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DOE OSTI2026

Determination of proton PDF uncertainties with Markov chain Monte Carlo

We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, 𝑊 and 𝑍 boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the Δ⁢𝜒 2 value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.

Risse, Peter Clemens [Universität Münster (Germany↗

DOE OSTI2012

Transition from interpulse to afterglow plasmas driven by repetitive short-pulse microwaves in a multicusp magnetic field

In the power-off phase, plasmas generated by repetitive short-pulse microwaves in a multicusp magnetic field show a transitive nature from interpulse to afterglow as a function of pulse duration t{sub w} = 20-200 {mu}s. The ionized medium can be driven from a highly non equilibrium to an equilibrium state inside the pulses, thereby dictating the behavior of the plasma in the power-off phase. Compared to afterglows, interpulse plasmas observed for t{sub w} < 50 {mu}s are characterized by a quasi-steady-state in electron density that persists for {approx} 20-40 {mu}s even after the end of the pulse and has a relatively slower decay rate ({approx} 4.3 Multiplication-Sign 10{sup 4} s{sup -1}) of the electron temperature, as corroborated by optical measurements. The associated electron energy probability function indicates depletion in low energy electrons which appear at higher energies just after the end of the pulse. The transition occurs at t{sub w} {approx} 50 {mu}s as confirmed by time evolution of integrated electron numbers densities obtained from the distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Modeling the spectral modification of lower hybrid wave in the presence of drift-wave type density fluctuation in the scrape-off-layer of the EAST tokamak

In this work, the spectrum change of the lower hybrid (LH) waves caused by a low-frequency density fluctuation in the scrape-off-layer is studied by applying the wave scattering model developed by Bonoli and Ott [Phys. Fluids 25, 359 (1982)] via a Monte Carlo method. A ray-tracing model specific to this purpose is developed to evaluate the probability distribution of both the poloidal refractive index (N θ ) and the parallel refractive index (N ∥ ) of the LH wave at the last closed flux surface (LCFS).The probability distributions of N ∥ and N θ at the LCFS are studied using the EAST parameters as a function of wave frequency, the initial N ∥ , and the polar injection position, which may influence the lower hybrid current drive efficiency.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Photon Counting Data Analysis: Application of the Maximum Likelihood and Related Methods for the Determination of Lifetimes in Mixtures of Rose Bengal and Rhodamine B

It is often convenient to know the minimum amount of data needed in order to obtain a result of desired accuracy and precision. It is a necessity in the case of subdiffraction-limited microscopies, such as stimulated emission depletion (STED) microscopy, owing to the limited sample volumes and the extreme sensitivity of the samples to photobleaching and photodamage. We present a detailed comparison of probability-based techniques (the maximum likelihood method and methods based on the binomial and the Poisson distributions) with residual minimization-based techniques for retrieving the fluorescence decay parameters for various two-fluorophore mixtures, as a function of the total number of photon counts, in time-correlated, single-photon counting experiments. The probability-based techniques proved to be the most robust (insensitive to initial values) in retrieving the target parameters and, in fact, performed equivalently to 2-3 significant figures. This is to be expected, as we demonstrate that the three methods are fundamentally related. Furthermore, methods based on the Poisson and binomial distributions have the desirable feature of providing a bin-by-bin analysis of a single fluorescence decay trace, which thus permits statistics to be acquired using only the one trace for not only the mean and median values of the fluorescence decay parameters but also for the associated standard deviations. Lastly, these probability-based methods lend themselves well to the analysis of the sparse data sets that are encountered in subdiffraction-limited microscopies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Subexponentially Growing Hilbert Space and Nonconcentrating Distributions in a Constrained Spin Model

Motivated by recent experiments with two-component Bose–Einstein condensates, we study fully-connected spin models subject to an additional constraint. The constraint is responsible for the Hilbert space dimension to scale only linearly with the system size. We discuss the unconventional statistical physical and thermodynamic properties of such a system, in particular the absence of concentration of the underlying probability distributions. As a consequence, expectation values are less suitable to characterize such systems, and full distribution functions are required instead. Sharp signatures of phase transitions do not occur in such a setting, but transitions from singly peaked to doubly peaked distribution functions of an “order parameter” may be present.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Emergent quantum mechanics at the boundary of a local classical lattice model

