Results for “sufficient statistics” — Page 9

DOE OSTI2021

Simulated effects of sample size and grain neighborhood on the modeling of extreme value fatigue response

Assessing the size of representative volume elements (RVEs) for fatigue-related applications is challenging. A RVE relevant to random microstructure requires a volume of material that is sufficiently large to capture the grain/phase heterogeneity that captures all statistical moments of the distribution of the driving force for fatigue crack formation at “hot spot” grains. Consequently, the large size of a microstructure RVE required to study fatigue phenomena is largely computationally intractable and difficult to explore. A more realistic objective in this work is to systematically study, as a function of the size of a statistical sample of microstructure, trends towards convergence of the simulated distribution of driving force for fatigue crack formation. Our present work accordingly leverages the recently developed open-source PRISMS-Fatigue framework to examine the trends in convergence of extreme value distributions (EVD) of Fatigue Indicator Parameters (FIPs) in progressively larger polycrystalline microstructure realizations of FCC Al alloy 7075-T6 using crystal plasticity finite element method simulations. The results are compared to the traditional method in which ensembles of statistical volume elements (SVEs) are simulated to build up statistics intended to approximate those associated with a larger volume of material. The convergence of EVDs with increase of size of a SVE of microstructure is closely related to the extent of grain nearest neighbor (NN) interactions. Accordingly, the sensitivity of the local micromechanical response at hot spot grains is quantitatively investigated by systematically varying the orientations of NN grains. Results indicate that SVEs with cubic crystallographic texture tend towards convergence of the EVD of FIPs with tens of thousands of grains while the random and rolled textures require larger volumes. Simple relationships based on microstructure parameters (e.g., Schmid Factor, grain size, NN misorientation) do not completely correlate to fatigue hot spot grains. Finally, the sensitivity of the extreme value fatigue response at hot spot grains extends to the 3rd NN when a single neighborhood grain orientation is altered.

36 MATERIALS SCIENCE↗

DOE OSTI2021

The impact of void environment on AGN

ABSTRACT We study the population of active galaxies in void environment in the Sloan Digital Sky Survey. We use optical spectroscopic information to analyse characteristics of the emission lines of galaxies, accomplished by WHAN and BPT diagrams. Also, we study Wide-field Infrared Survey Explorer(WISE) mid-IR colours to assess active galactic nucleus (AGN) activity. We investigate these different AGN classification schemes, both optical and mid-IR, and their dependence on the spatial location with respect to the void centres. To this end, we define three regions: void, the spherical region defined by voidcentric distance relative to void radius (distance/rvoid) smaller than 0.8, comprising overdensities lesser than −0.9, an intermediate/transition shell region (namely, void-wall) 0.8 < distance/rvoid < 1.2, and a region sufficiently distant from voids, the field: distance/rvoid > 2. We find statistical evidence for a larger fraction of AGN and star-forming galaxies in the void region, regardless of the classification scheme addressed (either BPT, WHAN, or WISE). Moreover, we obtain a significantly stronger nuclear activity in voids compared to the field. We find an unusually large fraction of the most massive black holes undergoing strong accretion when their host galaxies reside in voids. Our results suggest a strong influence of the void environment on AGN mechanisms associated with galaxy evolution.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Neural network based emulation of galaxy power spectrum covariances: A reanalysis of BOSS DR12 data

We train neural networks to quickly generate redshift-space galaxy power spectrum covariances from a given parameter set (cosmology and galaxy bias). This covariance emulator utilizes a combination of traditional fully connected network layers and transformer architecture to accurately predict covariance matrices for the high redshift, north galactic cap sample of the BOSS DR12 galaxy catalog. We run simulated likelihood analyses with emulated and brute-force computed covariances, and we quantify the network’s performance via two different metrics: (1) difference in Χ 2 and (2) likelihood contours for simulated BOSS DR 12 analyses. We find that the emulator returns excellent results over a large parameter range. We then use our emulator to perform a reanalysis of the BOSS HighZ NGC galaxy power spectrum, and find that varying covariance with cosmology along with the model vector produces Ω m = $0.27⁢6$$^{+0.013}_{–0.015}$, H 0 = 70.2 ± 1.9 km/s/Mpc, and σ 8 = $0.67⁢4$$^{+0.058}_{–0.077}$. These constraints represent an average 0.46⁢σ shift in best-fit values and a 5% increase in constraining power compared to fixing the covariance matrix (Ω m = 0.293 ± 0.017, H 0 = 70.3 ± 2.0 km/s/Mpc, σ 8 = $0.70⁢2$$^{+0.063}_{–0.075}$). As a result, this work demonstrates that emulators for more complex cosmological quantities than second-order statistics can be trained over a wide parameter range at sufficiently high accuracy to be implemented in realistic likelihood analyses.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

