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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Probing scrambling and operator size distributions using random mixed states and local measurements

The dynamical spreading of quantum information through a many-body system, typically called scrambling, is a complex process that has proven to be essential to describe many properties of out-of-equilibrium quantum systems. Scrambling can, in principle, be fully characterized via the use of out-of-time-ordered correlation functions, which are notoriously hard to access experimentally. In this work, we put forward an alternative toolbox of measurement protocols to experimentally probe scrambling by accessing properties of the operator size probability distribution, which tracks the size of the support of observables in a many-body system over time. Our measurement protocols require the preparation of separable mixed states together with local operations and measurements, and combine the tools of randomized operations, a modern development of near-term quantum algorithms, with the use of mixed states, a standard tool in NMR experiments. We demonstrate how to efficiently probe the probability-generating function of the operator distribution and discuss the challenges associated with obtaining the moments of the operator distribution. We further show that manipulating the initial state of the protocol allows us to directly obtain the individual elements of the distribution for small system sizes. Published by the American Physical Society 2024

Blocher, Philip Daniel (ORCID:0000000163027567)↗
DOE OSTI2012

Effect of Epistemic Uncertainty Modeling Approach on Decision-Making: Example using Equipment Performance Indicator

Quantitative risk assessments are an integral part of risk-informed regulation of current and future nuclear plants in the U.S. The Bayesian approach to uncertainty, in which both stochastic and epistemic uncertainties are represented with precise probability distributions, is the standard approach to modeling uncertainties in such quantitative risk assessments. However, there are long-standing criticisms of the Bayesian approach to epistemic uncertainty from many perspectives, and a number of alternative approaches have been proposed. Among these alternatives, the most promising (and most rapidly developing) would appear to be the concept of imprecise probability. In this paper, we employ a performance indicator example to focus the discussion. We first give a short overview of the traditional Bayesian paradigm and review some its controversial aspects, for example, issues with so-called noninformative prior distributions. We then discuss how the imprecise probability approach treats these issues and compare it with two other approaches: sensitivity analysis and hierarchical Bayes modeling. We conclude with some practical implications for risk-informed decision making.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2014

Is the Milky Way's hot halo convectively unstable?

We investigate the convective stability of two popular types of model of the gas distribution in the hot Galactic halo. We first consider models in which the halo density and temperature decrease exponentially with height above the disk. These halo models were created to account for the fact that, on some sight lines, the halo's X-ray emission lines and absorption lines yield different temperatures, implying that the halo is non-isothermal. We show that the hot gas in these exponential models is convectively unstable if γ < 3/2, where γ is the ratio of the temperature and density scale heights. Using published measurements of γ and its uncertainty, we use Bayes' theorem to infer posterior probability distributions for γ, and hence the probability that the halo is convectively unstable for different sight lines. We find that, if these exponential models are good descriptions of the hot halo gas, at least in the first few kiloparsecs from the plane, the hot halo is reasonably likely to be convectively unstable on two of the three sight lines for which scale height information is available. We also consider more extended models of the halo. While isothermal halo models are convectively stable if the density decreases with distance from the Galaxy, a model of an extended adiabatic halo in hydrostatic equilibrium with the Galaxy's dark matter is on the boundary between stability and instability. However, we find that radiative cooling may perturb this model in the direction of convective instability. If the Galactic halo is indeed convectively unstable, this would argue in favor of supernova activity in the Galactic disk contributing to the heating of the hot halo gas.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

CHARACTERIZATION OF THE DISTRIBUTION OF THE Ly{alpha} EMITTERS IN THE 53W002 FIELD AT z = 2.4

We present the results of our wide-field narrowband imaging of the field around the radio galaxy 53W002 at z = 2.390 with Subaru/Suprime-Cam. A custom-made filter, NB413, centered at 4140 A with a width of 83 A is used to observe the 31' Multiplication-Sign 24' area around the radio galaxy. We detected 204 Ly{alpha} emitters (LAEs) at z = 2.4 with a rest-frame equivalent width larger than 25 A to the depth of 26 AB mag (in NB413). The entire LAE population in the 53W002 field has an average number density and distributions of equivalent width and size that are similar to those of other fields at z {approx} 2. We identify a significant high-density region (53W002F-HDR) that spreads over Almost-Equal-To 5' Multiplication-Sign 4' near 53W002, where the LAE number density is nearly four times as large as the average of the entire field. Using the probability distribution function of density fluctuation, we evaluate the rareness probability of 53W002F-HDR to be 0.9{sup +2.4} {sub -0.62}%, which corresponds to a moderately rich structure. No notable environmental dependency at the comoving scale of 10 Mpc is found for the distributions of the Ly{alpha} equivalent width and luminosity in the field. We also detected four Ly{alpha} blobs, one of which is newly discovered. They are all located in the rims of high-density regions. The biased location and unique morphologies in Ly{alpha} suggest that galaxy interaction plays a key role in their formation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Distributionally robust polynomial chance-constraints under mixture ambiguity sets

