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At least 559 records · Page 31

A Full-Height Axial P 3 Solver for the 2D/1D Method in MPACT

This report encompasses the efforts to complete L3:RTM.PRT.P15.04, which relates to improvements to the axial solvers in MPACT. Over the past few years, a number of convergence issues have been encountered throughout the 2D/1D calculation. While many of these were related to transport-corrected stability, which has been much improved through the development of multigroup MOC kernels, there are still some instabilities that are more directly related to the 1D axial nodal solvers. The primary focus of this milestone is on the development of a full-height P 3 solver, which solves for a single linear system for the entire rod, compared to the one- and two-node solvers previously available in MPACT. To provide an efficient full-height solver, the SuperLU direct linear solver was leveraged and an alternative rod decomposition scheme is used in favor over the typically employed axial decomposition. In addition to the full-height solver, a number of stability observations are discussed pertaining to (1) cases with thin planes in the axial reflectors, (2) quadratic radial leakage interpolation, (3) the reset sol capability, which reinitializes the solution before continuing the calculation, and (4) the flux threshold used in the radial transverse leakage splitting logic. The last of these was improved by identifying an acceptable threshold, which greatly help provide stability to the default one-node P 3 solver approach. Results demonstrating the full-height solver are presented for (1) a single assembly case from the AP1000 reactor design, (2) VERA Progression Problem 5a, and (3) a Watts Bar Unit 1, Cycle 1 case that demonstrated convergence issues due to thin planes in the axial reflector. In total, the full-height solver appears to be 3–5× slower for the nodal solve time, yield a roughly 10–20% increase in total problem run time, and requires ~5% more memory. However, these increases may be justifiable if the solver is proven to be more stable than the current default. Additionally, the VERA Progression Problem 4a case with the 252-group library is shown for the one-node P 3 solver with the updated threshold for radial transverse leakage splitting. This case also previous failed very early in the calculation, but is now able to run to completion. Brief details are also included related to the refactoring the nodal sweeper design. Previously, all nodal sweeper options were available in one large module, which was cumbersome and difficult to extend. Before the work here began, the design was refactored to include a number of abstract and extended types, which will help make future extensions easier. All-in-all, this milestone successfully implemented a new axial solver and improved the stability of the current default axial solver. However, additional testing will be necessary on new cases that demonstrate convergence issues before a decision can be made to change the current default in MPACT.

97 MATHEMATICS AND COMPUTING↗

Method and apparatus for measuring web material wound on a reel

The method and apparatus for measuring the number of layers of a web material of known thickness wound on a storage or take-up reel is presented. The method and apparatus are based on the principle that, at a relatively large radius, the loci of layers of a thin web wound on the reel approximate a family of concentric circles having radii respectively successively increasing by a length equal to the web thickness. Tachometer pulses are generated in response to linear movement of the web and reset pulses are generated in response to rotation of the reel. A digital circuit, responsive to the tachometer and reset pulses, generates data indicative of the layer number of any layer of the web and of position of the web within the layer without requiring numerical interpolation.

Muller, R. M.↗

Parrallel Implementation of Fast Randomized Algorithms for Low Rank Matrix Decomposition

We analyze the parallel performance of randomized interpolative decomposition by de- composing low rank complex-valued Gaussian random matrices larger than 100 GB. We chose a Cray XMT supercomputer as it provides an almost ideal PRAM model permitting quick investigation of parallel algorithms without obfuscation from hardware idiosyncrasies. We obtain that on non-square matrices performance scales almost linearly with runtime about 100 times faster on 128 processors. We also verify that numerically discovered error bounds still hold on matrices two orders of magnitude larger than those previously tested.

Lucas, Andrew J.↗

The Linear Bicharacteristic Scheme for Electromagnetics

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on electromagnetic wave propagation problems. This paper extends the Linear Bicharacteristic Scheme for computational electromagnetics to model lossy dielectric and magnetic materials and perfect electrical conductors. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media and for perfect electrical conductors. Heterogeneous media are modeled through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for one-dimensional model problems on both uniform and nonuniform grids, and the FDTD algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has approximately one-third the phase velocity error. The LBS is also more accurate on nonuniform grids.

