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DOE OSTI2016

A NEW STATISTICAL PERSPECTIVE TO THE COSMIC VOID DISTRIBUTION

In this study, we obtain the size distribution of voids as a three-parameter redshift-independent log-normal void probability function (VPF) directly from the Cosmic Void Catalog (CVC). Although many statistical models of void distributions are based on the counts in randomly placed cells, the log-normal VPF that we obtain here is independent of the shape of the voids due to the parameter-free void finder of the CVC. We use three void populations drawn from the CVC generated by the Halo Occupation Distribution (HOD) Mocks, which are tuned to three mock SDSS samples to investigate the void distribution statistically and to investigate the effects of the environments on the size distribution. As a result, it is shown that void size distributions obtained from the HOD Mock samples are satisfied by the three-parameter log-normal distribution. In addition, we find that there may be a relation between the hierarchical formation, skewness, and kurtosis of the log-normal distribution for each catalog. We also show that the shape of the three-parameter distribution from the samples is strikingly similar to the galaxy log-normal mass distribution obtained from numerical studies. This similarity between void size and galaxy mass distributions may possibly indicate evidence of nonlinear mechanisms affecting both voids and galaxies, such as large-scale accretion and tidal effects. Considering the fact that in this study, all voids are generated by galaxy mocks and show hierarchical structures in different levels, it may be possible that the same nonlinear mechanisms of mass distribution affect the void size distribution.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

DLMP of Competitive Markets in Active Distribution Networks: Models, Solutions, Applications, and Visions

Traditionally, the electric distribution system operates with uniform energy prices across all system nodes. However, as the adoption of distributed energy resources (DERs) propels a shift from passive to active distribution network (ADN) operation, a distribution-level electricity market has been proposed to manage new complexities efficiently. In addition, distribution locational marginal price (DLMP) has been established in the literature as the primary pricing mechanism. The DLMP inherits the LMP concept in the transmission-level wholesale market but incorporates characteristics of the distribution system, such as high $R/X$ ratios and power losses, system imbalance, and voltage regulation needs. The DLMP provides a solution that can be essential for competitive market operation in future distribution systems. This article first provides an overview of the current distribution-level market architectures and their early implementations. Next, the general clearing model, model relaxations, and DLMP formulation are comprehensively reviewed. The state-of-the-art solution methods for distribution market clearing are summarized and categorized into centralized, distributed, and decentralized methods. Then, DLMP applications for the operation and planning of DERs and distribution system operators (DSOs) are discussed in detail. Finally, visions of future research directions and possible barriers and challenges are presented.

42 ENGINEERING↗

DOE OSTI2011

Development of activity pencil beam algorithm using measured distribution data of positron emitter nuclei generated by proton irradiation of targets containing {sup 12}C, {sup 16}O, and {sup 40}Ca nuclei in preparation of clinical application

Purpose: The purpose of this study is to develop a new calculation algorithm that is satisfactory in terms of the requirements for both accuracy and calculation time for a simulation of imaging of the proton-irradiated volume in a patient body in clinical proton therapy. Methods: The activity pencil beam algorithm (APB algorithm), which is a new technique to apply the pencil beam algorithm generally used for proton dose calculations in proton therapy to the calculation of activity distributions, was developed as a calculation algorithm of the activity distributions formed by positron emitter nuclei generated from target nuclear fragment reactions. In the APB algorithm, activity distributions are calculated using an activity pencil beam kernel. In addition, the activity pencil beam kernel is constructed using measured activity distributions in the depth direction and calculations in the lateral direction. {sup 12}C, {sup 16}O, and {sup 40}Ca nuclei were determined as the major target nuclei that constitute a human body that are of relevance for calculation of activity distributions. In this study, ''virtual positron emitter nuclei'' was defined as the integral yield of various positron emitter nuclei generated from each target nucleus by target nuclear fragment reactions with irradiated proton beam. Compounds, namely, polyethylene, water (including some gelatin) and calcium oxide, which contain plenty of the target nuclei, were irradiated using a proton beam. In addition, depth activity distributions of virtual positron emitter nuclei generated in each compound from target nuclear fragment reactions were measured using a beam ON-LINE PET system mounted a rotating gantry port (BOLPs-RGp). The measured activity distributions depend on depth or, in other words, energy. The irradiated proton beam energies were 138, 179, and 223 MeV, and measurement time was about 5 h until the measured activity reached the background level. Furthermore, the activity pencil beam data were made using the activity pencil beam kernel, which was composed of the measured depth data and the lateral data including multiple Coulomb scattering approximated by the Gaussian function, and were used for calculating activity distributions. Results: The data of measured depth activity distributions for every target nucleus by proton beam energy were obtained using BOLPs-RGp. The form of the depth activity distribution was verified, and the data were made in consideration of the time-dependent change of the form. Time dependence of an activity distribution form could be represented by two half-lives. Gaussian form of the lateral distribution of the activity pencil beam kernel was decided by the effect of multiple Coulomb scattering. Thus, the data of activity pencil beam involving time dependence could be obtained in this study. Conclusions: The simulation of imaging of the proton-irradiated volume in a patient body using target nuclear fragment reactions was feasible with the developed APB algorithm taking time dependence into account. With the use of the APB algorithm, it was suggested that a system of simulation of activity distributions that has levels of both accuracy and calculation time appropriate for clinical use can be constructed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Modeling efficient and equitable distribution of COVID-19 vaccines