Given $\mathrm{X}\subset\mathbb{R}^n, ε \in (0,1)$, a parametrized family of probability distributions $(μ_a)_{a\in \mathrm{A}}$ on $\mathrm{Ω}\subset \mathbb{R}^p$, we consider the feasible set $\mathrm{X}^*_ε \subset\mathrm{X}$ associated with the distributionally robust chance-constraint $\mathrm{X}^*_ε = \mathrm{x \in X : Prob}_μ[f(\mathrm{x}, ω) >0] > 1 - ε, \forall μ \in \mathscr{M}_{\mathrm{a}}$}, where $\mathscr{M}_{\mathrm{a}}$ is the set of all possibles mixtures of distributions $μ_{\mathrm{a}}, \mathrm{a \in A}$. For instance and typically, the family $\mathscr{M}_{\mathrm{a}}$ is the set of all mixtures of Gaussian distributions on $\mathbb{R}$ with mean and standard deviation $\mathrm{a}=(a,σ)$ in some compact set $\mathrm{A}\subset \mathbb{R}^2$. We provide a sequence of inner approximations $\mathrm{X}^d_ε = {\mathrm{x \in X} : w_d(\mathrm{x}) < ε}, d \in \mathbb{N}$, where $w_d$ is a polynomial of degree d whose vector of coefficients is an optimal solution of a semidefinite program. The size of the latter increases with the degree d. We also obtain the strong and highly desirable asymptotic guarantee that $λ(\mathrm{X}^*_ε$\$\mathrm{X}^d_ε$) → 0 as d increases, where λ is the Lebesgue measure on X. Same results are also obtained for the more intricated case of distributionally robust “joint” chance-constraints. Finally, there is a price to pay for this strong asymptotic guarantee which is the scalability of such a numerical scheme, and so far this important drawback makes it limited to problems of modest dimension.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Sub-daily Statistical Downscaling of Meteorological Variables Using Neural Networks

A new open source neural network temporal downscaling model is described and tested using CRU-NCEP reanal ysis and CCSM3 climate model output. We downscaled multiple meteorological variables in tandem from monthly to sub-daily time steps while also retaining consistent correlations between variables. We found that our feed forward, error backpropagation approach produced synthetic 6 hourly meteorology with biases no greater than 0.6% across all variables and variance that was accurate within 1% for all variables except atmospheric pressure, wind speed, and precipitation. Correlations between downscaled output and the expected (original) monthly means exceeded 0.99 for all variables, which indicates that this approach would work well for generating atmospheric forcing data consistent with mass and energy conserved GCM output. Our neural network approach performed well for variables that had correlations to other variables of about 0.3 and better and its skill was increased by downscaling multiple correlated variables together. Poor replication of precipitation intensity however required further post-processing in order to obtain the expected probability distribution. The concurrence of precipitation events with expected changes in sub ordinate variables (e.g., less incident shortwave radiation during precipitation events) were nearly as consistent in the downscaled data as in the training data with probabilities that differed by no more than 6%. Our downscaling approach requires training data at the target time step and relies on a weak assumption that climate variability in the extrapolated data is similar to variability in the training data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

HFIR Steady State Heat Transfer Code (HSSHTC) Statistical Uncertainty Analysis

HSSHTC, the safety basis steady state TH code for HFIR, uses a highly conservative approach in which all input and calculation uncertainties are resolved simultaneously at their most limiting setting. This results in excessive conservatism which does not account for the high unlikelihood of such simultaneous worst-case conditions. The present study explores an alternative approach, BEPU, in which reasonable working assumptions for the probability distribution of each input uncertainty are used to determine a relationship between burnout power margin and core fuel failure probability. This was performed under a philosophy of perturbing uncertainty parameters already defined within the HSSHTC methodology while preserving the HSSHTC calculation approach and solution methodology itself. Based on the assumptions employed in this study, the BEPU approach resulted in a 0.29 increase in burnout power ratio (25 MW increase in burnout power) compared to the latest HSSHTC calculations of C-HFIR-2026-004. The study can be refined in the future by employing fuel fabrication data to provide more realistic input distributions. Future changes to the HSSHTC methodology would potentially allow a more comprehensive treatment of uncertainties which may further increase the burnout power ratio.

