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DOE OSTI2017

The Transfer of Resonance Line Polarization with Partial Frequency Redistribution in the General Hanle–Zeeman Regime

The spectral line polarization encodes a wealth of information about the thermal and magnetic properties of the solar atmosphere. Modeling the Stokes profiles of strong resonance lines is, however, a complex problem both from a theoretical and computational point of view, especially when partial frequency redistribution (PRD) effects need to be taken into account. In this work, we consider a two-level atom in the presence of magnetic fields of arbitrary intensity (Hanle–Zeeman regime) and orientation, both deterministic and micro-structured. Working within the framework of a rigorous PRD theoretical approach, we have developed a numerical code that solves the full non-LTE radiative transfer problem for polarized radiation, in one-dimensional models of the solar atmosphere, accounting for the combined action of the Hanle and Zeeman effects, as well as for PRD phenomena. After briefly discussing the relevant equations, we describe the iterative method of solution of the problem and the numerical tools that we have developed and implemented. We finally present some illustrative applications to two resonance lines that form at different heights in the solar atmosphere, and provide a detailed physical interpretation of the calculated Stokes profiles. We find that magneto-optical effects have a strong impact on the linear polarization signals that PRD effects produce in the wings of strong resonance lines. We also show that the weak-field approximation has to be used with caution when PRD effects are considered.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Thermoelectric power of supported graphene - An iterative approach

Thermoelectric power, S, of graphene supported on SiO{sub 2} substrate is studied for 10K < T < 400K within the framework of Boltzmann transport formalism by an iterative method. Numerical calculations of diffusion thermopower, S{sub d}, as a function of temperature, are presented assuming the electrons to be scattered by impurities, vacancies, surface roughness, acoustic phonons, inelastic optical phonons and surface polar optical phonons. For the range of temperatures considered, S{sub d} is found to be dominated by impurities for T < 40K and by acoustic phonon and vacancy scatterings for T > 40K. The optical phonons are found to influence S{sub d} for T > 300K. Our calculations, assuming the drag component to be negligible, obtain good agreement with the recent experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

2022 AI Testbed Expeditions Report

By exploiting the coherent properties of a light source, coherent diffraction imaging (CDI) is able to obtain the sample image at a nanoscale resolution using the measured diffraction pattern. Bragg Coherent Diffraction Imaging (BCDI) has become valuable for recovering the displacement and strain field of crystals, providing a valuable tool in material science and solid-state physics. X-ray ptychography is another emerging CDI technique that can produce a high-resolution image of the extended sample and has become popular in many research areas (e.g., materials science, biology, electronics, and optics characterization). CDI including BCDI and ptychography has become an established technique in Synchrotron Facilities including the Advanced Photon Source (APS) and will greatly benefit from the 100x coherent flux increase of the upcoming APS Upgrade (APSU). The current image formation process in CDI employs iterative phase retrieval algorithms, which is a time-consuming and computationally expensive process. Especially after APSU, the traditional iterative methods will not be able to match the experimental data acquisition speed. We employ deep learning (DL) approach to replace the iterative approaches, therefore allowing hundreds of times faster recovery of the object. We developed AutoPhaseNN, a DL-based approach which learns to solve the inverse problem without labeled data. Taking 3D BCDI as a representative technique, AutoPhaseNN has been demonstrated to be one hundred times faster than traditional iterative phase retrieval methods while providing comparable image quality. The current network is trained with 64 x 64 x 64 data size, to achieve higher resolution imaging, we will need to scale the network to input and train/infer 3D arrays of size 256 x 256 x 256 (today) and of size 2560x2560x2560 (APSU). However, the scalability of the network is restricted due to the memory-intensive training process. To perform the training for a 256 x 256 x 256 data size, the required memory exceeds the capacity of the current machine. In this project, we explore using Sambanova system to train the network for the direct data inversion for CDI.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Attenuation correction in emission tomography using the emission data—A review

