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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Kernel principal component analysis for stochastic input model generation

Highlights: {yields} KPCA is used to construct a reduced order stochastic model of permeability. {yields} A new approach is proposed to solve the pre-image problem in KPCA. {yields} Polynomial chaos is used to provide a parametric stochastic input model. {yields} Flow in porous media with channelized permeability is considered. - Abstract: Stochastic analysis of random heterogeneous media provides useful information only if realistic input models of the material property variations are used. These input models are often constructed from a set of experimental samples of the underlying random field. To this end, the Karhunen-Loeve (K-L) expansion, also known as principal component analysis (PCA), is the most popular model reduction method due to its uniform mean-square convergence. However, it only projects the samples onto an optimal linear subspace, which results in an unreasonable representation of the original data if they are non-linearly related to each other. In other words, it only preserves the first-order (mean) and second-order statistics (covariance) of a random field, which is insufficient for reproducing complex structures. This paper applies kernel principal component analysis (KPCA) to construct a reduced-order stochastic input model for the material property variation in heterogeneous media. KPCA can be considered as a nonlinear version of PCA. Through use of kernel functions, KPCA further enables the preservation of higher-order statistics of the random field, instead of just two-point statistics as in the standard Karhunen-Loeve (K-L) expansion. Thus, this method can model non-Gaussian, non-stationary random fields. In this work, we also propose a new approach to solve the pre-image problem involved in KPCA. In addition, polynomial chaos (PC) expansion is used to represent the random coefficients in KPCA which provides a parametric stochastic input model. Thus, realizations, which are statistically consistent with the experimental data, can be generated in an efficient way. We showcase the methodology by constructing a low-dimensional stochastic input model to represent channelized permeability in porous media.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1997

Atomic, Molecular, and Optical Physics: Optical Excitation Function of H(1s-2p) Produced by electron Impact from Threshold to 1.8 keV

The optical excitation function of prompt Lyman-Alpha radiation, produced by electron impact on atomic hydrogen, has been measured over the extended energy range from threshold to 1.8 keV. Measurements were obtained in a crossed-beams experiment using both magnetically confined and electrostatically focused electrons in collision with atomic hydrogen produced by an intense discharge source. A vacuum-ultraviolet mono- chromator system was used to measure the emitted Lyman-Alpha radiation. The absolute H(1s-2p) electron impact excitation cross section was obtained from the experimental optical excitation function by normalizing to the accepted optical oscillator strength, with corrections for polarization and cascade. Statistical and known systematic uncertainties in our data range from +/- 4% near threshold to +/- 2% at 1.8 keV. Multistate coupling affecting the shape of the excitation function up to 1 keV impact energy is apparent in both the present experimental data and present theoretical results obtained with convergent close- coupling (CCC) theory. This shape function effect leads to an uncertainty in absolute cross sections at the 10% level in the analysis of the experimental data. The derived optimized absolute cross sections are within 7% of the CCC calculations over the 14 eV-1.8 keV range. The present CCC calculations converge on the Bethe- Fano profile for H(1s-2p) excitation at high energy. For this reason agreement with the CCC values to within 3% is achieved in a nonoptimal normalization of the experimental data to the Bethe-Fano profile. The fundamental H(1s-2p) electron impact cross section is thereby determined to an unprecedented accuracy over the 14 eV - 1.8 keV energy range.

