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At least 613 records · Page 34

A family of random walks with generalized Dirichlet steps

We analyze a class of continuous time random walks in R{sup d},d≥2, with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes of orientation, we provide the analytic form of the probability density function of the position (X{sub {sub d}}(t),t>0) reached, at time t > 0, by the random motion. In particular, we analyze the case of random walks with two steps. In general, it is a hard task to obtain the explicit probability distributions for the process (X{sub {sub d}}(t),t>0). Nevertheless, for suitable values for the basic parameters of the generalized Dirichlet probability distribution, we are able to derive the explicit conditional density functions of (X{sub {sub d}}(t),t>0). Furthermore, in some cases, by exploiting the fractional Poisson process, the unconditional probability distributions of the random walk are obtained. This paper extends in a more general setting, the random walks with Dirichlet displacements introduced in some previous papers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Breast dose in mammography is about 30% lower when realistic heterogeneous glandular distributions are considered

Purpose: Current dosimetry methods in mammography assume that the breast is comprised of a homogeneous mixture of glandular and adipose tissues. Three-dimensional (3D) dedicated breast CT (bCT) data sets were used previously to assess the complex anatomical structure within the breast, characterizing the statistical distribution of glandular tissue in the breast. The purpose of this work was to investigate the effect of bCT-derived heterogeneous glandular distributions on dosimetry in mammography. Methods: bCT-derived breast diameters, volumes, and 3D fibroglandular distributions were used to design realistic compressed breast models comprised of heterogeneous distributions of glandular tissue. The bCT-derived glandular distributions were fit to biGaussian functions and used as probability density maps to assign the density distributions within compressed breast models. The MCNPX 2.6.0 Monte Carlo code was used to estimate monoenergetic normalized mean glandular dose “DgN(E)” values in mammography geometry. The DgN(E) values were then weighted by typical mammography x-ray spectra to determine polyenergetic DgN (pDgN) coefficients for heterogeneous (pDgN{sub hetero}) and homogeneous (pDgN{sub homo}) cases. The dependence of estimated pDgN values on phantom size, volumetric glandular fraction (VGF), x-ray technique factors, and location of the heterogeneous glandular distributions was investigated. Results: The pDgN{sub hetero} coefficients were on average 35.3% (SD, 4.1) and 24.2% (SD, 3.0) lower than the pDgN{sub homo} coefficients for the Mo–Mo and W–Rh x-ray spectra, respectively, across all phantom sizes and VGFs when the glandular distributions were centered within the breast phantom in the coronal plane. At constant breast size, increasing VGF from 7.3% to 19.1% lead to a reduction in pDgN{sub hetero} relative to pDgN{sub homo} of 23.6%–27.4% for a W–Rh spectrum. Displacement of the glandular distribution, at a distance equal to 10% of the compressed breast width in the superior and inferior directions, resulted in a 37.3% and a −26.6% change in the pDgN{sub hetero} coefficient, respectively, relative to the centered distribution for the Mo–Mo spectrum. Lateral displacement of the glandular distribution, at a distance equal to 10% of the compressed breast width, resulted in a 1.5% change in the pDgN{sub hetero} coefficient relative to the centered distribution for the W–Rh spectrum. Conclusions: Introducing bCT-derived heterogeneous glandular distributions into mammography phantom design resulted in decreased glandular dose relative to the widely used homogeneous assumption. A homogeneous distribution overestimates the amount of glandular tissue near the entrant surface of the breast, where dose deposition is exponentially higher. While these findings are based on clinically measured distributions of glandular tissue using a large cohort of women, future work is required to improve the classification of glandular distributions based on breast size and overall glandular fraction.

60 APPLIED LIFE SCIENCES↗

Identification of topology changes in power grids using phasor measurements

Phasor measurement units (PMUs) are increasingly important for monitoring the state of an electrical power grid and quickly detecting topology changes caused by events such as lines going down or large loads being dropped. Phasors are complex‐valued measurements of voltage and current at various points of generation and consumption. If a line goes down or a load is removed, power flows change throughout the grid according to known physical laws, and the probability distribution of phasor measurements changes accordingly. This paper develops a method to estimate the current topology of a power grid from phasor measurements and considers the design goal of placing PMUs at strategic points in a distribution system to achieve good sensitivity to single‐line outages. From a vector of phasor measurements, probabilities are computed corresponding to the scenario that all power lines are operational and to alternate scenarios in which each line goes down individually. These probabilities are functions of the joint distributions of phasor measurements under each possible scenario, obtained through Monte Carlo simulations with random load profiles. We use log‐spline densities to estimate marginal distributions of phasor measurements and fold these into a multivariate Gaussian copula to capture important correlations. Sensitivity to outages varies according to which line goes down and where PMUs are placed on the grid. A greedy search algorithm is demonstrated for placing PMUs at locations that provide good sensitivity to single‐line outages. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