Wysocki, Aaron [ORNL] (ORCID:0000000222043779)↗
DOE OSTI2019

Coincidence Risk Analysis of Floods Using Multivariate Copulas: Case Study of Jinsha River and Min River, China

The coincidence of floods on the mainstream and its tributary may cause significant flood damages at downstream of the confluence. In this study, the coincidence risks of flood magnitudes and occurrence dates on Jinsha River and Min River, China were analyzed using multivariate copulas. The Pearson Type III (P-III) distribution and the Mixed von Mises distribution were selected to establish the marginal distributions of flood magnitude and occurrence date, respectively. The Clayton copula and Gumbel-Hougaard (GH) copula functions were then used to establish the joint probability distributions of flood magnitudes and occurrence dates of Jinsha River and Min River, respectively. The coincidence probabilities of flood magnitudes and occurrence dates on Jinsha River and Min River were investigated, and the interval of Annual Maximum (AM) flood occurrence dates of the two rivers was also analyzed. The results show that the higher coincidence probabilities of flood occurrence dates of the two rivers occur in the period from mid-June to early September, with three peaks of coincidence probability occurring on 28 th July, 14 th August, and 31 st August, respectively. The coincidence probability of flood magnitudes for 0.1%, 0.2%, 1%, 5%, and 10% design floods are 1.651×10-8, 6.601×10-8, 1.647×10-6, 4.071×10-5, and 1.606×10-4, respectively. The probability of AM flood occurrence date of Jinsha River and Min River with a time interval of ±3 days is 10.16%. These results can provide guidance for the reservoir operation of Xiluodu-Xiangjiaba cascade reservoirs and offer reference for flood control and disaster reduction at downstream of the confluence.

Peng, Yang↗
DOE OSTI2017

Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables

Noncommuting observables cannot be simultaneously measured; however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fréchet bounds limiting the joint probabilities, concluding that the latter may be negative. We use symmetrization, justified heuristically and then more carefully via the Moyal characteristic function, to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct Quasi-Bell inequalities, Bell inequalities containing products of noncommuting observables, on two qubits. These inequalities place limits on the local hidden variable models that define joint probabilities for noncommuting observables. We also found that the Quasi-Bell inequalities have a quantum to classical violation as high as 3/2 on two qubit, higher than conventional Bell inequalities. Our result demonstrates the theoretical importance of noncommutativity in the nonlocality of quantum mechanics and provides an insightful generalization of Bell inequalities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Intrinsic spontaneous emission-induced fluctuations of the output optical beam power and phase in a diode amplifier

Output optical beam intensity and phase fluctuations are analysed in a classical approach to describing the propagation and amplification of spontaneous emission in the active region of a laser diode with a gain saturated by input monochromatic light. We find their spectral densities and dispersion and the correlation coefficient of the two-dimensional probability distribution function of the fluctuations. (lasers)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

A new approach to detailed structural decomposition from the splash and phat surveys: Kicked-up disk stars in the Andromeda galaxy?

We characterize the bulge, disk, and halo subcomponents in the Andromeda galaxy (M31) over the radial range 4 kpc < R {sub proj} < 225 kpc. The cospatial nature of these subcomponents renders them difficult to disentangle using surface brightness (SB) information alone, especially interior to ∼20 kpc. Our new decomposition technique combines information from the luminosity function (LF) of over 1.5 million bright (20 < m {sub 814W} < 22) stars from the Panchromatic Hubble Andromeda Treasury survey, radial velocities of over 5000 red giant branch stars in the same magnitude range from the Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo survey, and integrated I-band SB profiles from various sources. We use an affine-invariant Markov chain Monte Carlo algorithm to fit an appropriate toy model to these three data sets. The bulge, disk, and halo SB profiles are modeled as a Sérsic, exponential, and cored power law, respectively, and the LFs are modeled as broken power laws. We present probability distributions for each of 32 parameters describing the SB profiles and LFs of the three subcomponents. We find that the number of stars with a disk-like LF is 5.2% ± 2.1% larger than the number with disk-like (dynamically cold) kinematics, suggesting that some stars born in the disk have been dynamically heated to the point that they are kinematically indistinguishable from halo members. This is the first kinematical evidence for a 'kicked-up disk' halo population in M31. The fraction of kicked-up disk stars is consistent with that found in simulations. We also find evidence for a radially varying disk LF, consistent with a negative metallicity gradient in the stellar disk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Unified, Geometric Framework for Nonequilibrium Protocol Optimization