James, G. K.↗
DOE OSTI2012

WEAK LENSING MEASUREMENT OF GALAXY CLUSTERS IN THE CFHTLS-WIDE SURVEY

We present the first weak gravitational lensing analysis of the completed Canada-France-Hawaii Telescope Legacy Survey (CFHTLS). We study the 64 deg{sup 2} W1 field, the largest of the CFHTLS-Wide survey fields, and present the largest contiguous weak lensing convergence 'mass map' yet made. 2.66 million galaxy shapes are measured, using the Kaiser Squires and Broadhurst Method (KSB) pipeline verified against high-resolution Hubble Space Telescope imaging that covers part of the CFHTLS. Our i'-band measurements are also consistent with an analysis of independent r'-band imaging. The reconstructed lensing convergence map contains 301 peaks with signal-to-noise ratio {nu} > 3.5, consistent with predictions of a {Lambda}CDM model. Of these peaks, 126 lie within 3.'0 of a brightest central galaxy identified from multicolor optical imaging in an independent, red sequence survey. We also identify seven counterparts for massive clusters previously seen in X-ray emission within 6 deg{sup 2} XMM-LSS survey. With photometric redshift estimates for the source galaxies, we use a tomographic lensing method to fit the redshift and mass of each convergence peak. Matching these to the optical observations, we confirm 85 groups/clusters with {chi}{sup 2}{sub reduced} < 3.0, at a mean redshift (z{sub c} ) = 0.36 and velocity dispersion ({sigma}{sub c}) = 658.8 km s{sup -1}. Future surveys, such as DES, LSST, KDUST, and EUCLID, will be able to apply these techniques to map clusters in much larger volumes and thus tightly constrain cosmological models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Accelerating Multivariate Functional Approximation Computation with Domain Decomposition Techniques⋆

Modeling large datasets through Multivariate Functional Approximations (MFA) provide an elegant way to handle many visualization and scientific analysis workflows. The process necessitates scalable data partitioning methods to compute MFA representations efficiently without compromising the accuracy or continuity of the reconstructed solution. We propose a domain -decomposed method for computing the MFA with B -spline bases, which reduces the total work per task and uses a restricted Additive Schwarz (RAS) method to converge the control point data degrees -of -freedom along subdomain boundaries. We provide an in-depth analysis of the parallel approach with domain decomposition solvers, aiming to minimize local subdomain error residuals and recover high -order continuity at subdomain interfaces with appropriate choices of knot overlaps. The communication cost, determined by the overlap regions in the RAS implementation, is optimized to recover the numerical error profile of the single subdomain case. Our proposed method stands in contrast to previous methods, which typically only recover either C 0 or at best C 1 continuity for arbitrary B -spline degree expansions, or those that require post -processing to blend discontinuities in the reconstructed data. We demonstrate the effectiveness of our approach using analytical and real -world datasets in 1D, 2D, and 3D through both strong and weak scaling studies. The performance results indicate that the overall cost of computing the approximation is directly proportional to the underlying nearest -neighbor communication implementation, and is only weakly dependent on the overlap region size that determines the size of the messages. This finding underscores the efficiency and scalability of our proposed method, making it a promising solution for handling large datasets in scientific workflows.

additive Schwarz solvers↗
DOE OSTI2022

A posteriori superlinear convergence bounds for block conjugate gradient

In this paper, we extend to the block case the a posteriori bound showing superlinear convergence of the conjugate gradient method developed by van der Vorst and Vuik in [J. Comput. Applied Math., 48 (1993), pp. 327–341]. That is, we obtain similar bounds but now for the block conjugate gradient method. We also present a series of computational experiments, illustrating the validity of the bound developed here as well as the bound by Simoncini and Szyld from [SIAM Review, 47 (2005), pp. 247–272] using angles between subspaces. Using these bounds, we make some observations on the onset of superlinearity and how this onset depends on the eigenvalue distribution and the block size.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

Relating the Hadamard Variance to MCS Kalman Filter Clock Estimation

The Global Positioning System (GPS) Master Control Station (MCS) currently makes significant use of the Allan Variance. This two-sample variance equation has proven excellent as a handy, understandable tool, both for time domain analysis of GPS cesium frequency standards, and for fine tuning the MCS's state estimation of these atomic clocks. The Allan Variance does not explicitly converge for the nose types of alpha less than or equal to minus 3 and can be greatly affected by frequency drift. Because GPS rubidium frequency standards exhibit non-trivial aging and aging noise characteristics, the basic Allan Variance analysis must be augmented in order to (a) compensate for a dynamic frequency drift, and (b) characterize two additional noise types, specifically alpha = minus 3, and alpha = minus 4. As the GPS program progresses, we will utilize a larger percentage of rubidium frequency standards than ever before. Hence, GPS rubidium clock characterization will require more attention than ever before. The three sample variance, commonly referred to as a renormalized Hadamard Variance, is unaffected by linear frequency drift, converges for alpha is greater than minus 5, and thus has utility for modeling noise in GPS rubidium frequency standards. This paper demonstrates the potential of Hadamard Variance analysis in GPS operations, and presents an equation that relates the Hadamard Variance to the MCS's Kalman filter process noises.