The problem of attenuation correction (AC) for quantitative positron emission tomography (PET) had been considered solved to a large extent after the commercial availability of devices combining PET with computed tomography (CT) in 2001; single photon emission computed tomography (SPECT) has seen a similar development. However, stimulated in particular by technical advances toward clinical systems combining PET and magnetic resonance imaging (MRI), research interest in alternative approaches for PET AC has grown substantially in the last years. In this comprehensive literature review, the authors first present theoretical results with relevance to simultaneous reconstruction of attenuation and activity. The authors then look back at the early history of this research area especially in PET; since this history is closely interwoven with that of similar approaches in SPECT, these will also be covered. We then review algorithmic advances in PET, including analytic and iterative algorithms. The analytic approaches are either based on the Helgason–Ludwig data consistency conditions of the Radon transform, or generalizations of John’s partial differential equation; with respect to iterative methods, we discuss maximum likelihood reconstruction of attenuation and activity (MLAA), the maximum likelihood attenuation correction factors (MLACF) algorithm, and their offspring. The description of methods is followed by a structured account of applications for simultaneous reconstruction techniques: this discussion covers organ-specific applications, applications specific to PET/MRI, applications using supplemental transmission information, and motion-aware applications. After briefly summarizing SPECT applications, we consider recent developments using emission data other than unscattered photons. In summary, developments using time-of-flight (TOF) PET emission data for AC have shown promising advances and open a wide range of applications. These techniques may both remedy deficiencies of purely MRI-based AC approaches in PET/MRI and improve standalone PET imaging.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2015

RADIATIVE TRANSFER MODELING OF THE ENIGMATIC SCATTERING POLARIZATION IN THE SOLAR Na i D{sub 1} LINE

The modeling of the peculiar scattering polarization signals observed in some diagnostically important solar resonance lines requires the consideration of the detailed spectral structure of the incident radiation field as well as the possibility of ground level polarization, along with the atom's hyperfine structure and quantum interference between hyperfine F-levels pertaining either to the same fine structure J-level, or to different J-levels of the same term. Here we present a theoretical and numerical approach suitable for solving this complex non-LTE radiative transfer problem. This approach is based on the density-matrix metalevel theory (where each level is viewed as a continuous distribution of sublevels) and on accurate formal solvers of the transfer equations and efficient iterative methods. We show an application to the D-lines of Na i, with emphasis on the enigmatic D{sub 1} line, pointing out the observable signatures of the various physical mechanisms considered. We demonstrate that the linear polarization observed in the core of the D{sub 1} line may be explained by the effect that one gets when the detailed spectral structure of the anisotropic radiation responsible for the optical pumping is taken into account. This physical ingredient is capable of introducing significant scattering polarization in the core of the Na i D{sub 1} line without the need for ground-level polarization.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

WE-G-204-06: Grid-Line Artifact Minimization for High Resolution Detectors Using Iterative Residual Scatter Correction

Purpose: Anti-scatter grid-line artifacts are more prominent for high-resolution x-ray detectors since the fraction of a pixel blocked by the grid septa is large. Direct logarithmic subtraction of the artifact pattern is limited by residual scattered radiation and we investigate an iterative method for scatter correction. Methods: A stationary Smit-Rοntgen anti-scatter grid was used with a high resolution Dexela 1207 CMOS X-ray detector (75 µm pixel size) to image an artery block (Nuclear Associates, Model 76-705) placed within a uniform head equivalent phantom as the scattering source. The image of the phantom was divided by a flat-field image obtained without scatter but with the grid to eliminate grid-line artifacts. Constant scatter values were subtracted from the phantom image before dividing by the averaged flat-field-with-grid image. The standard deviation of pixel values for a fixed region of the resultant images with different subtracted scatter values provided a measure of the remaining grid-line artifacts. Results: A plot of the standard deviation of image pixel values versus the subtracted scatter value shows that the image structure noise reaches a minimum before going up again as the scatter value is increased. This minimum corresponds to a minimization of the grid-line artifacts as demonstrated in line profile plots obtained through each of the images perpendicular to the grid lines. Artifact-free images of the artery block were obtained with the optimal scatter value obtained by this iterative approach. Conclusion: Residual scatter subtraction can provide improved grid-line artifact elimination when using the flat-field with grid “subtraction” technique. The standard deviation of image pixel values can be used to determine the optimal scatter value to subtract to obtain a minimization of grid line artifacts with high resolution x-ray imaging detectors. This study was supported by NIH Grant R01EB002873 and an equipment grant from Toshiba Medical Systems Corp.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2012

