi-empirical quantum approaches and reactive force fields through force matching to quantum simulation data for materials under reactive conditions. Our methodologies overcome the extreme computational cost of standard Kohn-Sham Density Functional Theory (DFT) by mapping DFT computed simulation data onto functional forms with linear dependence on their parameters. This allows for quick parameterization of our models by avoiding the non-linear fitting bottlenecks associated with most molecular dynamics model development. We illustrate our approach with two different systems: (i) determination of density functional tight binding models for aqueous glycine dimerization, and (ii) determination of the Chebyshev Interactional Model for Efficient Simulation (ChIMES) reactive force field for metallic liquid carbon. In each case, we observe that our approach is easy to parametrize and yields a model that is orders of magnitude faster than DFT while largely retaining its accuracy. Overall, our methods have potential use for studying complex long time and length scale chemical reactivity at extreme conditions, where there is a significant need for computationally efficient atomistic simulations methods to aid in the interpretation and design of experiments.
Lindsey, R.↗
Stronger field-emission science via coupling novel nanoscale imaging techniques
We implemented a vacuum field emission electron microscope (FEM) using the electron optics of a low-energy /photoemission electron microscope (LEEM/PEEM). Historically, there have been other FEM hardware platforms, and the distinctive feature of our method is that it integrates with the LEEM/PEEM and associated techniques, enabling a powerful multi-capability toolset for studying fundamental materials properties underpinning field emission (FE) and vacuum arc initiation. Typically, LEEM is used to image surface structure, which influences both work function and electric field distribution near a surface, while PEEM is used to map photoelectric work function across a surface. Our FEM adds the capability for spatially-correlated coincident-site measurements of FE currents to go-along with structure and work function. LEEM, PEEM, and our FEM implementation achieve nanoscale spatial resolution relevant for materials studies in nanoscience/engineering. Our approach requires a straightforward calibration of the electron optics to enable focused FEM imaging under intentional electric field variation. We demonstrate the FEM approach by imaging field emitter arrays relevant for vacuum nanoelectronics. We demonstrate submicron spatial resolution and dynamic measurement of FE versus applied electric field. We anticipate this capability will enable fundamental structure-function studies of FE and arc initiation.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
SU-F-SPS-06: Implementation of a Back-Projection Algorithm for 2D in Vivo Dosimetry with An EPID System
Purpose: To implement a back-projection algorithm for 2D dose reconstructions for in vivo dosimetry in radiation therapy using an Electronic Portal Imaging Device (EPID) based on amorphous silicon. Methods: An EPID system was used to calculate dose-response function, pixel sensitivity map, exponential scatter kernels and beam hardenig correction for the back-projection algorithm. All measurements were done with a 6 MV beam. A 2D dose reconstruction for an irradiated water phantom (30×30×30 cm{sup 3}) was done to verify the algorithm implementation. Gamma index evaluation between the 2D reconstructed dose and the calculated with a treatment planning system (TPS) was done. Results: A linear fit was found for the dose-response function. The pixel sensitivity map has a radial symmetry and was calculated with a profile of the pixel sensitivity variation. The parameters for the scatter kernels were determined only for a 6 MV beam. The primary dose was estimated applying the scatter kernel within EPID and scatter kernel within the patient. The beam hardening coefficient is σBH= 3.788×10{sup −4} cm{sup 2} and the effective linear attenuation coefficient is µAC= 0.06084 cm{sup −1}. The 95% of points evaluated had γ values not longer than the unity, with gamma criteria of ΔD = 3% and Δd = 3 mm, and within the 50% isodose surface. Conclusion: The use of EPID systems proved to be a fast tool for in vivo dosimetry, but the implementation is more complex that the elaborated for pre-treatment dose verification, therefore, a simplest method must be investigated. The accuracy of this method should be improved modifying the algorithm in order to compare lower isodose curves.
60 APPLIED LIFE SCIENCES↗
NASA’s NextGen Remote Sensing Instruments Have Arrived: Data Products For Studying Disease Vectors
Remote sensing can be used to measure, evaluate or estimate both the environment (state functions) and interfaces (processfunctions) defining vector habitats. The products of remote sensing can be integrated directly into the epidemiological equationsto significantly enhance our understanding of disease vector’s life cycles and habitats. The next generation of NASA’s remotesensing instruments which have become recently operational will provide a significant enhancement in our ability to studydisease vector’s life cycles and habitats. These instruments are on the International Space Station (ISS) and includeECOSTRESS, DESIS, and GEDI. ECOSTRESS is a 5 channel, thermal IR instrument with 70 m resolution and approximately1-5 day repeat cycle of day/night pairs. DESIS jointly developed by German Aerospace Center and Teledyne Brown Engineeringis a hyperspectral sensor system of 235 channels and 30 m resolution. DESIS data is only being acquired on demand. GEDI is ahigh-resolution laser ranger used for observing Earth’s forests and topography. NASA’s current ISS instrument configuration provides measurements of the critical environmental measures of environmentalstate functions important to vector & disease life cycles. Remote sensing data provide a spatial context and time series oflandscape scale process functions represented by land use mapping and measurements of ecological functions. Global publichealth is entering a new information age through the use of spatial models of disease vector/host ecologies driven by the use ofremotely sensed data to measure environmental and structural factors critical in determining disease vector habitats. In 2018, NASA initiated a new study for the Surface Biology and Geology (SBG) Designated Observable, identified in the 2018National Academies’ Decadal Survey entitled, “Thriving on Our Changing Planet: A Decadal Strategy for Earth Observationfrom Space.” (https://www.nap.edu/catalog/24938/thriving-on-our-changing-planet-a-decadal-strategy-for-earth) . The SBG isplanned to collect global remote sensing measurements using a hyperspectral spectrometer and multispectral thermal data. Thesedata sets will provide a significant enhancement in our ability to study disease vector’s life cycles and habitats globally. The 3sensors on the ISS provide precursor data to prepare the community for the application of future SBG data toward diseasestudies.
Disease Vectors↗
An Active Subspace Method for Accelerating Convergence in Delaunay-Based Optimization via Dimension Reduction
Delaunay-based derivative-free optimization, ∆DOGS, is an efficient and provably-convergent global optimization method for the problems which has computationally expensive objection function and the analytical expression for the objective function is not available. ∆-DOGS is a novel optimization scheme in the family of response surface methods (RSMs); however, it suffers from the curse of dimensionality since the computational cost increases dramatically as the number of design parameters increases. As a result, the number of design parameters in ∆-DOGS algorithm is relatively low (n.10). To avoid such problems, this paper proposes a combination of derivative-free optimization, seeking the global minimizer of an expensive and nonconvex objective function f(x) and active subspace method, detecting the directions of the most variability using evaluations of the gradient. The contribution of other directions to the objective function is bounded by a sufficiently small constant. This new algorithm iteratively applied Delaunay-based derivative-free optimization to seek the minimizer on the d-dimensional active subspace that has most function variation. Inverse mapping is needed to project data from active subspace to full-model for evaluating function values. This task is overcome by solving an inequality constrained problem that curves the response surface of the objective function. The test results show that this strategy is effective on a handful of optimization problems.
Bewley, Thomas R.↗