Hutsell, Steven T.↗
DOE OSTI2021

Excited State Intramolecular Proton Transfer with Nuclear-Electronic Orbital Ehrenfest Dynamics

The recent development of the Ehrenfest dynamics approach in the nuclear-electronic orbital (NEO) framework provides a promising way to simulate coupled nuclear-electronic dynamics. Our previous study showed that the NEO-Ehrenfest approach with a semi- classical traveling proton basis method yields accurate predictions of molecular vibrational frequencies. In this work, we provide a more thorough analysis of the semiclassical traveling proton basis method to elucidate its validity and convergence behavior. We also conduct NEO-Ehrenfest dynamics simulations to study an excited state intramolecular proton transfer process. These simulations reveal that nuclear quantum effects influence the predictions of proton transfer reaction rates and kinetic isotope effects due to the intrinsic delocalized nature of the quantum nuclear wave function. This work illustrates the importance of nuclear quantum effects in coupled nuclear-electronic dynamical processes and shows that the NEO-Ehrenfest approach can be a powerful tool to provide insights and predictions for these processes.

Zhao, Luning↗
DOE OSTI2021

Predicting nonresonant pressure-driven MHD modes in equilibria with low magnetic shear

Nonresonant internal modes can be difficult to anticipate as there is no resonant surface in the plasma. However, equilibria that are unstable to multiple nonresonant magnetohydrodynamic (MHD) modes may be more prone to global loss of confinement since these instabilities generate spatially extended linear displacements, potentially enhancing magnetic field line chaos via nonlinear interactions. Here, we successfully predict the unstable nonresonant pressure-driven modes for equilibria with zero shear in the plasma core, irrational q on axis, and a central pressure gradient, which is consistent with pre-crash profiles in sawtoothing tokamak plasmas in the large-aspect-ratio limit. A criterion for identifying nonresonant modes most likely to be unstable is developed from the convergents of the continued fraction representation of q 0 . A higher-order analysis of the standard Energy Principle reveals the conditions under which these modes are expected to dominate. Linear growth rate spectra, as a function of toroidal mode number (up to n = 30), calculated using the initial-value extended-MHD code, M3D-C1, recover the characteristic dependence observed for ideal infernal modes. Nonresonant modes have also been invoked in some ideal sawtooth crash models. Finally, this work provides a mechanism to predict the mode numbers of infernal modes and, potentially, the width of some post-sawtooth-crash profiles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

The point-spread function of fiber-coupled area detectors

The point-spread function (PSF) of a fiber-optic taper-coupled CCD area detector was measured over five decades of intensity using a 20 mm X-ray beam and 2000-fold averaging. The ‘tails’ of the PSF clearly revealed that it is neither Gaussian nor Lorentzian, but instead resembles the solid angle subtended by a pixel at a point source of light held a small distance (27 mm) above the pixel plane. This converges to an inverse cube law far from the beam impact point. Further analysis revealed that the tails are dominated by the fiber-optic taper, with negligible contribution from the phosphor, suggesting that the PSF of all fiber-coupled CCD-type detectors is best described as a Moffat function.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Provable Convergence of Plug-and-Play Priors With MMSE Denoisers

Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. Here we address this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Spectrograph stabilization using a single-delay interferometer on the Hale Telescope

We describe a technique for spectrograph stabilization useful when conventional mitigation techniques of vacuum tanks, thermal insulation, and laser frequency comb may be impractical, expensive, heavy, or bulky. This includes spectrographs on airborne platforms or mounted on telescopes where they suffer a changing gravity vector or other drifts. Placing a fixed-delay interferometer in series with a spectrograph forms an externally dispersed interferometer (EDI). This produces a uniform sinusoidal comb multiplying input spectrum, creating (through heterodyning) beats (moiré patterns). In Fourier space for low frequencies up to the comb frequency, the moiré generated signal counter-rotates to ordinary spectra under an unknown disperser wavenumber drift Δx. This generates a large negative feedback signal useful in a conceptual control loop, to converge rapidly to a stable spectrum and yield Δx. A modified EDI data analysis algorithm (“crossfading”) combines frequency-weighted moiré with conventional spectrum to cancel net output spectrum reaction to Δx. Needing only a single-delay, this is a practical improvement over prior crossfading analyses requiring multiple delays. We test crossfading on ThAr data near 4850 cm−1 taken on Hale telescope in an earlier project. In a single pass, we reduce drift 20 times. Using seven iterations, we reduce 0.5 cm−1 (31 km/s Doppler equivalent) drift to 4×10−7 cm−1 (2.5 cm/s). The interferometer delay can wander, because linearity of phase versus wavenumber interpolates science features between bracketing calibrating spectral references. Second, mathematically reversing the heterodyning effect doubles effective spectral resolution without changing disperser slit.

