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At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Goal-Oriented Optimal Approximations of Bayesian Linear Inverse Problems

We propose optimal dimensionality reduction techniques for the solution of goal-oriented linear-Gaussian inverse problems, where the quantity of interest (QoI) is a function of the inversion parameters. These approximations are suitable for large-scale applications. In particular, we study the approximation of the posterior covariance of the QoI as a low-rank negative update of its prior covariance and prove optimality of this update with respect to the natural geodesic distance on the manifold of symmetric positive definite matrices. Assuming exact knowledge of the posterior mean of the QoI, the optimality results extend to optimality in distribution with respect to the Kullback--Leibler divergence and the Hellinger distance between the associated distributions. We also propose the approximation of the posterior mean of the QoI as a low-rank linear function of the data and prove optimality of this approximation with respect to a weighted Bayes risk. Both of these optimal approximations avoid the explicit computation of the full posterior distribution of the parameters and instead focus on directions that are well informed by the data and relevant to the QoI. These directions stem from a balance among all the components of the goal-oriented inverse problem: prior information, forward model, measurement noise, and ultimate goals. We illustrate the theory using a high-dimensional inverse problem in heat transfer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Deep Learning without Global Optimization by Random Fourier Neural Networks

Here we introduce a new training algorithm for deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov chain Monte Carlo sampling procedure to iteratively train network layers, avoiding global and gradient-based optimization while maintaining error control. It consistently attains the theoretical approximation rate for residual networks with complex exponential activation functions, determined by network complexity. Additionally, it enables efficient learning of multiscale and high-frequency features, producing interpretable parameter distributions. Despite using sinusoidal basis functions, we do not observe Gibbs phenomena in approximating discontinuous target functions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2011

The Evolution of Ly-alpha Emitting Galaxies Between z = 2.1 and z = 3.l

We describe the results of a new, wide-field survey for z= 3.1 Ly-alpha emission-line galaxies (LAEs) in the Extended Chandra Deep Field South (ECDF-S). By using a nearly top-hat 5010 Angstrom filter and complementary broadband photometry from the MUSYC survey, we identify a complete sample of 141 objects with monochromatic fluxes brighter than 2.4E-17 ergs/cm^2/s and observers-frame equivalent widths greater than ~ 80 Angstroms (i.e., 20 Angstroms in the rest-frame of Ly-alpha). The bright-end of this dataset is dominated by x-ray sources and foreground objects with GALEX detections, but when these interlopers are removed, we are still left with a sample of 130 LAE candidates, 39 of which have spectroscopic confirmations. This sample overlaps the set of objects found in an earlier ECDF-S survey, but due to our filter's redder bandpass, it also includes 68 previously uncataloged sources. We confirm earlier measurements of the z=3.1 LAE emission-line luminosity function, and show that an apparent anti-correlation between equivalent width and continuum brightness is likely due to the effect of correlated errors in our heteroskedastic dataset. Finally, we compare the properties of z=3.1 LAEs to LAEs found at z=2.1. We show that in the approximately 1 Gyr after z approximately 3, the LAE luminosity function evolved significantly, with L * fading by approximately 0.4 mag, the number density of sources with L greater than 1.5E42 ergs/s declining by approximately 50%, and the equivalent width scalelength contracting from 70^{+7}_{-5} Angstroms to 50^{+9}_{-6} Angstroms. When combined with literature results, our observations demonstrate that over the redshift range z approximately 0 to z approximately 4, LAEs contain less than approximately 10% of the star-formation rate density of the universe.