SpotSDC: Revealing the Silent Data Corruption Propagation in High-Performance Computing Systems

We report the trend of rapid technology scaling is expected to make the hardware of high-performance computing (HPC) systems more susceptible to computational errors due to random bit flips. Some bit flips may cause a program to crash or have a minimal effect on the output, but others may lead to silent data corruption (SDC), i.e., undetected yet significant output errors. Classical fault injection analysis methods employ uniform sampling of random bit flips during program execution to derive a statistical resiliency profile. However, summarizing such fault injection result with sufficient detail is difficult, and understanding the behavior of the fault-corrupted program is still a challenge. In this article, we introduce SpotSDC, a visualization system to facilitate the analysis of a program's resilience to SDC. SpotSDC provides multiple perspectives at various levels of detail of the impact on the output relative to where in the source code the flipped bit occurs, which bit is flipped, and when during the execution it happens. SpotSDC also enables users to study the code protection and provide new insights to understand the behavior of a fault-injected program. Based on lessons learned, we demonstrate how what we found can improve the fault injection campaign method.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1964

Monte Carlo techniques for solving transport problems

The Monte Carlo procedure is a model sampling technique. A model is established, and the behavior of sample units in this model is followed. A sufficient number of sample units are followed to obtain a statistical average or macroscopic quantities, which are the quantities of interest. This technique was used in crude form by Fermi in connection with the building of the first atomic pile. Later, Von Neumann and Ulam developed and used the Monte Carlo procedure extensively in developing the atomic bomb. Since then this technique has gained considerable use in nuclear reactor problems (refs. 1 and 2), and we at the Lewis Research Center have been extending it to thermal radiation (refs. 3 and 4), rarefied gas flows, and plasma flow problems (ref. 5). This technique, which requires a large number of sample histories to obtain solutions with small variances, is receiving greater use because of the development of the high-speed electronic computers.

SAMPLED DATA SYSTEM↗

NASA NTRS1990

Imaging other planetary systems from the moon

This paper studies the problem of using a telescope like the HST, only larger and sensitive to a wider range of wavelengths, to image systems of planets like the solar system around other stars. Both reflected starlight and thermal radiation from the planets are treated. The instrumental effects of aperture diffraction, scattering due to the power spectral density of telescope mirror surface errors, and telescope thermal emission are included. The integration time required to achieve a signal-to-noise ratio is computed at 5 for photon-statistical random errors only, which is a necessary but not sufficient criterion for detection at a confidence level of five standard deviations. A cold telescope on the moon with 16m aperture and the optical quality of HST could detect and characterize planets around nearby stars.

Brown, Robert A.↗

NASA NTRS2010

Time-Dependent Selection of an Optimal Set of Sources to Define a Stable Celestial Reference Frame

Temporal statistical position stability is required for VLBI sources to define a stable Celestial Reference Frame (CRF) and has been studied in many recent papers. This study analyzes the sources from the latest realization of the International Celestial Reference Frame (ICRF2) with the Allan variance, in addition to taking into account the apparent linear motions of the sources. Focusing on the 295 defining sources shows how they are a good compromise of different criteria, such as statistical stability and sky distribution, as well as having a sufficient number of sources, despite the fact that the most stable sources of the entire ICRF2 are mostly in the Northern Hemisphere. Nevertheless, the selection of a stable set is not unique: studying different solutions (GSF005a and AUG24 from GSFC and OPA from the Paris Observatory) over different time periods (1989.5 to 2009.5 and 1999.5 to 2009.5) leads to selections that can differ in up to 20% of the sources. Observing, recording, and network improvement are some of the causes, showing better stability for the CRF over the last decade than the last twenty years. But this may also be explained by the assumption of stationarity that is not necessarily right for some sources.

Le Bail, Karine↗

NASA NTRS2016

Development and Evaluation of High-Resolution Climate Simulations Over the Mountainous Northeastern United States

The mountain regions of the northeastern United States are a critical socioeconomic resource for Vermont, New York State, New Hampshire, Maine, and southern Quebec. While global climate models (GCMs) are important tools for climate change risk assessment at regional scales, even the increased spatial resolution of statistically downscaled GCMs (commonly approximately 1/ 8 deg) is not sufficient for hydrologic, ecologic, and land-use modeling of small watersheds within the mountainous Northeast. To address this limitation, an ensemble of topographically downscaled, high-resolution (30"), daily 2-m maximum air temperature; 2-m minimum air temperature; and precipitation simulations are developed for the mountainous Northeast by applying an additional level of downscaling to intermediately downscaled (1/ 8 deg) data using high-resolution topography and station observations. First, observed relationships between 2-m air temperature and elevation and between precipitation and elevation are derived. Then, these relationships are combined with spatial interpolation to enhance the resolution of intermediately downscaled GCM simulations. The resulting topographically downscaled dataset is analyzed for its ability to reproduce station observations. Topographic downscaling adds value to intermediately downscaled maximum and minimum 2-m air temperature at high-elevation stations, as well as moderately improves domain-averaged maximum and minimum 2-m air temperature. Topographic downscaling also improves mean precipitation but not daily probability distributions of precipitation. Overall, the utility of topographic downscaling is dependent on the initial bias of the intermediately downscaled product and the magnitude of the elevation adjustment. As the initial bias or elevation adjustment increases, more value is added to the topographically downscaled product.