Beggs, John H.↗

Towards Energy Scale Calibration and Drift Correction of TES Detectors for Athena X-IFU

The Athena X-Ray Integral Field Unit (X-IFU) comprises a 2376-pixel array of transition edge sensors (TES) read out with time-division multiplexing (TDM). X-IFU will provide spatially resolved, high-resolution spectroscopy (2.5 eV full-width-half-maximum up to 7 keV) over the energy range 0.2 to 12 keV, with an absolute energy scale accuracy of 0.4 eV. The energy scale function maps the optimally filtered pulse height, in arbitrary engineering units, to real calibrated energy. Uncertainties in the calibration can result from imperfect fitting of the energy scale between the known calibration points. Furthermore, temporal changes in the TES operating environment, such as heat-sink temperature, magnetic field and bias voltage, can cause significant variations in the detector gain function over time. If not properly corrected, this can result in degradation of the energy resolution, and systematic errors in the absolute energy scale. The non-linear nature of TES detectors, coupled with the possibility of multiple simultaneously occurring sources of drift, can make effective corrections over the full bandpass of the instrument extremely challenging. Athena X-IFU will employ an on-board calibration source that provides known reference x-ray lines. This provides real-time monitoring of the gain stability of the detector system and information that can be used to correct for gain drifts. For X-IFU the baseline approach is to measure a series of calibration curves under different environmental conditions, which bound the expected drifts the instrument is predicted to see over the course of the mission. Using the information from the in-flight calibration source, these energy scale functions can be interpolated to generate a new corrected energy scale as a function of time. In this paper we discuss progress towards demonstrating that the X-IFU energy scale requirements can be met. We present measurements on ~ 200 pixels in a prototype X-IFU array read out with 8-column x 32-row TDM. We use a rotating target source containing 12 fluorescent targets to generate x-ray lines covering the energy range 4 keV (Sc-Kα) to 12 keV (Br-Kα). We present measurements of the non-linear energy scale function and show how variations in heat-sink temperature, TES bias voltage and magnetic field affect the shape of TES energy scale differently and introduce different residual gain errors over the bandpass. We explore different drift correction algorithms that use either a single or multiple referential lines to track and correct the gain from these various sources of drift. In addition to the pulse-height, the DC ‘baseline’ level of the TES can contain information about its bias conditions. Thus, we test a multi-parameter gain correction algorithm that attempts to incorporate both the pulse height and the additional baseline information into the algorithm.

Stephen J Smith↗

Nonlinear convergence in contact mechanics: Immersed boundary finite volume

In this report we present an immersed boundary finite volume (IBM) method for simulating quasistatic contact mechanics of linearly elastic domains at small strains. In IBM, all external boundaries and internal contacts of an object are represented by embedded surfaces inside a Cartesian mesh, which need not conform to the grid lines. The contact constraints consist of the non-penetrability condition and Coulomb’s friction law, which are discretized using special interpolation stencils and enforced via penalty parameters. The resulting nonlinear system depends on displacement unknowns only. To solve it, we use the Newton method but find that it diverges frequently. To understand the divergence pattern, we analyze a simplified 2-cell problem and show that the global convergence of Newton cannot be ensured for any choice of penalty parameters. We thus propose a modified Newton solver, which guarantees convergence for the 2-cell problem and is numerically verified to converge for all the challenging simulations considered herein. While both 1 st - and 2 nd -order variants of IBM, in displacement unknowns, are proposed, the modified Newton solver applies only to the 1 st -order variant.

42 ENGINEERING↗

Greedy Sampling and Incremental Surrogate Model-Based Tailoring of Aeroservoelastic Model Database for Flexible Aircraft

This paper presents a data analysis and modeling framework to tailor and develop linear parameter-varying (LPV) aeroservoelastic (ASE) model database for flexible aircrafts in broad 2D flight parameter space. The Kriging surrogate model is constructed using ASE models at a fraction of grid points within the original model database, and then the ASE model at any flight condition can be obtained simply through surrogate model interpolation. The greedy sampling algorithm is developed to select the next sample point that carries the worst relative error between the surrogate model prediction and the benchmark model in the frequency domain among all input-output channels. The process is iterated to incrementally improve surrogate model accuracy till a pre-determined tolerance or iteration budget is met. The methodology is applied to the ASE model database of a flexible aircraft currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that the proposed method can reduce the number of models in the original database by 67%. Even so the ASE models obtained through Kriging interpolation match the model in the original database constructed directly from the physics-based tool with the worst relative error far below 1%. The interpolated ASE model exhibits continuously-varying gains along a set of prescribed flight conditions. More importantly, the selected grid points are distributed non-uniformly in the parameter space, a) capturing the distinctly different dynamic behavior and its dependence on flight parameters, and b) reiterating the need and utility for adaptive space sampling techniques for ASE model database compaction. The present framework is directly extendible to high-dimensional flight parameter space, and can be used to guide the ASE model development, model order reduction, robust control synthesis and novel vehicle design of flexible aircraft.