Controlling thermodynamic cycles to minimize the dissipated heat is a long-standing goal in thermodynamics, and more recently, a central challenge in stochastic thermodynamics for nanoscale systems. Here, we introduce a theoretical and computational framework for optimizing nonequilibrium control protocols that can transform a system between two distributions in a minimally dissipative fashion. These protocols optimally transport a system along paths through the space of probability distributions that minimize the dissipative cost of a transformation. Furthermore, we show that the thermodynamic metric—determined via a linear response approach—can be directly derived from the same objective function that is optimized in the optimal transport problem, thus providing a unified perspective on thermodynamic geometries. As a result, we investigate this unified geometric framework in two model systems and observe that our procedure for optimizing control protocols is robust beyond linear response.

36 MATERIALS SCIENCE↗
DOE OSTI2019

The Fall Speed Variability of Similarly Sized Ice Particle Aggregates

The terminal velocity ( V t ) of ice hydrometeors is of high importance to atmospheric modeling. V t is governed by the physical characteristics of a hydrometeor, including mass and projected area, as well as environmental conditions. When liquid hydrometeors coalesce to form larger hydrometeors, the resulting hydrometeor can readily be characterized by its spherical or near-spherical shape. For ice hydrometeors, it is more complicated because of the variability of ice shapes possible in the atmosphere as well as the inherent randomness in the aggregation process, which leads to highly variable characteristics. The abundance of atmospheric processes affecting ice particle dimensional characteristics creates potential for highly variable V t for ice particles that are predicted or measured to be of the “same size.” In this article we explore the variability of ice hydrometeor V t both theoretically and through the use of experimental observations. Theoretically, the variability in V t is investigated by analyzing the microphysical characteristics of randomly aggregated hexagonal shapes. The modeled dimensional characteristics are then compared to aircraft probe measurements to constrain the variability in atmospheric ice hydrometeor V t . Results show that the spread in V t can be represented with Gaussian distributions relative to a mean. Variability expressed as the full width at half maximum of the normalized Gaussian probability distribution function is around 20%, with somewhat higher values associated with larger particle sizes and warmer temperatures. Field campaigns where mostly convective clouds were sampled displayed low variability, while Arctic and midlatitude winter campaigns showed broader V t spectra.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1988

Optimum structural sizing for gust induced response

The present paper describes an optimization capability for sizing airframe structures that are subjected to a combination of deterministic and random loads. Design constraints are implemented to prevent structural failure in fatigue and due to a single exceedance of the allowable stress. The random load is treated as a stationary, homogeneous process with a Gaussian probability distribution, and a frequency domain method is used for the computation of dynamic response parameters. An equal-probability-of-load-combination criterion is proposed in the formulation of strength constraints. This alleviates problems associated with the incomplete phase information available when using power spectral density methods. The optimization procedure is illustrated by examples using typical built-up structures.

Hajela, P.↗
NASA NTRS1995

A Bayesian approach to microwave precipitation profile retrieval

A multichannel passive microwave precipitation retrieval algorithm is developed. Bayes theorem is used to combine statistical information from numerical cloud models with forward radiative transfer modeling. A multivariate lognormal prior probability distribution contains the covariance information about hydrometeor distribution that resolves the nonuniqueness inherent in the inversion process. Hydrometeor profiles are retrieved by maximizing the posterior probability density for each vector of observations. The hydrometeor profile retrieval method is tested with data from the Advanced Microwave Precipitation Radiometer (10, 19, 37, and 85 GHz) of convection over ocean and land in Florida. The CP-2 multiparameter radar data are used to verify the retrieved profiles. The results show that the method can retrieve approximate hydrometeor profiles, with larger errors over land than water. There is considerably greater accuracy in the retrieval of integrated hydrometeor contents than of profiles. Many of the retrieval errors are traced to problems with the cloud model microphysical information, and future improvements to the algorithm are suggested.