Producing and distributing COVID-19 vaccine during the pandemic is a major logistical challenge requiring careful planning and efficient execution. This report presents information on logistical, policy and technical issues relevant to rapidly fielding a COVID-19 vaccination program. For this study we (a) conducted literature review and subject matter expert elicitation to understand current vaccine manufacturing and distribution capabilities and vaccine allocation strategies, (b) designed a baseline vaccine distribution strategy and modeling strategy to provide insight into the potential for targeted distribution of limited initial vaccine supplies, and (c) developed parametric interfaces to enable vaccine distribution scenarios to be analyzed in depth with Sandias Adaptive Recovery Model that will allow us evaluate the additional sub- populations and alternative distribution scenarios from a public health benefit and associated economic disruption Principal issues, challenges, and complexities that complicate COVID-19 vaccine delivery identified in our literature and subject matter expert investigation include these items: The United States has not mounted an urgent nationwide vaccination campaign in recent history. The existing global manufacturing and distribution infrastructure are not able to produce enough vaccine for the population immediately. Vaccines, once available will be scarce resources. Prioritization for vaccine allocation will be built on existing distribution networks. Vaccine distribution may not have a universal impact on disease transmission and morbidity because of scarcity, priority population demographics, and underlying disease transmission rates. Considerations for designing a vaccine distribution strategy are discussed. A baseline distribution strategy is designed and tested using the Adaptive Recovery Model, which couples a deterministic compartmental epidemiological model and a stochastic network model. We show the impact of this vaccine distribution strategy on hospitalizations, mortality, and contact tracing requirements. This model can be used to quantitatively evaluate alternative distribution scenarios, guiding policy decisions as vaccine candidates are narrowed down.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1994

A PV view of the zonal mean distribution of temperature and wind in the extratropical troposphere

The dependence of the temperature and wind distribution of the zonal mean flow in the extratropical troposphere on the gradient of pontential vorticity along isentropes is examined. The extratropics here refer to the region outside the Hadley circulation. Of particular interest is whether the distribution of temperature and wind corresponding to a constant potential vorticity (PV) along isentropes resembles the observed, and the implications of PV homogenization along isentropes for the role of the tropics. With the assumption that PV is homogenized along isentropes, it is found that the temperature distribution in the extratropical troposphere may be determined by a linear, first-order partial differential equation. When the observed surface temperature distribution and tropical lapse rate are used as the boundary conditions, the solution of the equation is close to the observed temperature distribution except in the upper troposphere adjacent to the Hadley circulation, where the troposphere with no PV gradient is considerably colder. Consequently, the jet is also stronger. It is also found that the meridional distribution of the balanced zonal wind is very sensitive to the meridional distribution of the tropopause temperature. The result may suggest that the requirement of the global momentum balance has no practical role in determining the extratropical temperature distribution. The authors further investigated the sensitivity of the extratropical troposphere with constant PV along isentropes to changes in conditions at the tropical boundary (the edge of the Hadley circulation). It is found that the temperature and wind distributions in the extratropical troposphere are sensitive to the vertical distribution of PV at the tropical boundary. With a surface distribution of temperature that decreases linearly with latitude, the jet maximum occurs at the tropical boundary and moves with it. The overall pattern of wind distribution is not sensitive to the change of the position of the tropical boundary. Finally, the temperature and wind distributions of an extratropical troposphere with a finite PV gradient are calculated. It is found that the larger the isentropic PV gradient, the warmer the troposphere and the weaker the jet.