Synchrotron-based coherent scatter x-ray projection imaging using an array of monoenergetic pencil beams

Traditional projection x-ray imaging utilizes only the information from the primary photons. Low-angle coherent scatter images can be acquired simultaneous to the primary images and provide additional information. In medical applications scatter imaging can improve x-ray contrast or reduce dose using information that is currently discarded in radiological images to augment the transmitted radiation information. Other applications include non-destructive testing and security. A system at the Canadian Light Source synchrotron was configured which utilizes multiple pencil beams (up to five) to create both primary and coherent scatter projection images, simultaneously. The sample was scanned through the beams using an automated step-and-shoot setup. Pixels were acquired in a hexagonal lattice to maximize packing efficiency. The typical pitch was between 1.0 and 1.6 mm. A Maximum Likelihood-Expectation Maximization-based iterative method was used to disentangle the overlapping information from the flat panel digital x-ray detector. The pixel value of the coherent scatter image was generated by integrating the radial profile (scatter intensity versus scattering angle) over an angular range. Different angular ranges maximize the contrast between different materials of interest. A five-beam primary and scatter image set (which had a pixel beam time of 990 ms and total scan time of 56 min) of a porcine phantom is included. For comparison a single-beam coherent scatter image of the same phantom is included. The muscle-fat contrast was 0.10 {+-} 0.01 and 1.16 {+-} 0.03 for the five-beam primary and scatter images, respectively. The air kerma was measured free in air using aluminum oxide optically stimulated luminescent dosimeters. The total area-averaged air kerma for the scan was measured to be 7.2 {+-} 0.4 cGy although due to difficulties in small-beam dosimetry this number could be inaccurate.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2013

Scharz Preconditioners for Krylov Methods: Theory and Practice

Several numerical methods were produced and analyzed. The main thrust of the work relates to inexact Krylov subspace methods for the solution of linear systems of equations arising from the discretization of partial differential equations. These are iterative methods, i.e., where an approximation is obtained and at each step. Usually, a matrix-vector product is needed at each iteration. In the inexact methods, this product (or the application of a preconditioner) can be done inexactly. Schwarz methods, based on domain decompositions, are excellent preconditioners for these systems. We contributed towards their understanding from an algebraic point of view, developed new ones, and studied their performance in the inexact setting. We also worked on combinatorial problems to help define the algebraic partition of the domains, with the needed overlap, as well as PDE-constraint optimization using the above-mentioned inexact Krylov subspace methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics

We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) based on the ensemble normal ordering of Mukherjee and Kutzelnigg (1997). This ensemble averages over all microstates of a given total spin quantum number, and therefore, it is invariant with respect to SU(2) transformations. As such, all equations may be reformulated in terms of spin-free quantities and they closely resemble those of spin-adapted closed-shell coupled cluster (CC) theory. The current implementation is used to assess the accuracy of various truncated MR-DSRG methods (perturbation theory up to third order and iterative methods with single and double excitations) in computing the constants of 33 first-row diatomic molecules. The accuracy trends for these first-row diatomics are consistent with our previous benchmark on a small subset of closed-shell diatomic molecules. We then present the first MR-DSRG application on transition-metal complexes by computing the spin splittings of the [Fe(H 2 O) 6 ] 2+ and [Fe(NH 3 ) 6 ] 2+ molecules. A focal point analysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. The FPA based on the linearized MR-DSRG theory with one- and two-body operators and up to a quintuple- ζ basis set predicts the spin splittings of [Fe(H 2 O) 6 ] 2+ and [Fe(NH 3 ) 6 ] 2+ to be –35.7 and –17.1 kcal mol –1 , respectively, showing good agreement with the results of local CC theory with singles, doubles, and perturbative triples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

