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At least 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Statistical Estimation of Strain Using Spatial Correlation Functions

Ex-situ estimation of strains from deformed micrographs is not possible as there are no persistent features which can be tracked. Two point spatial statistics enable the rigorous quantification of spatial patterns in heterogeneous media. In this paper, we propose a novel method for estimating strains directly from dissimilar micrographs using a continuum mechanics approach. Rather than operating directly on images from sequential frames, as is done in digital image correlation, we operate on different microstructure realizations. This is made possible by comparing the spatial autocorrelation maps of deformed and undeformed micrographs rather than direct comparison of images. Additionally, a Bayesian framework is proposed for quantifying uncertainty. We first illustrate the efficacy of this method on speckle pattern images from digital image correlation experiments. Then, we demonstrate that the method is capable of operating on dissimilar micrographs using deformed synthetic binary microstructures. Finally, we present a case study on polycrystalline additively manufactured 316L deformed via tension. The proposed method works well and we discuss implications and limitations of the presented work.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Dynamics, stability, and statistics on lattices and networks

These lectures aim at surveying some dynamical models that have been widely explored in the recent scientific literature as case studies of complex dynamical evolution, emerging from the spatio-temporal organization of several coupled dynamical variables. The first message is that a suitable mathematical description of such models needs tools and concepts borrowed from the general theory of dynamical systems and from out-of-equilibrium statistical mechanics. The second message is that the overall scenario is definitely reacher than the standard problems in these fields. For instance, systems exhibiting complex unpredictable evolution do not necessarily exhibit deterministic chaotic behavior (i.e., Lyapunov chaos) as it happens for dynamical models made of a few degrees of freedom. In fact, a very large number of spatially organized dynamical variables may yield unpredictable evolution even in the absence of Lyapunov instability. Such a mechanism may emerge from the combination of spatial extension and nonlinearity. Moreover, spatial extension allows one to introduce naturally disorder, or heterogeneity of the interactions as important ingredients for complex evolution. It is worth to point out that the models discussed in these lectures share such features, despite they have been inspired by quite different physical and biological problems. Along these lectures we describe also some of the technical tools employed for the study of such models, e.g., Lyapunov stability analysis, unpredictability indicators for “stable chaos,” hydrodynamic description of transport in low spatial dimension, spectral decomposition of stochastic dynamics on directed networks, etc.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

THE STATISTICAL MECHANICS OF PLANET ORBITS

The final “giant-impact” phase of terrestrial planet formation is believed to begin with a large number of planetary “embryos” on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities until their orbits cross and they collide and merge; through this process the number of surviving bodies declines until the system contains a small number of planets on well-separated, stable orbits. In this paper we explore a simple statistical model for the orbit distribution of planets formed by this process, based on the sheared-sheet approximation and the ansatz that the planets explore uniformly all of the stable region of phase space. The model provides analytic predictions for the distribution of eccentricities and semimajor axis differences, correlations between orbital elements of nearby planets, and the complete N-planet distribution function, in terms of a single parameter, the “dynamical temperature,” that is determined by the planetary masses. The predicted properties are generally consistent with N-body simulations of the giant-impact phase and with the distribution of semimajor axis differences in the Kepler catalog of extrasolar planets. A similar model may apply to the orbits of giant planets if these orbits are determined mainly by dynamical evolution after the planets have formed and the gas disk has disappeared.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Statistical mechanical model for crack growth

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. In this report an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.

36 MATERIALS SCIENCE↗
DOE OSTI2016

A statistical model of a metallic inclusion in semiconducting media

The properties of an isolated multicharged atom embedded into a semiconducting medium are discussed. The analysis generalizes the results of the known Thomas–Fermi theory for a multicharged (Z ≫ 1) atom in vacuum when it is immersed into an electron–hole gas of finite temperature. The Thomas–Fermi–Debye (TFD) atom problem is directly related to the properties of donors in low-doped semiconductors and is alternative in its conclusions to the ideal scenario of dissociation of donors. In the existing ideal statistics, an individual donor under infinitely low doping is completely ionized (a charged center does not hold its neutralizing counter-ions). A Thomas–Fermi–Debye atom (briefly, a TFD donor) remains a neutral formation that holds its screening “coat” even for infinitely low doping level, i.e., in the region of n{sub d}λ{sub 0}{sup 3} ≪ 1, where n{sub d} is the concentration of the doping impurity and λ{sub 0} is the Debye length with the parameters of intrinsic semiconductor. Various observed consequences in the behavior of a TFD donor are discussed that allow one to judge the reality of the implications of the TFD donor model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Statistical Methods and Tools for Hanford Staged Feed Tank Sampling