Sun, De-Zheng↗

NASA NTRS1952

Altitude Investigation of Gas Temperature Distribution at Turbine of Three Similar Axial-Flow Turbojet Engines

An investigation of the effect of inlet pressure, corrected engine speed, and turbine temperature level on turbine-inlet gas temperature distributions was conducted on a J40-WE-6, interim J40-WE-6, and prototype J40-WE-8 turbojet engine in the altitude wind tunnel at the NAC.4 Lewis laboratory. The engines were investigated over a range of simulated pressure altitudes from 15,000 to 55,000 feet, flight Mach numbers from 0.12 to 0.64, and corrected engine speeds from 7198 to 8026 rpm, The gas temperature distribution at the turbine of the three engines over the range of operating conditions investigated was considered satisfactory from the standpoint of desired temperature distribution with one exception - the distribution for the J40-WE-6 engine indicated a trend with decreasing engine-inlet pressure for the temperature to exceed the desired in the region of the blade hub. Installation of a compressor-outlet mixer vane assembly remedied this undesirable temperature distribution, The experimental data have shown that turbine-inlet temperature distributions are influenced in the expected manner by changes in compressor-outlet pressure or mass-flow distribution and by changes in combustor hole-area distribution. The similarity between turbine-inlet and turbine-outlet temperature distribution indicated only a small shift in temperature distribution imposed by the turbine rotors. The attainable jet thrusts of the three engines were influenced in different degrees and directions by changes in temperature distributions with change in engine-inlet pressure. Inability to match the desired temperature distribution resulted, for the J40-WE-6 engine, in an 11-percent thrust loss based on an average turbine-inlet temperature of 1500 F at an engine-inlet pressure of 500 pounds per square foot absolute. Departure from the desired temperature distribution in the Slade tip region results, for the prototype J40-WE-8 engine, in an attainable thrust increase of 3 to 4 percent as compared with that obtained if tip-region temperature limitations were observed.

Prince, W.R.↗

DOE OSTI2015

Impact of the differential fluence distribution of brachytherapy sources on the spectroscopic dose-rate constant

Purpose: To investigate why dose-rate constants for {sup 125}I and {sup 103}Pd seeds computed using the spectroscopic technique, Λ{sub spec}, differ from those computed with standard Monte Carlo (MC) techniques. A potential cause of these discrepancies is the spectroscopic technique’s use of approximations of the true fluence distribution leaving the source, φ{sub full}. In particular, the fluence distribution used in the spectroscopic technique, φ{sub spec}, approximates the spatial, angular, and energy distributions of φ{sub full}. This work quantified the extent to which each of these approximations affects the accuracy of Λ{sub spec}. Additionally, this study investigated how the simplified water-only model used in the spectroscopic technique impacts the accuracy of Λ{sub spec}. Methods: Dose-rate constants as described in the AAPM TG-43U1 report, Λ{sub full}, were computed with MC simulations using the full source geometry for each of 14 different {sup 125}I and 6 different {sup 103}Pd source models. In addition, the spectrum emitted along the perpendicular bisector of each source was simulated in vacuum using the full source model and used to compute Λ{sub spec}. Λ{sub spec} was compared to Λ{sub full} to verify the discrepancy reported by Rodriguez and Rogers. Using MC simulations, a phase space of the fluence leaving the encapsulation of each full source model was created. The spatial and angular distributions of φ{sub full} were extracted from the phase spaces and were qualitatively compared to those used by φ{sub spec}. Additionally, each phase space was modified to reflect one of the approximated distributions (spatial, angular, or energy) used by φ{sub spec}. The dose-rate constant resulting from using approximated distribution i, Λ{sub approx,i}, was computed using the modified phase space and compared to Λ{sub full}. For each source, this process was repeated for each approximation in order to determine which approximations used in the spectroscopic technique affect the accuracy of Λ{sub spec}. Results: For all sources studied, the angular and spatial distributions of φ{sub full} were more complex than the distributions used in φ{sub spec}. Differences between Λ{sub spec} and Λ{sub full} ranged from −0.6% to +6.4%, confirming the discrepancies found by Rodriguez and Rogers. The largest contribution to the discrepancy was the assumption of isotropic emission in φ{sub spec}, which caused differences in Λ of up to +5.3% relative to Λ{sub full}. Use of the approximated spatial and energy distributions caused smaller average discrepancies in Λ of −0.4% and +0.1%, respectively. The water-only model introduced an average discrepancy in Λ of −0.4%. Conclusions: The approximations used in φ{sub spec} caused discrepancies between Λ{sub approx,i} and Λ{sub full} of up to 7.8%. With the exception of the energy distribution, the approximations used in φ{sub spec} contributed to this discrepancy for all source models studied. To improve the accuracy of Λ{sub spec}, the spatial and angular distributions of φ{sub full} could be measured, with the measurements replacing the approximated distributions. The methodology used in this work could be used to determine the resolution that such measurements would require by computing the dose-rate constants from phase spaces modified to reflect φ{sub full} binned at different spatial and angular resolutions.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2023

