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At least 343 records · Page 19

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DOE OSTI2021

Generalized Bayesian Framework for Evaluation of Integral Benchmark Experiments

A recently published generalized Bayesian optimization framework has provided a way to retract any or all of the three common assumptions underlying the conventional Generalized Linear Least Squares (GLLS) optimization method based on the concepts introduced in reference two. These assumptions are: 1. Perfection: The model used for data evaluation and the prior probability distribution function (PDF) of generalized* data are perfect; 2. Normality: The prior and posterior PDF are normal; and 3. Linearity: The model is linear. In this work we outline how the framework in 1 could be directly adopted for improved evaluation of nuclear criticality integral benchmark experiments (IBEs) by: 1. Removing the first assumption alone by utilizing the concept of imperfections introduced in 1 to enable evaluation in the presence of discrepancies between the data and model or of missing covariance information by a GLLS method that will be seen as a generalization of the conventional GLLS method employed by the TSURFER code, and by 2. Removing the remaining two assumptions by implement- ing a Markov Chain Monte Carlo method for computation of the posterior PDF in the SAMPLER code, where TSURFER and SAMPLER are the uncertainty quantification (UQ) codes for IBEs in the SCALE code system based on the GLLS, and the stochastic method, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Bayesian Monte Carlo Evaluation Framework for Imperfect Data and Models [Abstract]

Nuclear data evaluation methods conventionally make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate for minimization of a cost function (even for non-linear models); and that both the model (of, e.g., neutron cross section) and experimental data (including their covariance data) are perfect. These assumptions are inherent to the well-known generalized linear least squares (GLLS) minimization method commonly used for evaluations of resolved resonance region (RRR) neutron cross sections. However, these assumptions are often not justified due to the presence of non-normal PDFs, non-linear models (e.g. R -matrix formalism), and inherent imperfections in data and models (e.g. discrepant data sets, discrepancies between the previous evaluation and newly measured data, or imperfect covariance data). We remove the said assumptions in a mathematical framework of Bayes’ theorem, and implement it using the Metropolis-Hastings Monte Carlo method. Parameters of a new kind are introduced to parameterize inherent imperfections, e.g. , any discrepancies between the theoretical model and measured data. These new parameters enable evaluators to quantify their expert judgement about any discrepancies or imperfections in a reproducible manner. We demonstrate the framework with an ongoing evaluation of 233 U in the eV region using the ENDF-B/VIII library and transmission data measured by Guber, et al. , and compare the posterior parameters to those obtained by conventional evaluation methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2013

Estimating anisotropic diffusion of neutrons near the boundary of a pebble bed random system

Due to the arrangement of the pebbles in a Pebble Bed Reactor (PBR) core, if a neutron is located close to a boundary wall, its path length probability distribution function in directions of flight parallel to the wall is significantly different than in other directions. Hence, anisotropic diffusion of neutrons near the boundaries arises. We describe an analysis of neutron transport in a simplified 3-D pebble bed random system, in which we investigate the anisotropic diffusion of neutrons born near one of the system's boundary walls. While this simplified system does not model the actual physical process that takes place near the boundaries of a PBR core, the present work paves the road to a formulation that may enable more accurate diffusion simulations of such problems to be performed in the future. Monte Carlo codes have been developed for (i) deriving realizations of the 3-D random system, and (ii) performing 3-D neutron transport inside the heterogeneous model; numerical results are presented for three different choices of parameters. These numerical results are used to assess the accuracy of estimates for the mean-squared displacement of neutrons obtained with the diffusion approximations of the Atomic Mix Model and of the recently introduced [1] Non-Classical Theory with angular-dependent path length distribution. The Non-Classical Theory makes use of a Generalized Linear Boltzmann Equation in which the locations of the scattering centers in the system are correlated and the distance to collision is not exponentially distributed. We show that the results predicted using the Non-Classical Theory successfully model the anisotropic behavior of the neutrons in the random system, and more closely agree with experiment than the results predicted by the Atomic Mix Model. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2015

Calculation and use of pointwise effective cross-sections in the unresolved resonance region - 14605