Erskine, David J [Lawrence Livermore National Labo↗
DOE OSTI2019

Interaction of the Westerlies with the Tibetan Plateau in Determining the Mei-Yu Termination

This article explores how the termination of the mei-yu is dynamically linked to the westerlies impinging on the Tibetan Plateau. It is found that the mei-yu stage terminates when the maximum upper-tropospheric westerlies shift beyond the northern edge of the plateau, around 40°N. This termination is accompanied by the disappearance of tropospheric northerlies over northeastern China. The link between the transit of the jet axis across the northern edge of the plateau, the disappearance of northerlies, and termination of the mei-yu holds on a range of time scales from interannual through seasonal and pentad. Diagnostic analysis indicates that the weakening of the meridional moisture contrast and meridional wind convergence, mainly resulting from the disappearance of northerlies, causes the demise of the mei-yu front. The authors propose that the westerlies migrating north of the plateau and consequent weakening of the extratropical northerlies triggers the mei-yu termination. Model simulations are employed to test the causality between the jet and the orographic downstream northerlies by repositioning the northern edge of the plateau. As the plateau edge extends northward, orographic forcing on the westerlies strengthens, leading to persistent strong downstream northerlies and a prolonged mei-yu. Idealized simulations with a dry dynamical core further demonstrate the dynamical link between the weakening of orographically forced downstream northerlies with the positioning of the jet from south to north of the plateau. Changes in the magnitude of orographically forced stationary waves are proposed to explain why the downstream northerlies disappear when the jet axis migrates beyond the northern edge of the plateau.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Spectral and temporal properties of optical signals with multiple sinusoidal phase modulations

Optical signals generated by multiple sinusoidal temporal phase modulations (multi-FMs) applied to a monochromatic field are studied from the viewpoint of their optical spectrum and temporal modulations arising from spectral impairments. Statistical analysis based on the central limit theorem shows that the signals' optical spectrum converges to a normal distribution as the number of modulations increases, allowing one to predict the frequency range containing a given fraction of the total energy with the associated cumulative density function. The conversion of frequency modulation to amplitude modulation is analyzed and simulated for arbitrary multi-FM signals. These developments are of theoretical and practical importance for high-energy laser systems, where optical pulses are phase modulated in the front end to smooth out the on-target beam profile and prevent potentially catastrophic damage to optical components.

Dorrer, C.↗
DOE OSTI2025

High-Resolution Simulations of Geological CO 2 Injection: Application to the SPE11 Benchmark

Geological carbon sequestration (GCS) will play a critical role in decarbonization and in facilitating the transition to clean energy systems. Because CO 2 is highly mobile, ensuring its safe and permanent injection into subsurface geological formations involves monitoring over larger spatial domains and longer time periods than is typical for hydrocarbon reservoirs. This can benefit from simulation tools capable of modeling key CO 2 trapping mechanisms, particularly those optimized for speed and scalability on high-performance computing systems. Using isothermal versions of the SPE11B and SPE11C benchmark cases, we conduct a mesh refinement study simulating CO 2 injection into kilometer-scale rock formations at centimeter resolution with the GEOS open-source simulation framework. We focus on how mesh refinement improves the accuracy of convective mixing in both 2D and 3D simulations. The computational costs associated with achieving a converged solution highlight the need for predictive upscaling techniques. A systematic performance scaling analysis—including both central processing unit (CPU) and graphics processing unit (GPU) architectures—complements the “Results” section.