numerical analysi↗

Algorithmic Classification of Raman Spectra Biosignatures: Improving Life Detection Confidence

“Agnostic” biosignatures – indicators of life (or the absence of life), independent of a particular biochemistry – are increasingly considered a high standard for life detection. The Ladder of Life Detection (2018) called for investigating how combinations of independent and different potential biosignatures affect confidence. To address this gap, statistical classification of elemental abundances, isotopic fractionation, and reflectance spectroscopy (VNIR) has been implemented. Raman spectroscopy, highly desirable due to its wide availability, has the potential to improve this predictive power. This work implemented biosignature classification algorithms on Raman data alone, in preparation for combination with the other data types. Raman spectroscopy data was collected from published databases and papers as part of a manually curated dataset of “indicative” and “non-indicative of life” samples. These currently include 61 non-indicative samples (meteorites, magnetite); 3 indicative living samples (bacteria); 20 indicative non-living samples (chalk, bone); and 12 indicative mixed (with non-indicative material) samples (soil, microbial mats). Laboratory work is ongoing to characterize additional samples, particularly a greater breadth of mixed systems. Spectra were interpolated, filtered with the Savitzsky-Golay filter, and de-noised. For a preliminary examination, agnostic features were manually extracted including mean intensity, number of peaks, and mean peak width. Different peak prominences and filtering polynomials were used to refine features. Classification algorithms were implemented: k-nearest neighbors (KNN), logistic regression (LR), linear support vector machines (SVM), random forest (RF), Gaussian naïve bayes (GNB). Lastly, Monte Carlo simulations on 1,000 50%-train-test-splits were used to validate classification performance and feature significance. The preliminary feature set achieved its highest AUC of 0.52 with LR, with no strongly discriminatory features. Work to improve feature extraction, such as through deep learning with back propagation, is planned. In future work, the Raman data will be combined with the other data types, and potentially new data types such as enantiomeric excess. This project was partially supported through the NASA Ames Project EXcellence (APEX) incubator program.

Astrobiology↗

Hausdorff dimension of quark trajectories from SCSB and confinement

The quark condensate is calculated using the effective-action formalism, by imposing an ansatz for the Wilson loop, which interpolates between the area-law for large loops and the area-squared law for small loops. For 3 colors and 2 light flavors, a lower bound of 460 MeV for the constituent quark mass is found to be accessible, provided an effective scale-dependent string tension of a light quark falls off linearly with the Schwinger proper time. This behavior of the effective string tension yields the Hausdorff dimension of a light-quark trajectory equal to 4, which shows that these trajectories are similar to branched polymers. A gluonic chain based on such trajectories provides an example of a model describing weak first-order deconfinement phase transition, which takes place in SU(3) Yang-Mills theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Developing Information Power Grid Based Algorithms and Software

This was an exploratory study to enhance our understanding of problems involved in developing large scale applications in a heterogeneous distributed environment. It is likely that the large scale applications of the future will be built by coupling specialized computational modules together. For example, efforts now exist to couple ocean and atmospheric prediction codes to simulate a more complete climate system. These two applications differ in many respects. They have different grids, the data is in different unit systems and the algorithms for inte,-rating in time are different. In addition the code for each application is likely to have been developed on different architectures and tend to have poor performance when run on an architecture for which the code was not designed, if it runs at all. Architectural differences may also induce differences in data representation which effect precision and convergence criteria as well as data transfer issues. In order to couple such dissimilar codes some form of translation must be present. This translation should be able to handle interpolation from one grid to another as well as construction of the correct data field in the correct units from available data. Even if a code is to be developed from scratch, a modular approach will likely be followed in that standard scientific packages will be used to do the more mundane tasks such as linear algebra or Fourier transform operations. This approach allows the developers to concentrate on their science rather than becoming experts in linear algebra or signal processing. Problems associated with this development approach include difficulties associated with data extraction and translation from one module to another, module performance on different nodal architectures, and others. In addition to these data and software issues there exists operational issues such as platform stability and resource management.

Dongarra, Jack↗

Application of Design Methodologies for Feedback Compensation Associated with Linear Systems

The work that follows is concerned with the application of design methodologies for feedback compensation associated with linear systems. In general, the intent is to provide a well behaved closed loop system in terms of stability and robustness (internal signals remain bounded with a certain amount of uncertainty) and simultaneously achieve an acceptable level of performance. The approach here has been to convert the closed loop system and control synthesis problem into the interpolation setting. The interpolation formulation then serves as our mathematical representation of the design process. Lifting techniques have been used to solve the corresponding interpolation and control synthesis problems. Several applications using this multiobjective design methodology have been included to show the effectiveness of these techniques. In particular, the mixed H 2-H performance criteria with algorithm has been used on several examples including an F-18 HARV (High Angle of Attack Research Vehicle) for sensitivity performance.