climatology↗

DOE OSTI2022

The DESI N -body simulation project – I. Testing the robustness of simulations for the DESI dark time survey

ABSTRACT Analysis of large galaxy surveys requires confidence in the robustness of numerical simulation methods. The simulations are used to construct mock galaxy catalogues to validate data analysis pipelines and identify potential systematics. We compare three N-body simulation codes, abacus, gadget-2, and swift, to investigate the regimes in which their results agree. We run N-body simulations at three different mass resolutions, 6.25 × 108, 2.11 × 109, and 5.00 × 109 h−1 M⊙, matching phases to reduce the noise within the comparisons. We find systematic errors in the halo clustering between different codes are smaller than the Dark Energy Spectroscopic Instrument (DESI) statistical error for $s\ \gt\ 20\ h^{-1}$ Mpc in the correlation function in redshift space. Through the resolution comparison we find that simulations run with a mass resolution of 2.1 × 109 h−1 M⊙ are sufficiently converged for systematic effects in the halo clustering to be smaller than the DESI statistical error at scales larger than $20\ h^{-1}$ Mpc. These findings show that the simulations are robust for extracting cosmological information from large scales which is the key goal of the DESI survey. Comparing matter power spectra, we find the codes agree to within 1 per cent for k ≤ 10 h Mpc−1. We also run a comparison of three initial condition generation codes and find good agreement. In addition, we include a quasi-N-body code, FastPM, since we plan use it for certain DESI analyses. The impact of the halo definition and galaxy–halo relation will be presented in a follow-up study.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2007

Star Confusion Effect on SIM PlanetQuest Astrometric Performance

SIM PlanetQuest will measure star positions to an accuracy of a few microarcseconds using precise white light fringe measurements. One challenge for SIM observation scenario is "star confusion," where multiple stars are present in the instrument field of view. This is especially relevant for observing dim science targets because the density of number of stars increases rapidly with star magnitude. We study the effect of star confusion on the SIM astrometric performance due to systematic fringe errors caused by the extra photons from the confusion star(s}. Since star confusion from multiple stars may be analyzed as a linear superposition of the effect from single star confusion, we quantify the astrometric errors due to single star confusion surveying over many spectral types, including AOV, FOV, K5III, and MOV, and for various visual magnitude differences. To the leading order, the star confusion effect is characterized by the magnitude difference, spectral difference, and the angular separation between the target and confusion stars.Strategies for dealing with star confusion are presented. For example, since the presence of additional sources in the field of view leads to inconsistent delay estimates from different channels, with sufficient signal to noise ratio, the star confusion can be detected using chi-square statistics of fringe measurements from multiple spectral channels. An interesting result is that the star confusion can be detected even though the interferometer cannot resolve the separation between the target and confusion stars when their spectra are sufficiently different. Other strategies for mitigating the star confusion effect are also discussed.

crowded field↗

NASA NTRS1983

Troposphere-stratosphere (surface-55 km) monthly winter general circulation statistics for the Northern Hemisphere Four year averages

In response to theoretically predicted anthropogenic depletion of stratospheric ozone, there has been, in recent years, an increased effort in stratospheric modeling. For comparison between models and observations, it is not sufficient to only compare the morphology of model-generated parameters with observed parameter values. Model-generated statistics should also be compared with observation. It is one of the objectives of the present investigation to discuss a data set which can be used for this purpose for the Northern Hemisphere troposphere and stratosphere. However, the investigation is mainly concerned with a presentation of some of the general circulation statistics derived with the aid of the data set. Attention is given to winter monthly general circulation statistics which were derived from four years of daily 1200 GMT NOAA/NMC Northern Hemisphere analyses.