LA100 Equity Strategies. Chapter 12: Distribution Grid Upgrades for Equitable Resilience and Solar, Storage, and Electric Vehicle Access

The LA100 Equity Strategies project integrates community guidance with robust research, modeling, and analysis to identify strategy options that can increase equitable outcomes in Los Angeles' clean energy transition. As Los Angeles transitions toward clean energy, existing distribution grid infrastructure will need to be updated and expanded to support reliable service during routine operations, enable interconnection with distributed energy resources and electrified loads, and provide access to energy-related services during disasters. This chapter focuses on equity in distribution grid upgrades, reliability, and resilience in Los Angeles. Specifically, NREL performed grid upgrade and resilience analyses using a detailed model of the distribution grid and income-differentiated household load profiles, electric vehicle (EV) adoption patterns, distributed solar adoption, and grid reliability to explore two key questions to inform how the City of Los Angeles can ensure a resilient and reliable distribution grid for all communities during the clean energy transition: Where can distribution system upgrades can be prioritized to enable equitable access to, and adoption of, clean energy technologies and how can Los Angeles provide equitable, resilient access to electricity-related services (e.g., health care, food) during disaster events like earthquakes and flooding? The electric distribution system is the "last mile" of the grid, linking the multistate bulk power system with customers; new loads, including EVs; and distributed energy resources, such as customer and community solar and storage. This analysis focuses on the 4.8-kilovolt (kV) system, including service transformers that represent the utility-side of the grid connection for most residential customers. Chapter 17 looks at the customer-side of the grid connection with a focus on electric panel upgrade needs. The transition toward clean energy can put additional stress on the distribution system from distributed energy resources and electrification - especially EVs and increased use of electricity for heating, cooling, cooking, and hot water. This stress, measured here as the number of equipment overloads and voltage violations, correlates strongly to grid reliability and therefore is used as a proxy for understanding additional upgrades needed and to help ensure equitable access to electrification and distributed energy resources. NREL also conducted community resilience analysis to examine customer-level access to both electricity and a larger range of services, such as hospitals and grocery stores during a disaster. This analysis explicitly considers equity to understand differences in current resilience and resilience strategies to effectively improve critical services access for all Angelenos. Research was guided by input from the community engagement process, and associated equity strategies are presented in alignment with that guidance.

14 SOLAR ENERGY↗

DOE OSTI2019

California Time-of-Use (TOU) Transition: Effects on Distributed Wind and Solar Economic Potential

Time-of-use (TOU) retail energy rates price electricity differently by the time of day, thereby communicating to consumers the costs of supplying electricity throughout the day. This study evaluates the impact of Decision D.15.07-001, which mandates a transition to default TOU rates in California, on the economic viability of behind-the-meter distributed wind and solar systems. We assess viability through 'economic potential,' a metric we define as the amount of generation capacity that exceeds a specified rate of return (5.4%) and therefore would be economic to construct; we do not attempt to project deployment or adoption. In addition, we identify cost improvements needed for a robust distributed wind market and the specific counties and sectors with substantial economic potential. Over the scenarios considered, model results indicate realistic pathways to reaching a robust, 1-GW distributed wind market in California though solar economic potential was found to be substantially larger than that of wind. Distributed wind's capacity factor does not appear to be strongly correlated to the periods of peak electricity prices as set by utility's TOU periods. Because of this disassociation and nuances in the billing of tiered electricity, the transition to TOU is projected to moderately decrease distributed wind economic potential and increase that of distributed solar. However, a limitation of this analysis is that it does not factor in the change in rate values as California works toward its goal of 100% renewables. As variable renewable energy penetration increases to meet this goal, our results suggest that wind generation will become increasingly correlated to periods of peak electricity prices. Increased variable renewable penetration, especially of solar, is likely to shift periods of higher electricity demand to later in the evening, and any periodic adjustments in TOU periods to reflect these new periods of demand will positively affect the value of wind generation more than the value of solar generation. High distributed wind capital costs are a significant barrier to large scale adoption; we explore the sensitivity of capital cost reductions on distributed wind economic potential. We find that distributed wind economic potential increases substantially in 2020 for capital costs below 3 dollars/W - particularly for residential- and commercial-scale turbines; capital costs must fall below 2 dollars/W in 2030 to support a significant increase in economic potential, in large part due to the expected continued cost reductions in solar. We identified an upper limit to the state's behind-the-meter distributed wind economic potential at approximately 5 GW. Overall, California exhibits over 1 GW of economic potential for distributed wind by 2030, even with the moderate decrease in potential under TOU. This potential is represented mostly by Southern California, which sees the most notable increase in economic viability as capital expenditure prices decline.