Wiel, Scott Vander↗

Effective long wavelength scalar dynamics in de Sitter

We discuss the effective infrared theory governing a light scalar's long wavelength dynamics in de Sitter spacetime. We show how the separation of scales around the physical curvature radius k / a ∼ H can be performed consistently with a window function and how short wavelengths can be integrated out in the Schwinger-Keldysh path integral formalism. At leading order, and for time scales Δ t >> H {sup −1}, this results in the well-known Starobinsky stochastic evolution. However, our approach allows for the computation of quantum UV corrections, generating an effective potential on which the stochastic dynamics takes place. The long wavelength stochastic dynamical equations are now second order in time, incorporating temporal scales Δ t ∼ H {sup −1} and resulting in a Kramers equation for the probability distribution—more precisely the Wigner function—in contrast to the more usual Fokker-Planck equation. This feature allows us to non-perturbatively evaluate, within the stochastic formalism, not only expectation values of field correlators, but also the stress-energy tensor of φ.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Application of Gaussian Process Modeling to Analysis of Functional Unreliability

This paper applies Gaussian Process (GP) modeling to analysis of the functional unreliability of a “passive system.” GPs have been used widely in many ways [1]. The present application uses a GP for emulation of a system simulation code. Such an emulator can be applied in several distinct ways, discussed below. All applications illustrated in this paper have precedents in the literature; the present paper is an application of GP technology to a problem that was originally analyzed [2] using neural networks (NN), and later [3, 4] by a method called “Alternating Conditional Expectations” (ACE). This exercise enables a multifaceted comparison of both the processes and the results. Given knowledge of the range of possible values of key system variables, one could, in principle, quantify functional unreliability by sampling from their joint probability distribution, and performing a system simulation for each sample to determine whether the function succeeded for that particular setting of the variables. Using previously available system simulation codes, such an approach is generally impractical for a plant-scale problem. It has long been recognized, however, that a well-trained code emulator or surrogate could be used in a sampling process to quantify certain performance metrics, even for plant-scale problems. “Response surfaces” were used for this many years ago. But response surfaces are at their best for smoothly varying functions; in regions of parameter space where key system performance metrics may behave in complex ways, or even exhibit discontinuities, response surfaces are not the best available tool. This consideration was one of several that drove the work in [2]. In the present paper, (1) the original quantification of functional unreliability using NN [2], and later ACE [3], is reprised using GP; (2) additional information provided by the GP about uncertainty in the limit surface, generally unavailable in other representations, is discussed; (3) a simple forensic exercise is performed, analogous to the inverse problem of code calibration, but with an accident management spin: given an observation about containment pressure, what can we say about the system variables? References 1. For an introduction to GPs, see (for example) Gaussian Processes for Machine Learning, C. E. Rasmussen and C. K. I. Williams (MIT, 2006). 2. Reliability Quantification of Advanced Reactor Passive Safety Systems, J. J. Vandenkieboom, PhD Thesis (University of Michigan, 1996). 3. Z. Cui, J. C. Lee, J. J. Vandenkieboom, and R. W. Youngblood, “Unreliability Quantification of a Containment Cooling System through ACE and ANN Algorithms,” Trans. Am. Nucl. Soc. 85, 178 (2001). 4. Risk and Safety Analysis of Nuclear Systems, J. C. Lee and N. J. McCormick (Wiley, 2011). See especially §11.2.4.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Stochastic charging of dust grains in planetary rings: Diffusion rates and their effects on Lorentz resonances

Dust grains in planetary rings acquire stochastically fluctuating electric charges as they orbit through any corotating magnetospheric plasma. Here we investigate the nature of this stochastic charging and calculate its effect on the Lorentz resonance (LR). First we model grain charging as a Markov process, where the transition probabilities are identified as the ensemble-averaged charging fluxes due to plasma pickup and photoemission. We determine the distribution function P(t;N), giving the probability that a grain has N excess charges at time t. The autocorrelation function tau(sub q) for the strochastic charge process can be approximated by a Fokker-Planck treatment of the evolution equations for P(t; N). We calculate the mean square response to the stochastic fluctuations in the Lorentz force. We find that transport in phase space is very small compared to the resonant increase in amplitudes due to the mean charge, over the timescale that the oscillator is resonantly pumped up. Therefore the stochastic charge variations cannot break the resonant interaction; locally, the Lorentz resonance is a robust mechanism for the shaping of etheral dust ring systems. Slightly stronger bounds on plasma parameters are required when we consider the longer transit times between Lorentz resonances.