The pointwise neutron elastic scattering, absorption, fission and total cross-sections in the Unresolved Resonance Region (URR) can be calculated with a code C-007 [1]. The volume of these data is large and estimated to make about 106 numbers for each of the reactions. These data volumes may cause time and memory problems in solving radiation transport by the Monte Carlo method. There are methods to thin the data. These are, for example, the widely used probability tables [2] and subgroups [3]. The paper offers another data thinning approach which was successfully used for the Resolved Resonance Region (RRR) [4,5]. It transforms the pointwise resonance cross-sections into the pointwise monotone ones within some energy intervals with the use of cross-section probability distribution functions P(σ). A similar approach was used to calculate pointwise cross-sections in the URR [6]. (authors)

42 ENGINEERING↗

DOE OSTI2022

Thermal scattering law for structure-dependent-Doppler broadening in FLASSH

Traditional Doppler broadening methods assume that target nuclei velocities follow a Maxwell-Boltzmann distribution which inherently assumes that the atoms are a free gas or that their velocities are independent of each other. This approximation is reasonable at high target temperatures and high neutron energies. However, nuclei are not independent: the lattice temperature and chemical binding will define the atomic motion. The thermal scattering law (i.e., TSL or S(α,β)) is a material property which describes the chemical binding and temperature response in terms of available momentum and energy states. In the thermal energy range, this TSL will define the thermal scattering cross sections. In the resonance region, the TSL offers a first-principles description of the probability distribution function for the velocity of the target nuclei. Using the TSL in Doppler broadening captures the structure of the material consistently from the thermal range into the resonance cross sections. In this work, both traditional free-gas and precise TSL Doppler broadening methods for resonance cross section evaluation have been implemented within the Full Law Analysis Scattering System Hub (FLASSH). This framework provides a generalized formulation for evaluating low-lying resonance data and streamlines nuclear data processing methods. TSL data generated using ab initio lattice dynamics (AILD) can be used to broaden cross section libraries in ENDF format for high-fidelity input into reactor physics calculations. These capabilities are demonstrated for the lowest absorption resonances of {sup 238}U in UO{sub 2}, UC and UN. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Data-driven predictive probability density function control of fiber length stochastic distribution shaping in refining process

Pulp is the most important raw material in paper in paper industries, whose Fiber Length Stochastic Distribution (FLSD) shaping directly determines the energy consumption and paper quality of the subsequent papermaking processes. However, the mean and variance are insufficient to describe the output FLSD shaping, which display non-Gaussian distribution properties. Therefore, the traditional control, method based on the mean and variance of fiber length is difficult to control the FLSD shaping effectively. In this paper, a novel data-driven predictive probability density function (PDF) control method is proposed for output FLSD shaping in refining process. Primarily, in order to improve the approximation accuracy of the PDF employing RBF neural network, the parameters (center value and width) of each RBF basis functions are tuned via utilizing iterative learning control (ILC) law, and the corresponding estimations of weights law can be obtained. Secondly, considering that the conventional linear model of weights vector has drawbacks of low accuracy and weak generalization ability, random vector functional link networks (RVFLNs) based data driven nonlinear modelling method is employed to characterize the prediction model between the input variables and weights vector. Finally, in order to reduce the randomness of the output FLSD, a minimum entropy control method under mean constraint is employed to design the predictive PDF controller for the output FLSD shaping with the help of the established nonlinear stochastic distribution model. Both simulations and experiments are given to illustrate the effectiveness and practicability of the proposed method.

Probability debsity function, Fiber length distrib↗

DOE OSTI2021

An efficient method to estimate the probability density of seismic Green's functions

We present a computationally efficient method to approximate the probability distribution of seismic Green's functions given the uncertainty of an Earth model. The method is based on the Karhunen-Loève (KL) theorem and an approximation of the Green's function (or seismogram) covariance. Using Monte Carlo (MC) simulations as a control case, we demonstrate that our KL-based method can accurately reproduce a probability distribution of seismograms that results from an uncertain Earth model for a MC-derived seismogram covariance. We then describe a method to estimate the covariance of the seismograms resulting from those Earth models that is not based on MC simulations. We use the estimated Green's function covariance in conjunction with our KL-based method to produce a Green's function probability distribution, and compare that distribution to a Green's function probability distribution produced using a MC finite difference method. We find that the Green's function probability distribution approximated using our KL-based method generally mimics that produced using the MC simulations, especially for direct-arriving body waves. However the accuracy of the KL-based method generally decreases for later times in the simulated Green's function distribution.