We formulate a model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian H acting on n qubits, we define a local classical model with an additional spatial dimension whose boundary dynamics is approximately—but to arbitrary precision—described by Schrödinger's equation and H. The bulk consists of a lattice of classical bits that propagate towards the boundary through a circuit of stochastic matrices. The bits reaching the boundary are governed by a probability distribution whose deviation from the uniform distribution can be interpreted as the quantum-mechanical wave function. Bell nonlocality is achieved because information can move through the bulk much faster than the boundary speed of light. Finally, we analytically estimate how much the model deviates from quantum mechanics, and we validate these estimates using computer simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

Calculation of the performance of {sup 3}He alternative detectors with MCNPX

This paper describes the techniques that are available to calculate the performance of {sup 3}He alternative detectors using MCNPX. Calculations of the performance of safeguards detectors that use {sup 3}He have been successfully carried out for many years. In the case of coincidence or multiplicity counting, specific tallies have been implemented to calculate the Singles, Doubles and Triples counting rates. The implementation of the method was done in such a way that it equates every capture in some nuclide in the detection zone with the production of an electronic pulse from the detector. This is a very good approximation for {sup 3}He detectors and BF{sub 3} detectors. However it is not appropriate for detectors such as boron-lined proportional counters, in which the fraction of capture events leading to an electronic pulse above threshold is very dependent on the geometric arrangement, in particular the thickness and composition of the boron-containing layer. This paper gives calculations of the ideal pulse height distributions to be expected from different detector types and gives values for the probability, as a function of detector energy threshold, that a neutron capture reaction will cause an electronic pulse from the detector. This is termed the electronic efficiency. This electronic detection efficiency depends very little on the energy of the captured neutron, which in most practical cases are heavily weighted towards thermal energies. It does not depend on the position of the source neutron or moderation in the sample. For cases of interest to nuclear safeguards, measurement of uranium and plutonium in specially designed detectors, the spectrum of detected neutrons is fairly constant and thus the electronic detection efficiency becomes a detector constant. The paper discusses how the electronic detection efficiency needs to be included in the calculation of Singles, Doubles and Triples, and describes proposals to improve the tallying capability of MCNPX for such cases. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2012

Chance Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty

When uncontrollable resources fluctuate, Optimum Power Flow (OPF), routinely used by the electric power industry to re-dispatch hourly controllable generation (coal, gas and hydro plants) over control areas of transmission networks, can result in grid instability, and, potentially, cascading outages. This risk arises be cause OPF dispatch is computed without awareness of major uncertainty, in particular fluctuations in renewable output. As a result, grid operation under the OPF with renewable variability can lead to frequent conditions where power line flow ratings are significantly exceeded. Such a condition, which is borne by simulations of real grids, would likely resulting in automatic line tripping to protect lines from thermal stress, a risky and undesirable outcome which compromises stability. Smart grid goals include a commitment to large penetration of highly fluctuating renewables, thus calling to reconsider current practices, in particular the use of standard OPF. Our Chance Constrained (CC) OPF corrects the problem and mitigates dangerous renewable fluctuations with minimal changes in the current operational procedure. Assuming availability of a reliable wind forecast parameterizing the distribution function of the uncertain generation, our CC-OPF satisfies all the constraints with high probability while simultaneously minimizing the cost of economic re-dispatch. CC-OPF allows efficient implementation, e.g. solving a typical instance over the 2746-bus Polish network in 20s on a standard laptop.

Energy Planning, Policy, & Economy(29)↗

DOE OSTI2015

Delineating Hydrofacies Spatial Distribution by Integrating Ensemble Data Assimilation and Indicator Geostatistics

This study develops a new framework of facies-based data assimilation for characterizing spatial distribution of hydrofacies and estimating their associated hydraulic properties. This framework couples ensemble data assimilation with transition probability-based geostatistical model via a parameterization based on a level set function. The nature of ensemble data assimilation makes the framework efficient and flexible to be integrated with various types of observation data. The transition probability-based geostatistical model keeps the updated hydrofacies distributions under geological constrains. The framework is illustrated by using a two-dimensional synthetic study that estimates hydrofacies spatial distribution and permeability in each hydrofacies from transient head data. Our results show that the proposed framework can characterize hydrofacies distribution and associated permeability with adequate accuracy even with limited direct measurements of hydrofacies. Our study provides a promising starting point for hydrofacies delineation in complex real problems.