A Kriging Surrogate Model for Computing Gas Mixture Equations of State

Accurate simulation of the complex flow following the detonation of an explosive material is a challenging problem. In these flows, the detonation products of the explosive must be treated as a real gas while the surrounding air is treated as an ideal gas. As the detonation process unfolds and the blast wave moves into the surrounding ambient air, the products of detonation expand outward and interact with the air creating a mixture region. In this region, both of the state equations for air and the products must be satisfied. One of the most accurate, yet computationally expensive, methods to handle this problem is an algorithm that iterates between the equations of state until both pressure and temperature reach an equilibrium inside of a computational cell. Since this mixture region moves and grows over time, this algorithm must be performed millions, or even billions, of times in a typical detonation simulation. As such, these calculations can account for a large percentage of the overall solution time. This work aims to use a kriging surrogate model to replace this process. The iterative method solves a nonlinear system of equations created from the gas mixture density, internal energy, and composition using a Broyden iterative solver to obtain an output pressure and temperature. Kriging is used to produce curve fits which interpolate selected pressures and temperatures from this solver from appropriate ranges of the mixture input quantities. Using a finite volume hydrocode, the performance of the model with respect to the iterative solver is demonstrated in the simulation of a pentaerythritol tetranitrate (PETN) charge detonation. The model's computational speed and accuracy are quantified as a function of the choice of sampling points in order to try optimize the combination as well as to show the benefits of this novel approach.

Engineering↗

DOE OSTI2012

Note: Excited State Studies of Ozone using State-Specific Multireference Coupled Cluster Methods

Vertical excitation energies obtained with state-specific multi-reference coupled cluster (MRCC) methods are reported for the ozone molecule. Using state-specific MRCC non-iterative methods with singles, doubles, and non-iterative triples (MRCCSD(T)) we obtain 4.40 eV for the challenging doubly excited 21A1 state when using a reliable model space. This estimate is in good agreement with experiment (4.5 eV). We also compare our MRCC results with the excitation energies obtained with high-order equation-of-motion coupled cluster methods

ab initio↗

DOE OSTI2012

Improvements in the mesh-based convergence diagnostics for Monte Carlo eigenvalue simulations

Using the Monte Carlo method to compute eigenvalue problems based on the power iteration method is widely used. However, the convergence needs accurate diagnostics method in order to maintain the accuracy of the results and the efficiency of the simulation. Recently, we used the linear regression model for convergence diagnostics based on the local information, the mesh-wise cycle-wise flux estimates. Our previous analyses examined properties and demonstrated certain capability of this method. However, several aspects still need further investigation. In this paper, we use additional simulation examples and perform comparisons in order to better understand the capabilities and limitations of this diagnostics method. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

A general solution strategy of modified power method for higher mode solutions

A general solution strategy of the modified power iteration method for calculating higher eigenmodes has been developed and applied in continuous energy Monte Carlo simulation. The new approach adopts four features: 1) the eigen decomposition of transfer matrix, 2) weight cancellation for higher modes, 3) population control with higher mode weights, and 4) stabilization technique of statistical fluctuations using multi-cycle accumulations. The numerical tests of neutron transport eigenvalue problems successfully demonstrate that the new strategy can significantly accelerate the fission source convergence with stable convergence behavior while obtaining multiple higher eigenmodes at the same time. The advantages of the new strategy can be summarized as 1) the replacement of the cumbersome solution step of high order polynomial equations required by Booth's original method with the simple matrix eigen decomposition, 2) faster fission source convergence in inactive cycles, 3) more stable behaviors in both inactive and active cycles, and 4) smaller variances in active cycles. Advantages 3 and 4 can be attributed to the lower sensitivity of the new strategy to statistical fluctuations due to the multi-cycle accumulations. The application of the modified power method to continuous energy Monte Carlo simulation and the higher eigenmodes up to 4th order are reported for the first time in this paper. -- Graphical abstract: -- Highlights: •Modified power method is applied to continuous energy Monte Carlo simulation. •Transfer matrix is introduced to generalize the modified power method. •All mode based population control is applied to get the higher eigenmodes. •Statistic fluctuation can be greatly reduced using accumulated tally results. •Fission source convergence is accelerated with higher mode solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Efficient numerical methods to solve sparse linear equations with application to PageRank