Evans, K. Franklin↗
NASA NTRS1997

Applications of Bayesian Statistics to Problems in Gamma-Ray Bursts

This presentation will describe two applications of Bayesian statistics to Gamma Ray Bursts (GRBS). The first attempts to quantify the evidence for a cosmological versus galactic origin of GRBs using only the observations of the dipole and quadrupole moments of the angular distribution of bursts. The cosmological hypothesis predicts isotropy, while the galactic hypothesis is assumed to produce a uniform probability distribution over positive values for these moments. The observed isotropic distribution indicates that the Bayes factor for the cosmological hypothesis over the galactic hypothesis is about 300. Another application of Bayesian statistics is in the estimation of chance associations of optical counterparts with galaxies. The Bayesian approach is preferred to frequentist techniques here because the Bayesian approach easily accounts for galaxy mass distributions and because one can incorporate three disjoint hypotheses: (1) bursts come from galactic centers, (2) bursts come from galaxies in proportion to luminosity, and (3) bursts do not come from external galaxies. This technique was used in the analysis of the optical counterpart to GRB970228.

Meegan, Charles A.↗
DOE OSTI2013

Improved mesh based photon sampling techniques for neutron activation analysis

The design of fusion power systems requires analysis of neutron activation of large, complex volumes, and the resulting particles emitted from these volumes. Structured mesh-based discretization of these problems allows for improved modeling in these activation analysis problems. Finer discretization of these problems results in large computational costs, which drives the investigation of more efficient methods. Within an ad hoc subroutine of the Monte Carlo transport code MCNP, we implement sampling of voxels and photon energies for volumetric sources using the alias method. The alias method enables efficient sampling of a discrete probability distribution, and operates in 0(1) time, whereas the simpler direct discrete method requires 0(log(n)) time. By using the alias method, voxel sampling becomes a viable alternative to sampling space with the 0(1) approach of uniformly sampling the problem volume. Additionally, with voxel sampling it is straightforward to introduce biasing of volumetric sources, and we implement this biasing of voxels as an additional variance reduction technique that can be applied. We verify our implementation and compare the alias method, with and without biasing, to direct discrete sampling of voxels, and to uniform sampling. We study the behavior of source biasing in a second set of tests and find trends between improvements and source shape, material, and material density. Overall, however, the magnitude of improvements from source biasing appears to be limited. Future work will benefit from the implementation of efficient voxel sampling - particularly with conformal unstructured meshes where the uniform sampling approach cannot be applied. (authors)

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Practical Probabilistic Programming

Recent advances in probabilistic programming languages (PPLs) have provided the capability for exact inference: computing a closed-form probability distribution for a given probabilistic program. In particular, the new language Roulette uses a language oriented programming (LOP) approach, wherein analysts build new programming languages on top of a set of primitives provided by Roulette, which then translates these structures into a weighted model counting problem which can be solved by automated reasoning tools. However, because Roulette provides few convenience features, developing these new languages is challenging even for expert users. We developed a standard library of common probability functions for Roulette with the goal of improved usability. This included approximation of continuous probability density functions using discrete probability mass functions. We demonstrated this approach by modeling a cosmic ray striking a RAM controller. We found that Roulette provides a powerful interface for highly expressive probabilistic programs to be generated. In collaboration with the NNSA Advanced Simulation and Computing program, which resulted in development of a tool called Circulette, we were able to model complex circuits expressed in Verilog using probabilistic programs with an expressivity not previously possible. Our research question that motivated the development of a Roulette standard library was to determine whether non-experts could use a PPL to model relevant problems regarding radiation effects on microelectronics. This standard library improved the expressivity of Roulette by implementing common probability density functions, mathematical operators on distributions, and support for empirical distributions. While Roulette is a powerful modeling language, the untyped, LOP approach makes error messages difficult to understand and requires expert aid. We recommend further research on Roulette, especially with its error messages, to enable improved usability. At the same time, this project demonstrated that for users familiar with Roulette and the LOP approach, Roulette provides powerful new capabilities that can be integrated with other Sandia modeling capabilities.

97 MATHEMATICS AND COMPUTING↗