Schaffer, L.↗

Gravitational lensing, time delay, and gamma-ray bursts

The probability distributions of time delay in gravitational lensing by point masses and isolated galaxies (modeled as singular isothermal spheres) are studied. For point lenses (all with the same mass) the probability distribution is broad, and with a peak at delta(t) of about 50 S; for singular isothermal spheres, the probability distribution is a rapidly decreasing function with increasing time delay, with a median delta(t) equals about 1/h month, and its behavior depends sensitively on the luminosity function of galaxies. The present simplified calculation is particularly relevant to the gamma-ray bursts if they are of cosmological origin. The frequency of 'recurrent' bursts due to gravitational lensing by galaxies is probably between 0.05 and 0.4 percent. Gravitational lensing can be used as a test of the cosmological origin of gamma-ray bursts.

Mao, Shude↗

Probabilities and statistics for backscatter estimates obtained by a scatterometer

Methods for the recovery of winds near the surface of the ocean from measurements of the normalized radar backscattering cross section must recognize and make use of the statistics (i.e., the sampling variability) of the backscatter measurements. Radar backscatter values from a scatterometer are random variables with expected values given by a model. A model relates backscatter to properties of the waves on the ocean, which are in turn generated by the winds in the atmospheric marine boundary layer. The effective wind speed and direction at a known height for a neutrally stratified atmosphere are the values to be recovered from the model. The probability density function for the backscatter values is a normal probability distribution with the notable feature that the variance is a known function of the expected value. The sources of signal variability, the effects of this variability on the wind speed estimation, and criteria for the acceptance or rejection of models are discussed. A modified maximum likelihood method for estimating wind vectors is described. Ways to make corrections for the kinds of errors found for the Seasat SASS model function are described, and applications to a new scatterometer are given.

Pierson, Willard J., Jr.↗

A POLYTROPIC MODEL FOR SPACE AND LABORATORY PLASMAS DESCRIBED BY BI-MAXWELLIAN ELECTRON DISTRIBUTIONS

Non-local electron energy probability functions (EEPFs) are shown to have an important effect on the thermodynamic behavior of plasmas in the context of solar wind and laboratory plasmas. A conservation relation is held for electron enthalpy and plasma potential during the electron transport. For an adiabatic system governed by non-local electron dynamics, the correlation between electron temperature and density can be approximated by a polytropic relation, with different indexes demonstrated using three cases of bi-Maxwellian EEPFs. This scenario differs from a local thermodynamic equilibrium having a single polytropic index of 5/3 for adiabaticity.

79 ASTRONOMY AND ASTROPHYSICS↗

Effect of the link lifetime in a dynamical lattice on the properties of the avalanche processes on it

The properties of the avalanche processes that develop on a dynamical lattice, the structure of links in which changes due to a specific characteristic of each lattice node, namely, its “activity,” which determines the probability of connection of a certain node with neighboring nodes in one step of lattice evolution. The statistics of the sizes of the avalanches appearing in the lattice system is studied as a function of the node activity and the link lifetime (the lifetime of the links formed in the system). It is analytically and numerically shows that the type of avalanche dynamics in the system changes as a function of these parameters. The following three regimes can take place in the system: (1) avalanches of any sizes, from small to catastrophic, can appear, which is reflected in the power-law behavior of the probability density function of the appearance of avalanches of certain sizes; (2) avalanches of a certain average size mainly appear in the system, and the probability density is close to that of a normal distribution; and (3) transient regime, where the probability density function of the appearance of avalanches of certain sizes is close to an exponential function. These results open up the possibilities of controlling the behavior of a complex system; in particular, they can be used to prevent catastrophic avalanches by changing the link lifetime and the average node activity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Location and Environments of Neutron Star Mergers in an Evolving Universe

The simultaneous detection of gravitational and electromagnetic waves from a binary neutron star merger has both solidified the link between neutron star mergers and short-duration gamma-ray bursts (GRBs), and demonstrated the ability of astronomers to follow-up the gravitational wave detection to place constraints on the ejecta from these mergers, as well as the nature of the GRB engine and its surroundings. As the sensitivity of aLIGO and VIRGO increases, it is likely that a growing number of such detections will occur in the next few years, leading to a sufficiently large number of events to constrain the populations of these GRB events. While long-duration GRBs originate from massive stars and thus are located near their stellar nurseries, binary neutron stars may merge on much longer timescales, and thus may have had time to migrate appreciably. The strength and character of the electromagnetic afterglow emission of binary neutron star mergers is a sensitive function of the circum-merger environment. Though the explosion sites of short GRBs have been explored in the literature, the question has yet to be fully addressed in its cosmological context. We present cosmological simulations following the evolution of a galaxy cluster, including star formation combined with binary population synthesis models, to self-consistently track the locations and environmental gas densities of compact binary merger sites throughout the cosmic web. In conclusion, we present probability distributions for densities as a function of redshift and discuss model sensitivity to population synthesis model assumptions.