This report summarizes work conducted by Pacific Northwest National Laboratory to technically evaluate the current approach to staged feed sampling of high-level waste (HLW) sludge to meet waste acceptance criteria (WAC) for transfer from tank farms to the Hanford Waste Treatment and Immobilization Plant (WTP). The current sampling and analysis approach is detailed in the document titled Initial Data Quality Objectives for WTP Feed Acceptance Criteria, 24590-WTP-RPT-MGT-11-014, Revision 0 (Arakali et al. 2011). The goal of this current work is to evaluate and provide recommendations to support a defensible, technical and statistical basis for the staged feed sampling approach that meets WAC data quality objectives (DQOs).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Final Report for Statistical Nonlinear Optics of High Energy Density Plasmas: The Physics of Multiple Crossing Laser Beams

The various implementations of the STUD pulse program (spike trains of uneven duration and delay) for LPI (laser-plasma instability) control were studied in depth, and novel regimes were found. How to generate STUD pulses with large time-bandwidth products, how to measure their optical scattering signatures, and how to experimentally demonstrate their usefulness were explored. Theoretical and numerical studies were conducted on Stimulated Brillouin Scattering (SBS) and Crossed Beam Energy Transfer (CBET) including statistical models. We established how LPI can be tamed and gain democratized in space and time. Implementing STUD pulses on NIF was also studied. Future high rep rate lasers and fast diagnostics will aid in the adoption of the whole STUD pulse program for LPI control in High Energy Density Plasmas (HEDP).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Hybrid statistical testing for nuclear material accounting data and/or process monitoring data in nuclear safeguards

The aim of nuclear safeguards is to ensure that special nuclear material is used for peaceful purposes. Historically, nuclear material accounting (NMA) has provided the quantitative basis for monitoring for nuclear material loss or diversion, and process monitoring (PM) data is collected by the operator to monitor the process. PM data typically support NMA in various ways, often by providing a basis to estimate some of the in-process nuclear material inventory. We develop options for combining PM residuals and NMA residuals (residual = measurement - prediction), using a hybrid of period-driven and data-driven hypothesis testing. The modified statistical tests can be used on time series of NMA residuals (the NMA residual is the familiar material balance), or on a combination of PM and NMA residuals. The PM residuals can be generated on a fixed time schedule or as events occur.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1996

Testing of hypotheses about altitude decompression sickness by statistical analyses

This communication extends a statistical analysis of forced-descent decompression sickness at altitude in exercising subjects (J Appl Physiol 1994; 76:2726-2734) with a data subset having an additional explanatory variable, rate of ascent. The original explanatory variables for risk-function analysis were environmental pressure of the altitude, duration of exposure, and duration of pure-O2 breathing before exposure; the best fit was consistent with the idea that instantaneous risk increases linearly as altitude exposure continues. Use of the new explanatory variable improved the fit of the smaller data subset, as indicated by log likelihood. Also, with ascent rate accounted for, replacement of the term for linear accrual of instantaneous risk by a term for rise and then decay made a highly significant improvement upon the original model (log likelihood increased by 37 log units). The authors conclude that a more representative data set and removal of the variability attributable to ascent rate allowed the rise-and-decay mechanism, which is expected from theory and observations, to become manifest.

NASA Center JSC↗
NASA NTRS2020

Bayesian Statistical Models for Community Annoyance Survey Data

This paper demonstrates the use of two Bayesian statistical models to analyze single-event sonic boom exposure and human annoyance data from community response surveys. Each model is fit to data from a NASA pilot study.Unlike many community noise surveys, this study used a panel sample to collect multiple observations per participant instead of a single observation. Thus, a multilevel (also known as hierarchical or mixed-effects) model is used to account for the within-subject correlation in the panel sample data. This paper describes a multilevel logistic regression model and a multilevel ordinal regression model. The paper also proposes a method for calculating a summary dose-response curve from the multilevel models that represents the population. The two models’ summary dose-response curves are visually similar. However, their estimates differ when calculating the noise dose at a fixed percent highly annoyed.

Musical instruments↗
DOE OSTI2020

Enantioselective Intramolecular Allylic Substitution via Synergistic Palladium/Chiral Phosphoric Acid Catalysis: Insight into Stereoinduction through Statistical Modeling

The mode of asymmetric induction in an enantioselective intramolecular allylic substitution reaction catalyzed by a combination of palladium and a chiral phosphoric acid was investigated by a combined experimental and statistical modeling approach. Experiments to probe nonlinear effects, the reactivity of deuterium-labeled substrates, and control experiments revealed that nucleophilic attack to the π-allylpalladium intermediate is the enantio-determining step, in which the chiral phosphate anion is involved in stereoinduction. Here, using multivariable linear regression analysis, we determined that multiple noncovalent interactions with the chiral environment of the phosphate anion are integral to enantiocontrol in the transition state. The synthetic protocol to form chiral pyrrolidines was further applied to the asymmetric construction of C-O bonds at fully substituted carbon centers in the synthesis of chiral 2,2-disubstituted benzomorpholines.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Statistical analysis of an inter-laboratory comparison of small-scale safety and thermal testing of RDX