17 WIND ENERGY↗

DOE OSTI2013

INITIAL PLANETESIMAL SIZES AND THE SIZE DISTRIBUTION OF SMALL KUIPER BELT OBJECTS

The Kuiper Belt is a remnant from the early solar system and its size distribution contains many important constraints that can be used to test models of planet formation and collisional evolution. We show, by comparing observations with theoretical models, that the observed Kuiper Belt size distribution is well matched by coagulation models, which start with an initial planetesimal population with radii of about 1 km, and subsequent collisional evolution. We find that the observed size distribution above R {approx} 30 km is primordial, i.e., it has not been modified by collisional evolution over the age of the solar system, and that the size distribution below R {approx} 30 km has been modified by collisions and that its slope is well matched by collisional evolution models that use published strength laws. We investigate in detail the resulting size distribution of bodies ranging from 0.01 km to 30 km and find that its slope changes several times as a function of radius before approaching the expected value for an equilibrium collisional cascade of material strength dominated bodies for R {approx}< 0.1 km. Compared to a single power-law size distribution that would span the whole range from 0.01 km to 30 km, we find in general a strong deficit of bodies around R {approx} 10 km and a strong excess of bodies around 2 km in radius. This deficit and excess of bodies are caused by the planetesimal size distribution left over from the runaway growth phase, which left most of the initial mass in small planetesimals while only a small fraction of the total mass is converted into large protoplanets. This excess mass in small planetesimals leaves a permanent signature in the size distribution of small bodies that is not erased after 4.5 Gyr of collisional evolution. Observations of the small Kuiper Belt Object (KBO) size distribution can therefore test if large KBOs grew as a result of runaway growth and constrained the initial planetesimal sizes. We find that results from recent KBO occultation surveys and the observed KBO size distribution can be best matched by an initial planetesimal population that contained about equal mass per logarithmic mass bin in bodies ranging from 0.4 km to 4 km in radius. We further find that we cannot match the observed KBO size distribution if most of the planetesimal mass was contained in bodies that were 10 km in radius or larger simply because their resulting size distribution cannot be sufficiently depleted over 4.5 Gyr to match observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

THE GALACTIC SPATIAL DISTRIBUTION OF OB ASSOCIATIONS AND THEIR SURROUNDING SUPERNOVA-GENERATED SUPERBUBBLES

The Galactic spatial distribution of OB associations and their surrounding superbubbles (SBs) reflect the distribution of a wide range of important processes in our Galaxy. In particular, it can provide a three-dimensional measure not only of the major source distribution of Galactic cosmic rays, but also the Galactic star formation distribution, the Lyman continuum ionizing radiation distribution, the core-collapse supernova distribution, the neutron star and stellar black hole production distribution, and the principal source distribution of freshly synthesized elements. Thus, we construct a three-dimensional spatial model of the massive-star distribution based primarily on the emission of the H II envelopes that surround the giant SBs and are maintained by the ionizing radiation of the embedded O stars. The Galactic longitudinal distribution of the 205 μm N II radiation, emitted by these H II envelopes, is used to infer the spatial distribution of SBs. We find that the Galactic SB distribution is dominated by the contribution of massive-star clusters residing in the spiral arms.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Comparison of methods for the measurement of radiation dose distributions in high dose rate (HDR) brachytherapy: Ge-doped optical fiber, EBT3 Gafchromic film, and PRESAGE{sup Registered-Sign} radiochromic plastic