Geller, M. A.↗

NASA NTRS2014

Statistical Mechanics of Turbulent Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V.↗

NASA NTRS2014

MHD Turbulence and Magnetic Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V↗

DOE OSTI2021

Using statistical modeling to predict and understand fusion experiments

Over 300 cryogenic layered direct-drive inertial confinement fusion implosions have been successfully executed on the OMEGA Laser System in the last decade. However, extracting sufficient understanding from these experiments to develop new designs or to identify or mitigate degradation sources remains challenging. Recently, a statistical modeling approach was developed to successfully design and predict improved implosion experiments on OMEGA. Here, we show that one-dimensional simulations can be used to predict the outcomes of systematically perturbed three-dimensional simulations and that this statistical modeling approach can be used to identify or rule out physical mechanisms for some of the degradation sources observed on the OMEGA Laser System for direct-drive cryogenic inertial confinement fusion. In this instance, we investigate the fusion yield dependencies on the ion temperature asymmetries and laser beam size observed in experiments by comparing with trends in three-dimensional synthetic simulation databases. Using the statistical model on these systematically perturbed simulations, we find that the statistically inferred dependency on the measured ion temperature asymmetries is well explained by imposed ℓ =1 modes. However, we find that the dependency on the laser beam size is only dominated by the illumination non-uniformity for some extreme cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

The Maximal Entanglement Limit in Statistical and High-energy Physics

These lectures advocate the idea that quantum entanglement provides a unifying foundation for both statistical physics and high-energy interactions. I argue that, at sufficiently long times or high energies, most quantum systems approach a Maximal Entanglement Limit (MEL) in which phases of quantum states become unobservable, reduced density matrices acquire a thermal form, and probabilistic descriptions emerge without invoking ergodicity or classical randomness. Within this framework, the emergence of probabilistic parton model, thermalization in the break-up of confining strings and in high-energy collisions, and the universal small-x behavior of structure functions arise as direct consequences of entanglement and geometry of high-dimensional Hilbert space.

36 MATERIALS SCIENCE↗

NASA NTRS1980

On the simultaneous analysis of several complete samples - The V/Vmax and Ve/Va variables, with applications to quasars

Methods are derived for applying the V/Vmax variable when several complete samples are analyzed simultaneously. A new, related, variable, V(e)/V(a), which is superior to V/Vmax when sufficient observational data are available, is introduced. It is shown how statistically independent complete samples can be generated from partially overlapping samples such that each observed object appears only once in the analysis. These methods make it possible to combine the information from different complete samples, and to make an efficient use of all available data. Illustrative examples for quasars are given. It is shown how the generalized V/Vmax and V(e)/V(a) can be used to find the amount of cosmological evolution of quasars and its associated range of uncertainty.

Avni, Y.↗

NASA NTRS1991

Pluto-Charon stellar occultation candidates - 1990-1995

A search to identify stars that might be occulted by Pluto or Charon during the period 1990-1995 and part of 1996 is studied. This search was made with an unfiltered CCD camera operated in the strip scanning mode, and it reaches an R magnitude of approximately 17.5 - about 1.5 mag fainter than previous searches. Circumstances for each of the 162 potential occultations are given, including an approximate R magnitude of the star, which allows estimation of the signal-to-noise ratio (S/N) for observation of each occultation. The faintest stars in the list would yield an S/N of about 20 for a 1 s integration when observed with a CCD detector on an 8 m telescope under a dark sky. The astrometric precision (+/- 0.2 arcsec, with larger systematic errors possible for individual cases) is insufficient to serve as a final prediction for these potential occultations, but is sufficient to identify stars deserving of further, more accurate, astrometric observations. Statistically, about 32 of these events to be observable somewhere on earth are expected. The number of events actually observed will be substantially smaller because of clouds and the sparse distribution of large telescopes. Finder charts for each of the 91 stars involved are presented.

Dunham, E. W.↗

NASA NTRS1991

Center for Space Power, Texas A and M University

Johnson Controls is a 106 year old company employing 42,000 people worldwide with $4.7 billion annual sales. Though we are new to the aerospace industry we are a world leader in automobile battery manufacturing, automotive seating, plastic bottling, and facilities environment controls. The battery division produces over 24,000,000 batteries annually under private label for the new car manufacturers and the replacement market. We are entering the aerospace market with the nickel hydrogen battery with the help of NASA's Center for Space Power at Texas A&M. Unlike traditional nickel hydrogen battery manufacturers, we are reaching beyond the space applications to the higher volume markets of aircraft starting and utility load leveling. Though space applications alone will not provide sufficient volume to support the economies of scale and opportunities for statistical process control, these additional terrestrial applications will. For example, nickel hydrogen batteries do not have the environmental problems of nickel cadmium or lead acid and may someday start your car or power your electric vehicle. However you envision the future, keep in mind that no manufacturer moves into a large volume market without fine tuning their process. The Center for Space Power at Texas A&M is providing indepth technical analysis of all of the materials and fabricated parts of our battery as well as thermal and mechanical design computer modeling. Several examples of what we are doing with nickel hydrogen chemistry to lead to these production efficiencies are presented.

Jones, Ken↗