Ciardullo, Robin↗
DOE OSTI2015

A comparative density functional study on electrical properties of layered penta-graphene

We present a comparative study of the influence of the number of layers, the biaxial strain in the range of −3% to 3%, and the stacking misalignments on the electronic properties of a new 2D carbon allotrope, penta-graphene (PG), based on hybrid-functional method within the density functional theory (DFT). In comparison with local exchange-correlation approximation in the DFT, the hybrid-functional provides an accurate description on the degree of p{sub z} orbitals localization and bandgap. Importantly, the predicted bandgap of few-layer PG has a weak layer dependence. The bandgap of monolayer PG is 3.27 eV, approximately equal to those of GaN and ZnO; and the bandgap of few-layer PG decreases slowly with the number of layers (N) and converge to 2.57 eV when N ≥ 4. Our calculations using HSE06 functional on few-layer PG reveal that bandgap engineering by stacking misalignment can further tune the bandgap down to 1.37 eV. Importantly, there is no direct-to-indirect bandgap transition in PG by varying strain, layer number, and stacking misalignment. Owing to its tunable, robustly direct, and wide bandgap characteristics, few-layer PG is promising for optoelectronic and photovoltaic applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Design of Distributed Controllers Seeking Optimal Power Flow Solutions Under Communication Constraints

This paper focuses on power distribution networks featuring inverter-interfaced distributed energy resources (DERs), and develops feedback controllers that drive the DER output powers to solutions of time-varying AC optimal power flow (OPF) problems. Control synthesis is grounded on primal-dual-type methods for regularized Lagrangian functions, as well as linear approximations of the AC power-flow equations. Convergence and OPF-solution-tracking capabilities are established while acknowledging: i) communication-packet losses, and ii) partial updates of control signals. The latter case is particularly relevant since it enables asynchronous operation of the controllers where DER setpoints are updated at a fast time scale based on local voltage measurements, and information on the network state is utilized if and when available, based on communication constraints. As an application, the paper considers distribution systems with high photovoltaic integration, and demonstrates that the proposed framework provides fast voltage-regulation capabilities, while enabling the near real-time pursuit of solutions of AC OPF problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Intensity Distribution of the Three-Wave Diffraction from Dislocation Epitaxial Layers in the Reciprocal Space

The three-wave X-ray diffraction in strongly disordered epitaxial layers of GaN and ZnO is experimentally investigated. The charts of the intensity distribution in the reciprocal space are plotted in coordinates q{sub θ} and q{sub ϕ} for the most intensive three-wave combination (1010)/(1011) by means of subsequent θ- and ϕ-scanning. A nontrivial shape of the θ-sections of these contours at a distance from the ϕ center of reflection is revealed; it is different for different samples. For the θ-curves at the center of reflection, we observed a common peak that may be approximated by the Voigt function with a power-low decrease in the intensity at the wings; the decrease law (from–4.5 to–5.0) is found to be considerably greater than that for the similar curves of two-wave diffraction and not depending on the dislocation density and distribution in layers. In some films we observed a coarse-block structure; in addition, it follows from the distribution in the reciprocal space that these blocks are turned with respect to each other around a normal to the surface, which allows us to suggest the existence of low-angle boundaries between them, consisting exclusively of edge dislocations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Quinone 1 e – and 2 e – /2 H + Reduction Potentials: Identification and Analysis of Deviations from Systematic Scaling Relationships

Quinones participate in diverse electron transfer and proton-coupled electron transfer processes in chemistry and biology. To understand the relationship between these redox processes, an experimental study was carried out to probe the 1 e – and 2 e – /2 H + reduction potentials of a number of common quinones. The results reveal a non-linear correlation between the 1 e – and 2 e – /2 H + reduction potentials. This unexpected observation prompted a computational study of 134 different quinones, probing their 1 e – reduction potentials, p K a values, and 2 e – /2 H + reduction potentials. We report the density functional theory calculations reveal an approximately linear correlation between these three properties and an effective Hammett constant associated with the quinone substituent(s). However, deviations from this linear scaling relationship are evident for quinones that feature intramolecular hydrogen bonding, halogen substituents, charged substituents, and/or sterically bulky substituents. These results, particularly the different substituent effects on the 1 e – versus 2 e – /2 H + reduction potentials, have important implications for designing quinones with tailored redox properties.