58 GEOSCIENCES↗

DOE OSTI2018

Stochastic Optimal Power Flow Based on Data-Driven Distributionally Robust Optimization

We propose a data-driven method to solve a stochastic optimal power flow (OPF) problem based on limited information about forecast error distributions. The objective is to determine power schedules for controllable devices in a power network to balance operational cost and conditional value-at-risk (CVaR) of device and network constraint violations. These decisions include scheduled power output adjustments and reserve policies, which specify planned reactions to forecast errors in order to accommodate fluctuating renewable energy sources. Instead of assuming the uncertainties across the networks follow prescribed probability distributions, we assume the distributions are only observable through a finite training dataset. By utilizing the Wasserstein metric to quantify differences between the empirical data-based distribution and the real data-generating distribution, we formulate a distributionally robust optimization OPF problem to search for power schedules and reserve policies that are robust to sampling errors inherent in the dataset. A multi-stage closed-loop control strategy based on model predictive control (MPC) is also discussed. A simpIe numerical example illustrates inherent tradeoffs between operational cost and risk of constraint violation, and we show how our proposed method offers a data-driven framework to balance these objectives.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2011

The energy level shifts, wave functions and the probability current distributions for the bound scalar and spinor particles moving in a uniform magnetic field

We discuss the equations for the bound one-active electron states based on the analytic solutions of the Schrödinger and Pauli equations for a uniform magnetic field and a single attractive δ(r )-potential. We show that the magnetic field indeed plays a stabilizing role in considered systems in a case of the weak intensity, but the opposite occurs in the case of strong intensity. These properties may be important for real quantum mechanical fermionic systems in two and three dimensions. In addition, we obtained that including the spin in the framework of the nonrelativistic approach allows correctly taking the effect of the magnetic field on the electric current into account.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2012

Transversity from First Principles in QCD

Transversity observables, such as the T-odd Sivers single-spin asymmetry measured in deep inelastic lepton scattering on polarized protons and the distributions which are measured in deeply virtual Compton scattering, provide important constraints on the fundamental quark and gluon structure of the proton. In this talk I discuss the challenge of computing these observables from first principles; i.e.; quantum chromodynamics, itself. A key step is the determination of the frame-independent light-front wavefunctions (LFWFs) of hadrons - the QCD eigensolutions which are analogs of the Schroedinger wavefunctions of atomic physics. The lensing effects of initial-state and final-state interactions, acting on LFWFs with different orbital angular momentum, lead to T-odd transversity observables such as the Sivers, Collins, and Boer-Mulders distributions. The lensing effect also leads to leading-twist phenomena which break leading-twist factorization such as the breakdown of the Lam-Tung relation in Drell-Yan reactions. A similar rescattering mechanism also leads to diffractive deep inelastic scattering, as well as nuclear shadowing and non-universal antishadowing. It is thus important to distinguish 'static' structure functions, the probability distributions computed the target hadron's light-front wavefunctions, versus 'dynamical' structure functions which include the effects of initial- and final-state rescattering. I also discuss related effects such as the J = 0 fixed pole contribution which appears in the real part of the virtual Compton amplitude. AdS/QCD, together with 'Light-Front Holography', provides a simple Lorentz-invariant color-confining approximation to QCD which is successful in accounting for light-quark meson and baryon spectroscopy as well as hadronic LFWFs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Survey on stochastic distribution systems: A full probability density function control theory with potential applications