Song, Xuehang↗

DOE OSTI2017

The Nature of Turbulence in the LITTLE THINGS Dwarf Irregular Galaxies

We present probability density functions and higher order (skewness and kurtosis) analyses of the galaxy-wide and spatially resolved distributions of H i column density in the LITTLE THINGS sample of dwarf irregular galaxies. This analysis follows that of Burkhart et al. for the Small Magellanic Cloud (SMC). About 60% of our sample have galaxy-wide values of kurtosis that are similar to that found for the SMC, with a range up to much higher values, and kurtosis increases with integrated star formation rate. Kurtosis and skewness were calculated for radial annuli and for a grid of 32 pixel × 32 pixel kernels across each galaxy. For most galaxies, kurtosis correlates with skewness. For about half of the galaxies, there is a trend of increasing kurtosis with radius. The range of kurtosis and skewness values is modeled by small variations in the Mach number close to the sonic limit and by conversion of H i to molecules at high column density. The maximum H i column densities decrease with increasing radius in a way that suggests molecules are forming in the weak-field limit, where H{sub 2} formation balances photodissociation in optically thin gas at the edges of clouds.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime

Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Quantifying the Long‐Range Coupling of Electronic Properties in Proteins with ab initio Molecular Dynamics**

Abstract The delicate interplay of covalent and non‐covalent interactions in proteins is inherently quantum mechanical and highly dynamic in nature. To directly interrogate the evolving nature of the electronic structure of proteins, we carry out 100‐ps‐scale ab initio molecular dynamics simulations of three representative small proteins with range‐separated hybrid density functional theory. We quantify the nature and length‐scale of the coupling of residue‐specific charge probability distributions in these proteins. While some nonpolar residues exhibit expectedly narrow charge distributions, most polar and charged residues exhibit broad, multimodal distributions. Even for nonpolar residues, we observe sequence‐specific deviations corresponding to charge accumulation or depletion that would be challenging to capture in a fixed charge force field. We quantify the effect of residue‐residue interactions on charge distributions first with linear cross‐correlations. We then show how additional insight can be gained from evaluating the mutual information of charge distributions. We show that a significant number of residues couple most strongly with residues that are distant in both sequence and space over a range of secondary structures including α‐helical, β‐sheet, disulfide bridging, and lasso motifs. The mutual information analysis is necessary to capture coupling between some polar and charged residues that would be otherwise missed.

Yang, Zhongyue↗

DOE OSTI2011

Non-Gaussian extrema counts for CMB maps

In the context of the geometrical analysis of weakly non-Gaussian cosmic microwave background maps, the 2D differential extrema counts as functions of the excursion set threshold is derived from the full moments expansion of the joint probability distribution of an isotropic random field, its gradient, and invariants of the Hessian. Analytic expressions for these counts are given to second order in the non-Gaussian correction, while a Monte Carlo method to compute them to arbitrary order is presented. Matching count statistics to these estimators is illustrated on fiducial non-Gaussian Planck data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Characteristics of vertical air motion in isolated convective clouds

The vertical velocity and air mass flux in isolated convective clouds are statistically analyzed using aircraft in situ data collected from three field campaigns: High-Plains Cumulus (HiCu) conducted over the midlatitude High Plains, COnvective Precipitation Experiment (COPE) conducted in a midlatitude coastal area, and Ice in Clouds Experiment-Tropical (ICE-T) conducted over a tropical ocean. The results show that small-scale updrafts and downdrafts (< 500 m in diameter) are frequently observed in the three field campaigns, and they make important contributions to the total air mass flux. The probability density functions (PDFs) and profiles of the observed vertical velocity are provided. The PDFs are exponentially distributed. The updrafts generally strengthen with height. Relatively strong updrafts (> 20 m s −1 ) were sampled in COPE and ICE-T. The observed downdrafts are stronger in HiCu and COPE than in ICE-T. The PDFs of the air mass flux are exponentially distributed as well. The observed maximum air mass flux in updrafts is of the order 10 4 kg m −1 s −1 . The observed air mass flux in the downdrafts is typically a few times smaller in magnitude than that in the updrafts. Since this study only deals with isolated convective clouds, and there are many limitations and sampling issues in aircraft in situ measurements, more observations are needed to better explore the vertical air motion in convective clouds.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2011