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

Exploring the Random Phase Approximately for materials chemistry and physics

This proposal focuses on improved accuracy for the delicate energy differences of interest in materials chemistry with the fully nonlocal random phase approximation (RPA) in a density functional context. Could RPA or RPA-like approaches become standard methods of first-principles electronic-structure calculation for atoms, molecules, solids, surfaces, and nano-structures? Direct RPA includes the full exact exchange energy and a nonlocal correlation energy from the occupied and unoccupied Kohn-Sham orbitals and orbital energies, with an approximate but universal description of long-range van der Waals attraction. RPA also improves upon simple pair-wise interaction potentials or vdW density functional theory. This improvement is essential to capture accurate energy differences in metals and different phases of semiconductors. The applications in this proposal are challenges for the simpler approximations of Kohn-Sham density functional theory, which are part of the current “standard model” for quantum chemistry and condensed matter physics. Within this project we already applied RPA on different structural phase transitions on semiconductors, metals and molecules. Although RPA predicts accurate structural parameters, RPA has proven not equally accurate in all kinds of structural phase transitions. Therefore a correction to RPA can be necessary in many cases. We are currently implementing and testing a nonempirical, spatially nonlocal, frequency-dependent model for the exchange-correlation kernel in the adiabatic-connection fluctuation-dissipation context. This kernel predicts a nearly-exact correlation energy for the electron gas of uniform density. If RPA or RPA-like approaches prove to be reliably accurate, then expected increases in computer power may make them standard in the electronic-structure calculations of the future.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Generation, dynamics, and correlations of the fission fragments' angular momenta

The generation of angular momentum in fissioning nuclei is not well understood. The predictions of different models disagree, particularly concerning the correlation between the fragments' angular momenta. In this article, a time-dependent collective Hamiltonian model is proposed to treat the generation of the angular momentum in the fission fragments due to the quantum uncertainty principle as well as the dynamics of the collective wave function during and after scission. The model is constructed in the framework of the frozen Hartree-Fock approximation using a Skyrme energy functional to extract deformations of the fission fragments as well as the interactions in a derived collective Hamiltonian. The fission reactions studied are $^{240}$Pu $\rightarrow$ $^{132}$Sn+$^{108}$Ru and $^{240}$Pu $\rightarrow$ $^{144}$Ba+$^{96}$Sr. The model can account for a large part of the angular momentum found in experimental data. The orientation of the angular momentum of each fragment is found to be mainly in the plane perpendicular to the fission axis, in agreement with the experiment. The magnitudes of the angular momenta in the two fragments are nearly uncorrelated, in agreement with the recent experimental data of Wilson et al., Nature (London) 590, 566 (2021). Some of the conclusions of the traditional collective vibration model are supported by the present model but some are not. Surprisingly, it is found that the angular momenta of the fragments are slightly correlated positively as in a wriggling mode. As a result, it is also found that the presence of an octupole deformation in a fragment can significantly increase the generated angular momentum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1992

Inference in infinite-dimensional inverse problems - Discretization and duality

Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.

Stark, Philip B.↗
DOE OSTI2017

Robust Cross-correlation-based Measurement of Clump Sizes in Galaxies

Stars form in molecular complexes that are visible as giant clouds (∼10{sup 5−6} M{sub ⊙}) in nearby galaxies and as giant clumps (∼10{sup 8−9} M{sub ⊙}) in galaxies at redshifts z≈1–3. Theoretical inferences on the origin and evolution of these complexes often require robust measurements of their characteristic size, which is hard to measure at limited resolution and often ill-defined due to overlap and quasi-fractal substructure. We show that maximum and luminosity-weighted sizes of clumps seen in star formation maps (e.g., Hα) can be recovered statistically using the two-point correlation function (2PCF) if an approximate stellar surface density map is taken as the normalizing random field. After clarifying the link between Gaussian clumps and the 2PCF analytically, we design a method for measuring the diameters of Gaussian clumps with realistic quasi-fractal substructure. This method is tested using mock images of clumpy disk galaxies at different spatial resolutions and perturbed by Gaussian white noise. We find that the 2PCF can recover the input clump scale at ∼20% accuracy, as long as this scale is larger than the spatial resolution. We apply this method to the local spiral galaxy NGC 5194, as well as to three clumpy turbulent galaxies from the DYNAMO-HST sample. In both cases, our statistical measurements of Hα clump size agree with previous measurements and with the estimated Jeans lengths. However, the new measurements are free from subjective choices when fitting individual clumps.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1997