Complex systems seen either in general engineering practice or economics are subjected to ever increased uncertainties that are mostly represented as random variables or parameters, and the characteristics of random variables are represented by their probability density functions (PDFs). Controlling their PDFs means to shape their stochastic distributions and in general it would provide a full treatment for system analysis and operational control and optimization. This leads to the development of stochastic distribution control (SDC) systems theory in the past decades, where the original aim of the controller design is to realize a shape control of the distributions of certain random variables in their PDFs sense for some engineering processes. Indeed, once the PDFs of these random variables or parameters are used to describe their distribution characters, the control task is to obtain control signals so that the output PDFs of stochastic systems are made to follow their target PDFs. The subject of SDC was initially originated for non-Gaussian stochastic control systems design but has found a wide spectrum of applications in general systems in terms of data-driven modeling, analysis, signal processing (filtering), data mining via multivariable statistics, decision-making (optimization) for systems subjected to uncertainties and even in economics. In this context, SDC constitutes an effective primer tool for complex system analysis, control and operational optimizations. In this review paper, a detailed survey of the developments on the research of SDC systems will be made together with their wide spectrum applications and future perspectives.

42 ENGINEERING↗

DOE OSTI2011

Novel QCD Phenomenology

I review a number of topics where conventional wisdom in hadron physics has been challenged. For example, hadrons can be produced at large transverse momentum directly within a hard higher-twist QCD subprocess, rather than from jet fragmentation. Such 'direct' processes can explain the deviations from perturbative QCD predictions in measurements of inclusive hadron cross sections at fixed x{sub T} = 2p{sub T}/{radical}s, as well as the 'baryon anomaly', the anomalously large proton-to-pion ratio seen in high centrality heavy ion collisions. Initial-state and final-state interactions of the struck quark, the soft-gluon rescattering associated with its Wilson line, lead to Bjorken-scaling single-spin asymmetries, diffractive deep inelastic scattering, the breakdown of the Lam-Tung relation in Drell-Yan reactions, as well as nuclear shadowing and antishadowing. The Gribov-Glauber theory predicts that antishadowing of nuclear structure functions is not universal, but instead depends on the flavor quantum numbers of each quark and antiquark, thus explaining the anomalous nuclear dependence measured in deep-inelastic neutrino scattering. Since shadowing and antishadowing arise from the physics of leading-twist diffractive deep inelastic scattering, one cannot attribute such phenomena to the structure of the nucleus itself. It is thus important to distinguish 'static' structure functions, the probability distributions computed from the square of the target light-front wavefunctions, versus 'dynamical' structure functions which include the effects of the final-state rescattering of the struck quark. The importance of the J = 0 photon-quark QCD contact interaction in deeply virtual Compton scattering is also emphasized. The scheme-independent BLM method for setting the renormalization scale is discussed. Eliminating the renormalization scale ambiguity greatly improves the precision of QCD predictions and increases the sensitivity of searches for new physics at the LHC. Other novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Concentration fluctuations and flammability of cryo-compressed hydrogen and methane jets

Compressed hydrogen stored at cryogenic temperatures has a much higher density than room-temperature storage, which enables large-scale hydrogen storage and transport. An understanding of the release of cryogenic hydrogen from pressurized vessels is needed to evaluate the risk and safety concerns with the use of this fuel. Here, the present work extends the analysis of previous experimental studies that measured the gas concentrations of cryo-compressed hydrogen jets and methane jets using a laser Raman scattering diagnostic system. Since the Raman signals are very small, a denoising algorithm was applied to significantly reduce the noise to enable statistical analysis of the data. The transient features of the turbulent jets were characterized by their concentration intermittencies and probability density functions (PDFs). A two-part PDF was developed to predict the bimodal features of the jet concentration distributions. Then, the flammability factors of the cryogenic jets were calculated based on the intermittency and the PDF.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2012

Stringy mechanism for a small cosmological constant

Based on the probability distributions of products of random variables, we propose a simple stringy mechanism that prefers the meta-stable vacua with a small cosmological constant. We state some relevant properties of the probability distributions of functions of random variables. We then illustrate the mechanism within the flux compactification models in Type IIB string theory. As a result of the stringy dynamics, we argue that the generic probability distribution for the meta-stable vacua typically peaks with a divergent behavior at the zero value of the cosmological constant. However, its suppression in the single modulus model studied here is modest.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