Smith, Monty J.↗

Design Process for High Speed Civil Transport Aircraft Improved by Neural Network and Regression Methods

A key challenge in designing the new High Speed Civil Transport (HSCT) aircraft is determining a good match between the airframe and engine. Multidisciplinary design optimization can be used to solve the problem by adjusting parameters of both the engine and the airframe. Earlier, an example problem was presented of an HSCT aircraft with four mixed-flow turbofan engines and a baseline mission to carry 305 passengers 5000 nautical miles at a cruise speed of Mach 2.4. The problem was solved by coupling NASA Lewis Research Center's design optimization testbed (COMETBOARDS) with NASA Langley Research Center's Flight Optimization System (FLOPS). The computing time expended in solving the problem was substantial, and the instability of the FLOPS analyzer at certain design points caused difficulties. In an attempt to alleviate both of these limitations, we explored the use of two approximation concepts in the design optimization process. The two concepts, which are based on neural network and linear regression approximation, provide the reanalysis capability and design sensitivity analysis information required for the optimization process. The HSCT aircraft optimization problem was solved by using three alternate approaches; that is, the original FLOPS analyzer and two approximate (derived) analyzers. The approximate analyzers were calibrated and used in three different ranges of the design variables; narrow (interpolated), standard, and wide (extrapolated).

Hopkins, Dale A.↗

A statistically defined anthropomorphic software breast phantom

Purpose: Digital anthropomorphic breast phantoms have emerged in the past decade because of recent advances in 3D breast x-ray imaging techniques. Computer phantoms in the literature have incorporated power-law noise to represent glandular tissue and branching structures to represent linear components such as ducts. When power-law noise is added to those phantoms in one piece, the simulated fibroglandular tissue is distributed randomly throughout the breast, resulting in dense tissue placement that may not be observed in a real breast. The authors describe a method for enhancing an existing digital anthropomorphic breast phantom by adding binarized power-law noise to a limited area of the breast. Methods: Phantoms with (0.5 mm){sup 3} voxel size were generated using software developed by Bakic et al. Between 0% and 40% of adipose compartments in each phantom were replaced with binarized power-law noise ({beta} = 3.0) ranging from 0.1 to 0.6 volumetric glandular fraction. The phantoms were compressed to 7.5 cm thickness, then blurred using a 3 Multiplication-Sign 3 boxcar kernel and up-sampled to (0.1 mm){sup 3} voxel size using trilinear interpolation. Following interpolation, the phantoms were adjusted for volumetric glandular fraction using global thresholding. Monoenergetic phantom projections were created, including quantum noise and simulated detector blur. Texture was quantified in the simulated projections using power-spectrum analysis to estimate the power-law exponent {beta} from 25.6 Multiplication-Sign 25.6 mm{sup 2} regions of interest. Results: Phantoms were generated with total volumetric glandular fraction ranging from 3% to 24%. Values for {beta} (averaged per projection view) were found to be between 2.67 and 3.73. Thus, the range of textures of the simulated breasts covers the textures observed in clinical images. Conclusions: Using these new techniques, digital anthropomorphic breast phantoms can be generated with a variety of glandular fractions and patterns. {beta} values for this new phantom are comparable with published values for breast tissue in x-ray projection modalities. The combination of conspicuous linear structures and binarized power-law noise added to a limited area of the phantom qualitatively improves its realism.

60 APPLIED LIFE SCIENCES↗

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.