Nonguiding Center Motion and Substorm Effects in the Magnetotail

Thick and thin models of the middle magnetotail were developed using a consistent orbit tracing technique. It was found that currents carried near the equator by groups of ions with anisotropic distribution functions are not well approximated by the guiding center expressions. The guiding center equations fail primarily because the calculated pressure tensor is not magnetic field aligned. The pressure tensor becomes field aligned as one moves away from the equator, but here there is a small region in which the guiding center equations remain inadequate because the two perpendicular components of the pressure tensor are unequal. The significance of nonguiding center motion to substorm processes then was examined. One mechanism that may disrupt a thin cross-tail current sheet involves field changes that cause ions to begin following chaotic orbits. The lowest-altitude chaotic region, characterized by an adiabaticity parameter kappa approx. equal to 0.8, is especially important. The average cross-tail particle drift is slow, and we were unable to generate a thin current sheet using such ions. Therefore, any process that tends to create a thin current sheet in a region with kappa approaching 0.8 may cause the cross-tail current to get so low that it becomes insufficient to support the lobes. A different limit may be important in resonant orbit regions of a thin current sheet because particles reach a maximum cross-tail drift velocity. If the number of ions per unit length decreases as the tail is stretched, this part of the plasma sheet also may become unable to carry the cross-tail current needed to support the lobes. Thin sheets are needed for both resonant and chaotic orbit mechanisms because the distribution function must be highly structured. A description of current continuity is included to show how field aligned currents can evolve during the transition from a two-dimensional (2-D) to a 3-D configuration.

Kaufmann, Richard L.↗
DOE OSTI2018

A Fast All-sky Radiation Model for Solar applications with Narrowband Irradiances on Tilted surfaces (FARMS-NIT): Part I. The clear-sky model

The solar energy industry often uses individual steps to empirically compute plane-of-array (POA) irradiance from horizontal irradiance and decompose it to narrow-wavelength bands. Conventional radiative transfer models designed for meteorological applications requires significant computing efforts in practice; however, they provide a physics-based solution of radiance and therefore are capable of computing spectral POA irradiances in a single step. In this study, we integrate the advantages of the current models and develop an innovative radiative transfer model, the Fast All-sky Radiation Model for Solar applications with Narrowband Irradiances on Tilted surfaces (FARMS-NIT), to efficiently compute irradiances on inclined photovoltaics (PV) panels for 2002 narrow-wavelength bands from 0.28 to 4.0 um. This study is reported in two parts. Part I presents the methodology and performance evaluation of the new model under clear-sky conditions. The Simple Model of the Atmospheric Radiative Transfer of Sunshine (SMARTS), which was designed to compute clear-sky irradiances, is employed to rapidly provide the optical properties of a given clear-sky atmosphere. The clear-sky radiances in the narrow-wavelength bands are computed by considering three paths of photon transmission and solving the radiative transfer equation with the single-scattering approximation. The Bi-directional Transmittance Distribution Function (BTDF) of aerosols is given by their single-scattering phase function with a correction using a two-stream approximation. The validation analysis confirms that FARMS-NIT has improved accuracy compared to TMYSPEC as evaluated by both surface observations and a state-of-the-art radiative transfer model. This model substantially improves computational efficiency compared to other radiative transfer models though it uses slightly more computing time than TMYSPEC. Part II of this study addresses the model in cloud-sky conditions and will be published as a companion paper.