79 ASTRONOMY AND ASTROPHYSICS↗

Uncertainty quantification of microstructural properties due to variability in measured pole figures

Experimental pole figures are an important input for microstructure homogenization models. In this paper, we derive an exact analytical formulation to quantify the uncertainties in homogenized properties due to uncertainty in the experimentally measured pole figures. The pole figures are acquired from a set of Ti-7Al alloy samples. These samples were obtained from the same process: by compressing a beta forged ingot at room temperature followed by annealing. The samples were taken from different regions of the original ingot, and this created variability in the resulting pole figures. The joint multivariate probability distributions of the computed orientation distribution function (ODF) is then found using the method of characteristic functions based on a Gaussian model of the pole figures. Engineering properties such as elastic modulus can be obtained by volume averaging over the ODF. We also show that uncertainty in elastic properties can be analytically obtained using direct transformation of random variables in the homogenization approach.

36 MATERIALS SCIENCE↗

Bayesian Redshift Classification of Emission-line Galaxies with Photometric Equivalent Widths

We present a Bayesian approach to the redshift classification of emission-line galaxies when only a single emission line is detected spectroscopically. We consider the case of surveys for high-redshift Lyα-emitting galaxies (LAEs), which have traditionally been classified via an inferred rest-frame equivalent width (EW; W{sub Lyα}) greater than 20 Å. Our Bayesian method relies on known prior probabilities in measured emission-line luminosity functions and EW distributions for the galaxy populations, and returns the probability that an object in question is an LAE given the characteristics observed. This approach will be directly relevant for the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX), which seeks to classify ∼10{sup 6} emission-line galaxies into LAEs and low-redshift [O II] emitters. For a simulated HETDEX catalog with realistic measurement noise, our Bayesian method recovers 86% of LAEs missed by the traditional W{sub Lyα} > 20 Å cutoff over 2 < z < 3, outperforming the EW cut in both contamination and incompleteness. This is due to the method’s ability to trade off between the two types of binary classification error by adjusting the stringency of the probability requirement for classifying an observed object as an LAE. In our simulations of HETDEX, this method reduces the uncertainty in cosmological distance measurements by 14% with respect to the EW cut, equivalent to recovering 29% more cosmological information. Rather than using binary object labels, this method enables the use of classification probabilities in large-scale structure analyses. It can be applied to narrowband emission-line surveys as well as upcoming large spectroscopic surveys including Euclid and WFIRST.

79 ASTRONOMY AND ASTROPHYSICS↗

Ignition probability of polymer-bonded explosives accounting for multiple sources of material stochasticity

Accounting for the combined effect of multiple sources of stochasticity in material attributes, we develop an approach that computationally predicts the probability of ignition of polymer-bonded explosives (PBXs) under impact loading. The probabilistic nature of the specific ignition processes is assumed to arise from two sources of stochasticity. The first source involves random variations in material microstructural morphology; the second source involves random fluctuations in grain-binder interfacial bonding strength. The effect of the first source of stochasticity is analyzed with multiple sets of statistically similar microstructures and constant interfacial bonding strength. Subsequently, each of the microstructures in the multiple sets is assigned multiple instantiations of randomly varying grain-binder interfacial strengths to analyze the effect of the second source of stochasticity. Critical hotspot size-temperature states reaching the threshold for ignition are calculated through finite element simulations that explicitly account for microstructure and bulk and interfacial dissipation to quantify the time to criticality (t{sub c}) of individual samples, allowing the probability distribution of the time to criticality that results from each source of stochastic variation for a material to be analyzed. Two probability superposition models are considered to combine the effects of the multiple sources of stochasticity. The first is a parallel and series combination model, and the second is a nested probability function model. Results show that the nested Weibull distribution provides an accurate description of the combined ignition probability. The approach developed here represents a general framework for analyzing the stochasticity in the material behavior that arises out of multiple types of uncertainty associated with the structure, design, synthesis and processing of materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Initial Probabilistic Evaluation of Reactor Pressure Vessel Fracture with Grizzly and Raven