97 MATHEMATICS AND COMPUTING↗

Effective Landau-type model of a Hf x Zr 1 - x O 2 -graphene nanostructure

Here, to describe the charge-polarization coupling in the nanostructure formed by a thin Hf x Zr 1-x O 2 film with a single-layer graphene as a top electrode, we develop the “effective” Landau-Ginzburg-Devonshire model. This approach is based on the parametrization of the Landau expansion coefficients for the polar (FE) and antipolar (AFE) orderings in thin Hf 1-x Zr x O 2 films from a limited number of polarization-field curves and hysteresis loops. The Landau expansion coefficients are nonlinearly dependent on the film thickness h and Zr/[Hf+Zr] ratio x, in contrast to h-independent and linearly x-dependent expansion coefficients of a classical Landau energy. We explain the dependence of the Landau expansion coefficients by the strong nonmonotonic dependence of the Hf 1-x Zr x O 2 film polar properties on the film thickness, grain size and surface energy. The proposed Landau free energy with five “effective” expansion coefficients, which are interpolation functions of x and h, describes the continuous transformation of polarization dependences on applied electric field and hysteresis loop shapes induced by the changes of x and h in the range 0 < x < 1 and 5 nm < h < 35 nm. Using the effective free energy, we demonstrated that the polarization of Hf 1-x Zr x O 2 film influences strongly on the graphene conductivity, and the full correlation between the distribution of polarization and charge carriers in graphene is revealed. In accordance with our modeling, the polarization of the (5 – 25) nm thick Hf 1-x Zr x O 2 films, which are in the ferroelectric-like or antiferroelectric-like states for the chemical compositions 0.35 ≤ x ≤ 0.95, determine the concentration of carriers in graphene and can control its field dependence. The result can be promising for creation of next generation Si-compatible nonvolatile memories and graphene-ferroelectric FETs, because the working voltages applied to the Hf 1-x Zr x O 2 film (which acts as a gate) can be relatively low (less than 2 V). These low voltages are sufficient to induce the pronounced hysteresis of ferroelectric polarization in the Hf 1-x Zr x O 2 gate, which, due to the strong electric coupling, induces the hysteresis of the graphene charge.

36 MATERIALS SCIENCE↗

On the calculation of panel flutter boundaries.

Methods are described for the complete automation of flutter boundary calculations when the aerodynamic forces are derived from linear three-dimensional unsteady potential flow theory. The usual process of visual curve fairing in the mass ratio versus structural damping plane is replaced by numerical procedures for ordering the eigenvalues in such a way that the n-th eigenvalue is always associated with the same flutter boundary. The mass ratio versus structural damping curves are interpolated via parametric cubic spline functions to produce the desired plots in the stiffness-parameter/mass-ratio plane. The entire process is accomplished in a single computer run.

Gaspers, P. A., Jr.↗

High Order And High Resolution Methods For a Model CAA Problem

The initial value problem for the first order linear wave equation in one space dimension is treated for two cases with specified initial data and grid, and data from solutions at t = 400 and t = 800 are presented, as prescribed for Problem 1 in Category 1. Results are shown from computations with a sequence of recently developed high order and high resolution methods which combine Hermite interpolation, Cauchy-Kowaleskya recursion for time derivatives, and Taylor series time advancement. These methods have the same order of accuracy in time as in space. Results are shown from methods that range from third to nineteenth order. The stated problems with the prescribed coarse grid can be simulated with errors that are at the level of machine accuracy if the method is sufficiently high order. In addition, the growth of the maximum absolute error out to t = 100,000 is given for simulations with the stated problem data.

Goodrich, John W.↗

Quantifying Transient Uncertainty in the BEAVRS Benchmark Using Time Series Analysis Methods

Advances in computation have brought about significant improvements in creating fast-running high-fidelity simulations of nuclear cores. The BEAVRS benchmark is a highly-detailed PWR specification with two cycles of measured operational data used to validate high-fidelity core analysis methods. This PWR depletion benchmark captures the fine details of the LWR fuel assemblies, burnable absorbers, in-core fission detectors, core loading and shuffling patterns. Specifically, 58 of the 193 assemblies contain in-core detectors with measurements taken over 61 axial positions every month. These detectors are U-235 fission chambers with slightly varying mass of U-235. The collected signals are normalized on a given assembly permitting full core comparisons. The fuel layout for cycle 1 and instrument tube locations for the reactor are given in figures 1 and 2 respectively. Through a series of data processing and comparisons, it was shown that axially integrated radial maps of reaction rates were in close agreement between provided detector data and calculated data. More recently, the focus of the BEAVRS project has been on quantifying uncertainty to further assess the validity of aforementioned results. A close investigation of sources of error shows that uncertainties from operational nuclear data arise primarily from data measurements and processing. While the errors in axial realignment and interpolation seem significant, these sources affect only a small subset of data points near grid spacers and do not persist throughout the entire core. Instead, measurement uncertainty from detector count rates and radial integration dominate the uncertainty in measured data are determined as the most significant sources of error. This uncertainty analysis treated each given burnup step as independent of comparable data at neighboring burnup steps. More recent work has been targeted at understanding how reaction rates vary over time, in order to determine whether calculated reaction rates follow any observable trends. This abstract hones in on transient uncertainty quantification, in order to compare observed data against models for transient behavior. The first section of the paper uses linear regression tools to fit operational data, while the latter portion of the paper explores more complex simulation tools to fit operational data. Ultimately, the BEAVRS benchmark aims to serve as a true non-proprietary international benchmark for the validation of high-fidelity tools. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