A stringy mechanism for a small cosmological constant — multi-moduli cases

Based on the properties of probability distributions of functions of random variables, we proposed earlier a simple stringy mechanism that prefers the meta-stable vacua with a small cosmological constant Λ. As an illustration of this approach, we study in this paper particularly simple but non-trivial models of the Kähler uplift in the large volume flux compactification scenario in Type IIB string theory, where all parameters introduced in the model are treated either as fixed constants motivated by physics, or as random variables with some given uniform probability distributions. We determine the value w{sub 0} of the superpotential W{sub 0} at the supersymmetric minima, and find that the resulting probability distribution P(w{sub 0}) peaks at w{sub 0} = 0; furthermore, this peaking behavior strengthens as the number of complex structure moduli increases. The resulting probability distribution P(Λ) for meta-stable vacua also peaks as Λ → 0, for both positive and negative Λ. This peaking/divergent behavior of P(Λ) strengthens as the number of moduli increases. In some scenarios for Λ > 0, the likely value of Λ decreases exponentially as the number of moduli increases. The light cosmological moduli issue accompanying a very small Λ is also mentioned.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Rigorous force field optimization principles based on statistical distance minimization

We use the concept of statistical distance to define a measure of distinguishability between a pair of statistical mechanical systems, i.e., a model and its target, and show that its minimization leads to general convergence of the model’s static measurable properties to those of the target. We exploit this feature to define a rigorous basis for the development of accurate and robust effective molecular force fields that are inherently compatible with coarse-grained experimental data. The new model optimization principles and their efficient implementation are illustrated through selected examples, whose outcome demonstrates the higher robustness and predictive accuracy of the approach compared to other currently used methods, such as force matching and relative entropy minimization. We also discuss relations between the newly developed principles and established thermodynamic concepts, which include the Gibbs-Bogoliubov inequality and the thermodynamic length.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Stochastic microstructural analysis of ceramic matrix composites using a high-fidelity multiscale framework

This paper presents a high-fidelity multiscale framework to simulate the mechanical behavior of ceramic matrix composites (CMCs), accounting for the complex micromorphology captured using detailed material characterization. First, high-resolution micrographs are obtained for the specific carbon fiber silicon-carbide-nitride matrix (C/SiNC) CMC to characterize the variability of the architectural features and manufacturing-induced defects at the microscale. An image processing algorithm is then used to precisely estimate the size and distribution of all subscale features and defects from the micrographs. The information is then used to generate a three-dimensional stochastic representative volume element (SRVE) to reconstruct microscale constituents accounting for the variability. As a result, the generated SRVEs are simulated using the high-fidelity generalized method of cells (HFGMC) micromechanics theory to investigate the effects of defects on the elastic properties of C/SiNC CMCs.

Ceramic Matrix Composites↗

DOE OSTI2016

A STATISTICAL ANALYSIS OF 50 YEARS OF DAILY SOLAR WIND VELOCITY DATA

Daily mean value of solar wind velocity measured by various spacecraft near the Earth’s orbit from 1963 November 27 to 2013 December 31 given by OMNIWeb is utilized to investigate its characteristics through statistical analyses. The percent probability distribution of solar wind velocity can be described well by the Γ distribution function with the most probable velocity to be 373 km s{sup -1}. It is found that solar wind could be statistically classified into three groups: (1) the low-velocity wind, v<450 km s{sup -1}, which positively responds to, and in the cycle phase lags, the solar activity cycle; (2) the high-velocity wind, 450≤v<725 km s{sup -1}, which negatively responds to, and in the cycle phase leads, the solar activity cycle, but in a short timescale (one-rotation-period) lags the solar activity cycle; and (3) the extreme-high-velocity wind, v≥725 km s{sup -1}, which positively responds to, and in cycle phase leads, the solar activity cycle. A period of about 27 days is determined for solar wind in the first two groups, so that solar wind in the groups is modulated by the solar rotation and related with solar long-life magnetic structures. Solar wind of extreme high velocity appears mainly at the descending phases of the solar cycles.

79 ASTRONOMY AND ASTROPHYSICS↗