Purpose: Dose distribution measurement in clinical high dose rate (HDR) brachytherapy is challenging, because of the high dose gradients, large dose variations, and small scale, but it is essential to verify accurate treatment planning and treatment equipment performance. The authors compare and evaluate three dosimetry systems for potential use in brachytherapy dose distribution measurement: Ge-doped optical fibers, EBT3 Gafchromic film with multichannel analysis, and the radiochromic material PRESAGE{sup Registered-Sign} with optical-CT readout. Methods: Ge-doped SiO{sub 2} fibers with 6 {mu}m active core and 5.0 mm length were sensitivity-batched and their thermoluminescent properties used via conventional heating and annealing cycles. EBT3 Gafchromic film of 30 {mu}m active thickness was calibrated in three color channels using a nominal 6 MV linear accelerator. A 48-bit transmission scanner and advanced multichannel analysis method were utilized to derive dose measurements. Samples of the solid radiochromic polymer PRESAGE{sup Registered-Sign }, 60 mm diameter and 100 mm height, were analyzed with a parallel beam optical CT scanner. Each dosimetry system was used to measure the dose as a function of radial distance from a Co-60 HDR source, with results compared to Monte Carlo TG-43 model data. Each system was then used to measure the dose distribution along one or more lines through typical clinical dose distributions for cervix brachytherapy, with results compared to treatment planning system (TPS) calculations. Purpose-designed test objects constructed of Solid Water and held within a full-scatter water tank were utilized. Results: All three dosimetry systems reproduced the general shape of the isolated source radial dose function and the TPS dose distribution. However, the dynamic range of EBT3 exceeded those of doped optical fibers and PRESAGE{sup Registered-Sign }, and the latter two suffered from unacceptable noise and artifact. For the experimental conditions used in this study, the useful range from an isolated HDR source was 5-40 mm for fibers, 3-50 mm for EBT3, and 4-21 mm for PRESAGE{sup Registered-Sign }. Fibers demonstrated some over-response at very low dose levels, suffered from volume averaging effects in the dose distribution measurement, and exhibited up to 9% repeatability variation over three repeated measurements. EBT3 demonstrated excellent agreement with Monte Carlo and TPS dose distributions, with up to 3% repeatability over three measurements. PRESAGE{sup Registered-Sign} gave promising results, being the only true 3D dosimeter, but artifacts and noise were apparent. Conclusions: The comparative response of three emerging dosimetry systems for clinical brachytherapy dose distribution measurement has been investigated. Ge-doped optical fibers have excellent spatial resolution for single-direction measurement but are currently too large for complex dose distribution assessment. The use of PRESAGE{sup Registered-Sign} with optical-CT readout gave promising results in the measurement of true 3D dose distributions but further development work is required to reduce noise and improve dynamic range for brachytherapy dose distribution measurements. EBT3 Gafchromic film with multichannel analysis demonstrated accurate and reproducible measurement of dose distributions in HDR brachytherapy. Calibrated dose measurements were possible with agreement within 1.5% of TPS dose calculations. The suitability of EBT3 as a dosimeter for 2D quality control or commissioning work has been demonstrated.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2011

THE MASS DISTRIBUTION OF STELLAR-MASS BLACK HOLES

We perform a Bayesian analysis of the mass distribution of stellar-mass black holes using the observed masses of 15 low-mass X-ray binary systems undergoing Roche lobe overflow and 5 high-mass, wind-fed X-ray binary systems. Using Markov Chain Monte Carlo calculations, we model the mass distribution both parametrically-as a power law, exponential, Gaussian, combination of two Gaussians, or log-normal distribution-and non-parametrically-as histograms with varying numbers of bins. We provide confidence bounds on the shape of the mass distribution in the context of each model and compare the models with each other by calculating their relative Bayesian evidence as supported by the measurements, taking into account the number of degrees of freedom of each model. The mass distribution of the low-mass systems is best fit by a power law, while the distribution of the combined sample is best fit by the exponential model. This difference indicates that the low-mass subsample is not consistent with being drawn from the distribution of the combined population. We examine the existence of a 'gap' between the most massive neutron stars and the least massive black holes by considering the value, M{sub 1%}, of the 1% quantile from each black hole mass distribution as the lower bound of black hole masses. Our analysis generates posterior distributions for M{sub 1%}; the best model (the power law) fitted to the low-mass systems has a distribution of lower bounds with M{sub 1%}>4.3 M{sub sun} with 90% confidence, while the best model (the exponential) fitted to all 20 systems has M{sub 1%}>4.5 M{sub sun} with 90% confidence. We conclude that our sample of black hole masses provides strong evidence of a gap between the maximum neutron star mass and the lower bound on black hole masses. Our results on the low-mass sample are in qualitative agreement with those of Ozel et al., although our broad model selection analysis more reliably reveals the best-fit quantitative description of the underlying mass distribution. The results on the combined sample of low- and high-mass systems are in qualitative agreement with Fryer and Kalogera, although the presence of a mass gap remains theoretically unexplained.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