Geosciences↗
DOE OSTI2017

Sampling-Based Motion Planning Algorithms for Replanning and Spatial Load Balancing

The common theme of this dissertation is sampling-based motion planning with the two key contributions being in the area of replanning and spatial load balancing for robotic systems. Here, we begin by recalling two sampling-based motion planners: the asymptotically optimal rapidly-exploring random tree (RRT*), and the asymptotically optimal probabilistic roadmap (PRM*). We also provide a brief background on collision cones and the Distributed Reactive Collision Avoidance (DRCA) algorithm. The next four chapters detail novel contributions for motion replanning in environments with unexpected static obstacles, for multi-agent collision avoidance, and spatial load balancing. First, we show improved performance of the RRT* when using the proposed Grandparent-Connection (GP) or Focused-Refinement (FR) algorithms. Next, the Goal Tree algorithm for replanning with unexpected static obstacles is detailed and proven to be asymptotically optimal. A multi-agent collision avoidance problem in obstacle environments is approached via the RRT*, leading to the novel Sampling-Based Collision Avoidance (SBCA) algorithm. The SBCA algorithm is proven to guarantee collision free trajectories for all of the agents, even when subject to uncertainties in the knowledge of the other agents’ positions and velocities. Given that a solution exists, we prove that livelocks and deadlock will lead to the cost to the goal being decreased. We introduce a new deconfliction maneuver that decreases the cost-to-come at each step. This new maneuver removes the possibility of livelocks and allows a result to be formed that proves convergence to the goal configurations. Finally, we present a limited range Graph-based Spatial Load Balancing (GSLB) algorithm which fairly divides a non-convex space among multiple agents that are subject to differential constraints and have a limited travel distance. The GSLB is proven to converge to a solution when maximizing the area covered by the agents. The analysis for each of the above mentioned algorithms is confirmed in simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Stochastic Richardson Extrapolation Based Numerical Error Estimation for Kinetic Plasma Simulations

We present a numerical error estimation technique specifically formulated to deal with stochastic code output with multiple discretization parameters. This method is based on multiple fits to an error model with arbitrary convergence rates and cross-coupling terms, performed using nonlinear optimization. The fitting approach varies by the type of residual norm which influences the importance of outliers, and weights which influences the relative importance of data points in the coarse and refined regions of discretization parameter space. To account for the influence of stochastic noise, these fits are performed on multiple bootstrap values based on the underlying response data set. Using an automated discretization domain selection scheme, the fits are performed on a series of reduced sets of discretization levels in order to find an optimal fully-converged result estimate in the minimum variance sense; this automated approach enables straightforward analysis of multiple quantities of interest and/or time and spatially-dependent response data. The overall numerical error analysis method is useful for verification and validation problems for stochastic simulation methods and forms a key component in the overall uncertainty quantification process. The method was demonstrated for steady and unsteady electron diode problems simulated using a particle-in-cell kinetic plasma code, demonstrating excellent results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1975

Numerical procedure for analyzing Langmuir probe data

A numerical procedure is proposed for analyzing Langmuir probe data in the presence of a two-group plasma containing both primary and Maxwellian electrons. The procedure is known as a least-squares differential-correction technique for determining the unknown coefficients of the governing equation. It is shown that for a given set of input data the results of the analysis are unique and independent of the initial estimate of electron temperature, that convergence is fastest when electron temperature is overestimated, that the results are sensitive to the region of the curve used as input and also to the voltage increment, and that plasma properties determined by the proposed numerical procedure are either consistent with those determined graphically or closer to expected values. With a suitable data acquisition system, the Fortran IV program worked out for this procedure could be used to provide real-time plasma diagnostic information for an operating ion thruster.

Beattie, J. R.↗
NASA NTRS1975

Design parameters for a stereoptic television system based on direct vision depth perception cues

Remotely controlled systems which use television for visual feedback require that depth cues be available to the operator. A number of techniques have been developed to provide stereoptic video. An analysis of parameters of such systems as related to the depth cues of convergence and retinal disparity was carried out. Parameter requirements were determined for the provision of natural and exaggerated stereoptic cues and expressions were developed for range resolution limits based on the retinal disparity threshold. An empirical study was conducted using a stereoptic video system to determine threshold values

Shields, N. L., Jr.↗