The Grizzly code is being developed with the goal of creating a general tool that can be applied to study a variety of degradation mechanisms in nuclear power plant components. The first application of Grizzly has been to study fracture in embrittled reactor pressure vessels (RPVs). Grizzly can be used to model the thermal/mechanical response of an RPV under transient conditions that would be observed in a pressurized thermal shock (PTS) scenario. The global response of the vessel provides boundary conditions for local models of the material in the vicinity of a flaw. Fracture domain integrals are computed to obtain stress intensity factors, which can in turn be used to assess whether a fracture would initiate at a pre-existing flaw. These capabilities have been demonstrated previously. A typical RPV is likely to contain a large population of pre-existing flaws introduced during the manufacturing process. This flaw population is characterized stastistically through probability density functions of the flaw distributions. The use of probabilistic techniques is necessary to assess the likelihood of crack initiation during a transient event. This report documents initial work to perform probabilistic analysis of RPV fracture during a PTS event using a combination of the RAVEN risk analysis code and Grizzly. This work is limited in scope, considering only a single flaw with deterministic geometry, but with uncertainty introduced in the parameters that influence fracture toughness. These results are benchmarked against equivalent models run in the FAVOR code. When fully developed, the RAVEN/Grizzly methodology for modeling probabilistic fracture in RPVs will provide a general capability that can be used to consider a wider variety of vessel and flaw conditions that are difficult to consider with current tools. In addition, this will provide access to advanced probabilistic techniques provided by RAVEN, including adaptive sampling and parallelism, which can dramatically decrease run times.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

X-Ray Diffraction Analysis of Features of the Crystal Structure of GaN/Al{sub 0.32}Ga{sub 0.68}N HEMT-Heterostructures by the Williamson–Hall Method

The fitting of θ/2θ and ω peaks in X-ray diffraction curves is shown to be most accurate in the case of using an inverse fourth-degree polynomial or probability density function with Student’s distribution (Pearson type VII function). These functions describe well both the highest-intensity central part of the experimental peak and its low-intensity broadened base caused by X-ray diffuse scattering. The mean microdeformation ε and mean vertical domain size D are determined by the Williamson–Hall method for layers of GaN (ε ≈ 0.00006, D ≈ 200 nm) and Al{sub 0.32}Ga{sub 0.68}N (ε = 0.0032 ± 0.0005, D = 24 ± 7 nm). The D value obtained for the Al{sub 0.32}Ga{sub 0.68}N layer is most likely to result from the nominal thickness of this layer, which is 11 nm.

36 MATERIALS SCIENCE↗

Effect of helium on spatial plasma parameters in low pressure argon-helium plasma

Spatial distributions of the electron energy probability function were measured using a Langmuir probe in side-type argon-helium inductively coupled plasma. Collisional dominated electron heating and a concave shape of plasma density profile were observed at 10 mTorr pure argon. As the helium proportion increased, the electron heating and density profile changed to collisionless dominated heating and a convex shape respectively, and the same tendency was shown when the pressure decreased in the pure argon plasma. These changes were due to the decrease in the e-n collision frequency and the expansion of the electron power dissipation region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simultaneous direct measurements of concentration and velocity in the Richtmyer–Meshkov instability

The Richtmyer–Meshkov instability (RMI) is experimentally investigated in a vertical shock tube using a broadband initial condition imposed on an interface between a helium–acetone mixture and argon (Atwood number $A\approx 0.7$ ). In the present work, a shear layer is introduced at the interface to serve as a statistically repeatable, broadband initial condition to the RMI, and the density interface is accelerated by either an $M=1.6$ or $M=2.2$ planar shock wave. The development of the ensuing mixing layer is investigated using simultaneous planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV). PLIF images are processed to reveal the light-gas mole fraction, while PIV particle image pairs yield corresponding two-component planar velocity results. Field structure and distribution are explored through probability density functions (PDFs), and a decomposition is performed on concentration and velocity results to obtain a mean flow field and define fluctuations. Simultaneous concentration and velocity field measurements allow – for the first time in this regime – experimentally determined turbulence quantities such as Reynolds stresses, turbulent mass-flux velocities and turbulent kinetic energy to be obtained. We show that by the latest times the mixing layer has passed the turbulent threshold, and there is evidence of turbulent mixing occurring sooner for the higher Mach number case. Interface measurements show nonlinear growth with a power-law fit to the thickness data, and that integral measurements of mixing layer thickness are proportional to threshold measurements. Spectral analysis demonstrates the emergence of an inertial range with a slope ${\sim}k^{-5/3}$ when considering both density and velocity effects in planar turbulent kinetic energy (TKE) measurements.

Mechanics↗