A Cyber-Resilience Risk Management Architecture for Distributed Wind

Distributed wind is an electric energy resource segment with strong potential to be deployed in many applications, but special consideration of resilience and cybersecurity is needed to address the unique conditions associated with distributed wind. Distributed wind is a strong candidate to help meet renewable energy and carbon-free energy goals. However, care must be taken as more systems are installed to ensure that the systems are reliable, resilient, and secure. The physical and communications requirements for distributed wind mean that there are unique cybersecurity considerations, but there is little to no existing guidance on best practices for cybersecurity risk management for distributed wind systems specifically. This research develops an architecture for the consideration of cyber risks associated with distributed wind systems. The architecture takes into account the configurations, challenges, and standards for distributed wind to create a risk-focused perspective that considers of threats, vulnerabilities, and consequences, with special emphasis on what sets distributed wind systems apart from other distributed energy resources (DER). We discuss common distributed wind architectures and how they are interconnected to larger power systems. Because cybersecurity cannot exist independently, the cyber-resilience architecture must consider the system holistically. Finally, we discuss the implementation of a risk assessment process that uses the cyber-resilience framework to address challenges specific to distributed wind.

17 WIND ENERGY↗

DOE OSTI2013

A Bayesian Modeling Approach for Estimation of a Shape-Free Groundwater Age Distribution using Multiple Tracers

The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated. A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; 3 H, 3 He, 85 Kr, 39 Ar) and the La Selva Biological Station (Costa-Rica; SF 6 , CFCs, 3 H, 4 He and 14 C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the freeform approach, especially for the cases where a larger amount of observed data is available and when the real groundwater distribution is more complex than can be represented by simple mathematical forms.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2013

Spatial frequency spectrum of the x-ray scatter distribution in CBCT projections

Purpose: X-ray scatter is a source of significant image quality loss in cone-beam computed tomography (CBCT). The use of Monte Carlo (MC) simulations separating primary and scattered photons has allowed the structure and nature of the scatter distribution in CBCT to become better elucidated. This work seeks to quantify the structure and determine a suitable basis function for the scatter distribution by examining its spectral components using Fourier analysis.Methods: The scatter distribution projection data were simulated using a CBCT MC model based on the EGSnrc code. CBCT projection data, with separated primary and scatter signal, were generated for a 30.6 cm diameter water cylinder [single angle projection with varying axis-to-detector distance (ADD) and bowtie filters] and two anthropomorphic phantoms (head and pelvis, 360 projections sampled every 1°, with and without a compensator). The Fourier transform of the resulting scatter distributions was computed and analyzed both qualitatively and quantitatively. A novel metric called the scatter frequency width (SFW) is introduced to determine the scatter distribution's frequency content. The frequency content results are used to determine a set basis functions, consisting of low-frequency sine and cosine functions, to fit and denoise the scatter distribution generated from MC simulations using a reduced number of photons and projections. The signal recovery is implemented using Fourier filtering (low-pass Butterworth filter) and interpolation. Estimates of the scatter distribution are used to correct and reconstruct simulated projections.Results: The spatial and angular frequencies are contained within a maximum frequency of 0.1 cm{sup −1} and 7/(2π) rad{sup −1} for the imaging scenarios examined, with these values varying depending on the object and imaging setup (e.g., ADD and compensator). These data indicate spatial and angular sampling every 5 cm and π/7 rad (∼25°) can be used to properly capture the scatter distribution, with reduced sampling possible depending on the imaging scenario. Using a low-pass Butterworth filter, tuned with the SFW values, to denoise the scatter projection data generated from MC simulations using 10{sup 6} photons resulted in an error reduction of greater than 85% for the estimating scatter in single and multiple projections. Analysis showed that the use of a compensator helped reduce the error in estimating the scatter distribution from limited photon simulations by more than 37% when compared to the case without a compensator for the head and pelvis phantoms. Reconstructions of simulated head phantom projections corrected by the filtered and interpolated scatter estimates showed improvements in overall image quality.Conclusions: The spatial frequency content of the scatter distribution in CBCT is found to be contained within the low frequency domain. The frequency content is modulated both by object and imaging parameters (ADD and compensator). The low-frequency nature of the scatter distribution allows for a limited set of sine and cosine basis functions to be used to accurately represent the scatter signal in the presence of noise and reduced data sampling decreasing MC based scatter estimation time. Compensator induced modulation of the scatter distribution reduces the frequency content and improves the fitting results.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2022