Over the last two decades, the PageRank problem has received increased interest from the academic community as an efficient tool to estimate web-page importance in information retrieval. Despite numerous developments, the design of efficient optimization algorithms for the PageRank problem is still a challenge. Here, we propose three new algorithms with a linear time complexity for solving the problem over a bounded-degree graph. The idea behind them is to set up the PageRank as a convex minimization problem over a unit simplex, and then solve it using iterative methods with small iteration complexity. Our theoretical results are supported by an extensive empirical justification using real-world and simulated data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Atomic electron tomography in three and four dimensions

Atomic electron tomography (AET) has become a powerful tool for atomic-scale structural characterization in three and four dimensions. It provides the ability to correlate structures and properties of materials at the single-atom level. With recent advances in data acquisition methods, iterative three-dimensional (3D) reconstruction algorithms, and post-processing methods, AET can now determine 3D atomic coordinates and chemical species with sub-Angstrom precision, and reveal their atomic-scale time evolution during dynamical processes. In this work, we review the recent experimental and algorithmic developments of AET and highlight several groundbreaking experiments, which include pinpointing the 3D atom positions and chemical order/disorder in technologically relevant materials and capturing how atoms rearrange during early nucleation at four-dimensional atomic resolution.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2013

Downscaling Solar Power Output to 4-Seconds for Use in Integration Studies (Presentation)

High penetration renewable integration studies require solar power data with high spatial and temporal accuracy to quantify the impact of high frequency solar power ramps on the operation of the system. Our previous work concentrated on downscaling solar power from one hour to one minute by simulation. This method used clearness classifications to categorize temporal and spatial variability, and iterative methods to simulate intra-hour clearness variability. We determined that solar power ramp correlations between sites decrease with distance and the duration of the ramp, starting at around 0.6 for 30-minute ramps between sites that are less than 20 km apart. The sub-hour irradiance algorithm we developed has a noise floor that causes the correlations to approach ~0.005. Below one minute, the majority of the correlations of solar power ramps between sites less than 20 km apart are zero, and thus a new method to simulate intra-minute variability is needed. These intra-minute solar power ramps can be simulated using several methods, three of which we evaluate: a cubic spline fit to the one-minute solar power data; projection of the power spectral density toward the higher frequency domain; and average high frequency power spectral density from measured data. Each of these methods either under- or over-estimates the variability of intra-minute solar power ramps. We show that an optimized weighted linear sum of methods, dependent on the classification of temporal variability of the segment of one-minute solar power data, yields time series and ramp distributions similar to measured high-resolution solar irradiance data.

14 SOLAR ENERGY↗

DOE OSTI2013

Downscaling Solar Power Output to 4-Seconds for Use in Integration Studies: Preprint

14 SOLAR ENERGY↗

DOE OSTI2019

High precision beam steering using a liquid crystal spatial light modulator

Liquid crystal spatial light modulators (LCSLMs) are novel phase modulation devices. Due to the dielectric properties of the orientation layer, the orientation layer has a voltage division effect on the driving voltage. A more effective analysis of the relationship between the driving voltage and phase modulation properties of LCSLMs is needed, as well as improved beam steering accuracy. In this paper, we establish an electrical model of an LCSLM, and propose a method for quantitatively calculating the liquid crystal (LC) layer voltage. This differential iterative method based on nonlinear least squares is used to analyze the LC molecular directors. Considering the thickness of the orientation layer, we calculate the LC director distribution and the voltage division effect of the LC layer, obtaining a more accurate electro-optic characteristic curve of the LCSLM, and verify the calculations by experiment. Experimentally, the average beam pointing error of the LCSLM was 0.0098° at 532 nm, representing a significant improvement of the beam steering accuracy.

42 ENGINEERING↗