Dosimetric Effect of Intrafraction Motion and Residual Setup Error for Hypofractionated Prostate Intensity-Modulated Radiotherapy With Online Cone Beam Computed Tomography Image Guidance

Purpose: To quantify the dosimetric effect and margins required to account for prostate intrafractional translation and residual setup error in a cone beam computed tomography (CBCT)-guided hypofractionated radiotherapy protocol. Methods and Materials: Prostate position after online correction was measured during dose delivery using simultaneous kV fluoroscopy and posttreatment CBCT in 572 fractions to 30 patients. We reconstructed the dose distribution to the clinical tumor volume (CTV) using a convolution of the static dose with a probability density function (PDF) based on the kV fluoroscopy, and we calculated the minimum dose received by 99% of the CTV (D{sub 99}). We compared reconstructed doses when the convolution was performed per beam, per patient, and when the PDF was created using posttreatment CBCT. We determined the minimum axis-specific margins to limit CTV D{sub 99} reduction to 1%. Results: For 3-mm margins, D{sub 99} reduction was {<=}5% for 29/30 patients. Using post-CBCT rather than localizations at treatment delivery exaggerated dosimetric effects by {approx}47%, while there was no such bias between the dose convolved with a beam-specific and patient-specific PDF. After eight fractions, final cumulative D{sub 99} could be predicted with a root mean square error of <1%. For 90% of patients, the required margins were {<=}2, 4, and 3 mm, with 70%, 40%, and 33% of patients requiring no right-left (RL), anteroposterior (AP), and superoinferior margins, respectively. Conclusions: For protocols with CBCT guidance, RL, AP, and SI margins of 2, 4, and 3 mm are sufficient to account for translational errors; however, the large variation in patient-specific margins suggests that adaptive management may be beneficial.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2012

A probabilistic model for the identification of confinement regimes and edge localized mode behavior, with implications to scaling laws

Pattern recognition is becoming an important tool in fusion data analysis. However, fusion diagnostic measurements are often affected by considerable statistical uncertainties, rendering the extraction of useful patterns a significant challenge. Therefore, we assume a probabilistic model for the data and perform pattern recognition in the space of probability distributions. We show the considerable advantage of our method for identifying confinement regimes and edge localized mode behavior, and we discuss the potential for scaling laws.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Contactless electronic transport in a bio-molecular junction

Molecular electronics hold promise for next generation ultra-low power, nano-scale integrated electronics. The main challenge in molecular electronics is to make a reliable interface between molecules and metal electrodes. Interfacing metals and molecules detrimentally affects the characteristics of nano-scale molecular electronic devices. It is therefore essential to investigate alternative arrangements such as contact-less tunneling gaps wherever such configurations are feasible. We conduct ab initio density functional theory and non-equilibrium Green's functions calculations to investigate the transport properties of a biocompatible glycine molecular junction. By analyzing the localized molecular orbital energy distributions and transmission probabilities in the transport-gap, we find a glycine molecule confined between two gold electrodes, without making a contact, is energetically stable and possesses high tunneling current resembling an excellent ohmic-like interface.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Retrieval of the molecular orientation distribution from atom-pair angular distributions

Imaging laser-induced rotational dynamics is an important and active field due to its applications in capturing reactions in the molecular frame and in molecular imaging. Experimental measurement of the molecular orientation distribution, as a function of the Euler angles, has only been demonstrated for special cases when the detectable signal is generated along the molecular symmetry axis. Here we developed the general theory that maps the probability density distribution of the molecular orientation to the atom-pair angular distributions for nonlinear molecules. With the theory, the molecular orientation distribution can be retrieved from the measured atom-pair angular distribution, which we demonstrate experimentally using ultrafast electron diffractive imaging of impulsively aligned trifluoro-iodomethane molecules. Here, the retrieved molecular orientation distribution is in good agreement with direct numerical simulations of the time-dependent Schrodinger equation using the experimental conditions. Unlike the existing retrieval methods, the retrieval method does not require solving Schrodinger equation, works for any alignment method, and is in principle applicable to asymmetric top molecules.

74 ATOMIC AND MOLECULAR PHYSICS↗