Automated Identification of Characteristic Droplet Size Distributions in Stratocumulus Clouds Utilizing a Data Clustering Algorithm

Abstract Droplet-level interactions in clouds are often parameterized by a modified gamma fitted to a “global” droplet size distribution. Do “local” droplet size distributions of relevance to microphysical processes look like these average distributions? This paper describes an algorithm to search and classify characteristic size distributions within a cloud. The approach combines hypothesis testing, specifically, the Kolmogorov–Smirnov (KS) test, and a widely used class of machine learning algorithms for identifying clusters of samples with similar properties: density-based spatial clustering of applications with noise (DBSCAN) is used as the specific example for illustration. The two-sample KS test does not presume any specific distribution, is parameter free, and avoids biases from binning. Importantly, the number of clusters is not an input parameter of the DBSCAN-type algorithms but is independently determined in an unsupervised fashion. As implemented, it works on an abstract space from the KS test results, and hence spatial correlation is not required for a cluster. The method is explored using data obtained from the Holographic Detector for Clouds (HOLODEC) deployed during the Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) field campaign. The algorithm identifies evidence of the existence of clusters of nearly identical local size distributions. It is found that cloud segments have as few as one and as many as seven characteristic size distributions. To validate the algorithm’s robustness, it is tested on a synthetic dataset and successfully identifies the predefined distributions at plausible noise levels. The algorithm is general and is expected to be useful in other applications, such as remote sensing of cloud and rain properties. Significance Statement A typical cloud can have billions of drops spread over tens or hundreds of kilometers in space. Keeping track of the sizes, positions, and interactions of all of these droplets is impractical, and, as such, information about the relative abundance of large and small drops is typically quantified with a “size distribution.” Droplets in a cloud interact locally, however, so this work is motivated by the question of whether the cloud droplet size distribution is different in different parts of a cloud. A new method, based on hypothesis testing and machine learning, determines how many different size distributions are contained in a given cloud. This is important because the size distribution describes processes such as cloud droplet growth and light transmission through clouds.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2011

SEPARATION OF THE INTERSTELLAR BOUNDARY EXPLORER RIBBON FROM GLOBALLY DISTRIBUTED ENERGETIC NEUTRAL ATOM FLUX

The Interstellar Boundary Explorer (IBEX) observes a remarkable feature, the IBEX ribbon, which has energetic neutral atom (ENA) flux over a narrow region {approx}20{sup 0} wide, a factor of 2-3 higher than the more globally distributed ENA flux. Here, we separate ENA emissions in the ribbon from the distributed flux by applying a transparency mask over the ribbon and regions of high emissions, and then solve for the distributed flux using an interpolation scheme. Our analysis shows that the energy spectrum and spatial distribution of the ribbon are distinct from the surrounding globally distributed flux. The ribbon energy spectrum shows a knee between {approx}1 and 4 keV, and the angular distribution is approximately independent of energy. In contrast, the distributed flux does not show a clear knee and more closely conforms to a power law over much of the sky. Consistent with previous analyses, the slope of the power law steepens from the nose to tail, suggesting a weaker termination shock toward the tail as compared to the nose. The knee in the energy spectrum of the ribbon suggests that its source plasma population is generated via a distinct physical process. Both the slope in the energy distribution of the distributed flux and the knee in the energy distribution of the ribbon are ordered by latitude. The heliotail may be identified in maps of globally distributed flux as a broad region of low flux centered {approx}44{sup 0}W of the interstellar downwind direction, suggesting heliotail deflection by the interstellar magnetic field.

79 ASTRONOMY AND ASTROPHYSICS↗