14 SOLAR ENERGY↗
NASA NTRS1983

Superrotation of atmosphere and its effect on the attitude motion of spacecraft

This paper describes some recent results concerning the effect of rotation of the upper atmosphere (superrotation) on the attitude motion of spacecraft. From the data taken by several satellites, an approximate model of the atmospheric rotation rate as a function of altitude has been developed. An approximate, closed-form analytical description is obtained of the attitude motion of a momentum-biased, near-earth spacecraft which is subjected to an aerodynamic torque that includes the contribution from superrotation of the atmosphere. Results from the analysis are compared with simulation and flight data and are found to be in close agreement.

Sellappan, R. G.↗
NASA NTRS1995

Probability Density Functions of Observed Rainfall in Montana

The question of whether a rain rate probability density function (PDF) can vary uniformly between precipitation events is examined. Image analysis on large samples of radar echoes is possible because of advances in technology. The data provided by such an analysis easily allow development of radar reflectivity factors (and by extension rain rate) distribution. Finding a PDF becomes a matter of finding a function that describes the curve approximating the resulting distributions. Ideally, one PDF would exist for all cases; or many PDF's that have the same functional form with only systematic variations in parameters (such as size or shape) exist. Satisfying either of theses cases will, validate the theoretical basis of the Area Time Integral (ATI). Using the method of moments and Elderton's curve selection criteria, the Pearson Type 1 equation was identified as a potential fit for 89 percent of the observed distributions. Further analysis indicates that the Type 1 curve does approximate the shape of the distributions but quantitatively does not produce a great fit. Using the method of moments and Elderton's curve selection criteria, the Pearson Type 1 equation was identified as a potential fit for 89% of the observed distributions. Further analysis indicates that the Type 1 curve does approximate the shape of the distributions but quantitatively does not produce a great fit.

Larsen, Scott D.↗
DOE OSTI2016

On the existence of the optimal order for wavefunction extrapolation in Born-Oppenheimer molecular dynamics

Wavefunction extrapolation greatly reduces the number of self-consistent field (SCF) iterations and thus the overall computational cost of Born-Oppenheimer molecular dynamics (BOMD) that is based on the Kohn–Sham density functional theory. Going against the intuition that the higher order of extrapolation possesses a better accuracy, we demonstrate, from both theoretical and numerical perspectives, that the extrapolation accuracy firstly increases and then decreases with respect to the order, and an optimal extrapolation order in terms of minimal number of SCF iterations always exists. We also prove that the optimal order tends to be larger when using larger MD time steps or more strict SCF convergence criteria. By example BOMD simulations of a solid copper system, we show that the optimal extrapolation order covers a broad range when varying the MD time step or the SCF convergence criterion. Therefore, we suggest the necessity for BOMD simulation packages to open the user interface and to provide more choices on the extrapolation order. Another factor that may influence the extrapolation accuracy is the alignment scheme that eliminates the discontinuity in the wavefunctions with respect to the atomic or cell variables. We prove the equivalence between the two existing schemes, thus the implementation of either of them does not lead to essential difference in the extrapolation accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Towards solution and refinement of organic crystal structures by fitting to the atomic pair distribution function

In this study, a method towards the solution and refinement of organic crystal structures by fitting to the atomic pair distribution function (PDF) is developed. Approximate lattice parameters and molecular geometry must be given as input. The molecule is generally treated as a rigid body. The positions and orientations of the molecules inside the unit cell are optimized starting from random values. The PDF is obtained from carefully measured X-ray powder diffraction data. The method resembles `real-space' methods for structure solution from powder data, but works with PDF data instead of the diffraction pattern itself. As such it may be used in situations where the organic compounds are not long-range-ordered, are poorly crystalline, or nanocrystalline. The procedure was applied to solve and refine the crystal structures of quinacridone (β phase), naphthalene and allopurinol. In the case of allopurinol it was even possible to successfully solve and refine the structure in P1 with four independent molecules. As an example of a flexible molecule, the crystal structure of paracetamol was refined using restraints for bond lengths, bond angles and selected torsion angles. In all cases, the resulting structures are in excellent agreement with structures from single-crystal data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