In this study, the Integrated Data Collection Analysis (IDCA) program has conducted a proficiency test for small-scale safety and thermal (SSST) testing of homemade explosives (HMEs). Described here are statistical analyses of the results from this test for impact, friction, electrostatic discharge, and differential scanning calorimetry analysis of the RDX Class 5 Type II standard. The material was tested as a well-characterized standard several times during the proficiency test to assess differences among participants and the range of results that may arise for well-behaved explosive materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Statistical framework to assess long-term spatio-temporal climate changes: East River mountainous watershed case study

Abstract Evaluation of long-term temporal and spatial climatic change in mountainous regions is a critical challenge because of the interactive effects of multiple land and climatic factors and processes. Here we present the application of the statistical framework to the assessment of changes of climatic conditions, using data from 17 meteorological stations across the East River watershed near Crested Butte, Colorado, USA, and spanning the period from 1966 to 2021. The framework is developed based on (1) a time-series analysis of daily, monthly, and yearly averaged meteorological parameters (temperature, relative humidity, precipitation, wind speed, etc.), (2) evaluation and time series analysis of potential evapotranspiration (ET o ), actual evapotranspiration (ET), aridity index (AI), standard precipitation index (SPI) and standard precipitation-evapotranspiration index (SPEI), and (3) a temporal-spatial climatic zonation of the studied area based on the hierarchical clustering and PCA analysis of the SPEI, because the SPEI can be considered an integrative characteristic of the changes of climatic conditions. The Budyko model, with the application of the Penman–Monteith equation for the estimation of ET o , was used to determine the ET. The time series analysis of the AI is used to identify the periods with energy limited and water limited conditions. Hierarchical clustering of site locations for the three temporal segments of the SPEI showed a significant temporal-spatial shifts, indicating that dynamic climatic processes drive zonation patterns. Therefore, the watershed climatic zonation requires periodic re-evaluation based on the structural time series analysis of meteorological and water balance data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Stochastic Spatial Models in Ecology: A Statistical Physics Approach

Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions accounting for general empirical patterns in communities of competing species. However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several open problems, limiting the quantitative understanding of spatial biodiversity. In this review, we discuss the state of the art in spatial neutral theory. We emphasize the connection between spatial ecological models and the physics of non-equilibrium phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa. We focus on non-trivial scaling laws arising at the critical dimension D=2 of spatial neutral models, and their relevance for biological populations inhabiting two-dimensional environments. We conclude by discussing models incorporating non-neutral effects in the form of spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Statistical Analysis of the First Passage Path Ensemble of Jump Processes

The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Statistical Physics Approach to Thermophoresis of Colloids

Brownian colloidal particles dispersed in a fluid with a temperature gradient experience a driving force which produces a large biased steady density profile. This phenomenon, named thermophoresis, is quantified by the Soret coefficient S{sub T}. This problem is studied here within the Fokker–Planck formalism. Using the experimental observation of S{sub T} it is possible to extract relevant analytical information about a temperature dependent nonequilibrium effective potential which can produce the thermophoresis force. It will be presented here a statistical physics derivation of this effective potential in terms of some physical parameters. Experimental data are analyzed within this theoretical scenario.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

D-Guaranteed Discrimination of Statistical Hypotheses: a Review of Results and Unsolved Problems

We compare two sequential d-guaranteed tests and an optimal d-guaranteed test based on a fixed number of observations with respect to the average number of observations within the most accepted practical applications of Bayesian probabilistic models. We consider the sequential “first skipping” test, the sequential locally efficient test based on the score statistic, and the test based on a fixed number of observations that minimizes the necessary sample size. We study various characteristics of these tests connected with the number of observations within three probabilistic models, namely, the normal (ϑ, σ{sup 2}) distribution of the observed random variable and the normal a priori distribution of ϑ with fixed σ{sup 2}; the exponential distribution with the intensity parameter ϑ and the a priori gamma distribution of ϑ; and the Bernoulli sampling with the success probability ϑ and the a priori beta distribution of ϑ. We discuss the connection of the d-posterior approach with the compound decision problem as applied to the analysis of data provided by microchips (when the false discovery rate, or FDR, for short, is treated as the d-risk of the first kind). We present the vast data on characteristics of the mentioned tests obtained by the method of mathematical modeling in several tables. We discuss unsolved problems of the d-guaranteed discrimination of hypotheses with the minimal number of observations and approaches to their solution.

97 MATHEMATICS AND COMPUTING↗