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DOE OSTI2016

Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels

To each hyperbolic Landau level of the Poincaré disc is attached a generalized negative binomial distribution. In this paper, we compute the moment generating function of this distribution and supply its atomic decomposition as a perturbation of the negative binomial distribution by a finitely supported measure. Using the Mandel parameter, we also discuss the nonclassical nature of the associated coherent states. Next, we derive a Lévy-Khintchine-type representation of its characteristic function when the latter does not vanish and deduce that it is quasi-infinitely divisible except for the lowest hyperbolic Landau level corresponding to the negative binomial distribution. By considering the total variation of the obtained quasi-Lévy measure, we introduce a new infinitely divisible distribution for which we derive the characteristic function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Statistical analysis of non-Maxwellian electron distribution functions measured with angularly resolved Thomson scattering

Angularly resolved Thomson scattering is a novel extension of Thomson scattering, enabling the measurement of the electron velocity distribution function over many orders of magnitude. Here, details of the theoretical basis of the technique and the instrument designed for this measurement are described. Angularly resolved Thomson-scattering data from several experiments are shown with descriptions of the corresponding distribution functions. A reduced model describing the distribution function is given and used to perform a Monte Carlo analysis of the uncertainty in the measurements. The electron density and temperature were determined to a precision of 12% and 21%, respectively, on average, while all other parameters defining the distribution function were generally determined to better than 20%. It was found that these uncertainties were primarily due to limited signal to noise and instrumental effects. Furthermore, measurements with this level of precision were sufficient to distinguish between Maxwellian and non-Maxwellian distribution functions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

2D microspatial distribution uniformity of photon detection efficiency and crosstalk probability of multi-pixel photon counters

Two-dimensional (2D) microspatial distribution uniformity of photon detection efficiency (PDE) and optical crosstalk probability P{sub ct} of multi-pixel photon counters (MPPCs) is studied. The experimental results show that the 2D spatial distribution of P{sub ct} is obviously uneven, i.e. P{sub ct} is larger at the corners and edges of a single pixel in MPPCs, which suggest a higher electrical field in the depletion region of the pixel at the corners and edges. The nonuniformity of the 2D spatial distribution of PDE also become evident when the size of the pixels of MPPCs is small, which signifies higher nonuniformity of the electric field distribution in MPPCs with small pixel size. A method is proposed for characterization of the 2D electrical field spatial distribution uniformity in a single pixel of MPPCs, which can be used for guiding the optimisation of the fabrication process of MPPCs and their properties. This promising method can naturally be extended to any Geiger avalanche photodiodes (G-APDs) and their arrays. (laser applications and other topics in quantum electronics)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

The color–magnitude distribution of small Jupiter Trojans

We present an analysis of survey observations targeting the leading L4 Jupiter Trojan cloud near opposition using the wide-field Suprime-Cam CCD camera on the 8.2 m Subaru Telescope. The survey covered about 38 deg{sup 2} of sky and imaged 147 fields spread across a wide region of the L4 cloud. Each field was imaged in both the g' and the i' band, allowing for the measurement of g – i color. We detected 557 Trojans in the observed fields, ranging in absolute magnitude from H = 10.0 to H = 20.3. We fit the total magnitude distribution to a broken power law and show that the power-law slope rolls over from 0.45 ± 0.05 to 0.36{sub -0.09}{sup +0.05} at a break magnitude of H{sub b}=14.93{sub -0.88}{sup +0.73}. Combining the best-fit magnitude distribution of faint objects from our survey with an analysis of the magnitude distribution of bright objects listed in the Minor Planet Center catalog, we obtain the absolute magnitude distribution of Trojans over the entire range from H = 7.2 to H = 16.4. We show that the g – i color of Trojans decreases with increasing magnitude. In the context of the less-red and red color populations, as classified in Wong et al. using photometric and spectroscopic data, we demonstrate that the observed trend in color for the faint Trojans is consistent with the expected trend derived from extrapolation of the best-fit color population magnitude distributions for bright cataloged Trojans. This indicates a steady increase in the relative number of less-red objects with decreasing size. Finally, we interpret our results using collisional modeling and propose several hypotheses for the color evolution of the Jupiter Trojan population.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

PROBING THE ROLE OF DYNAMICAL FRICTION IN SHAPING THE BSS RADIAL DISTRIBUTION. I. SEMI-ANALYTICAL MODELS AND PRELIMINARY N-BODY SIMULATIONS

We present semi-analytical models and simplified N-body simulations with 10{sup 4} particles aimed at probing the role of dynamical friction (DF) in determining the radial distribution of blue straggler stars (BSSs) in globular clusters. The semi-analytical models show that DF (which is the only evolutionary mechanism at work) is responsible for the formation of a bimodal distribution with a dip progressively moving toward the external regions of the cluster. However, these models fail to reproduce the formation of the long-lived central peak observed in all dynamically evolved clusters. The results of N-body simulations confirm the formation of a sharp central peak, which remains as a stable feature over time regardless of the initial concentration of the system. In spite of noisy behavior, a bimodal distribution forms in many cases, with the size of the dip increasing as a function of time. In the most advanced stages, the distribution becomes monotonic. These results are in agreement with the observations. Also, the shape of the peak and the location of the minimum (which, in most of cases, is within 10 core radii) turn out to be consistent with observational results. For a more detailed and close comparison with observations, including a proper calibration of the timescales of the dynamical processes driving the evolution of the BSS spatial distribution, more realistic simulations will be necessary.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Pseudorapidity distributions of charged particles in pp($\bar p$), p(d)A and AA collisions using Tsallis thermodynamics

The pseudorapidity distributions of charged particles measured in p + p($\overline{\text{p}}$) collisions for energies ranging from $\sqrt{{s}_{\mathrm{N}\mathrm{N}}}=23.6$ GeV to 13 TeV and A + A collisions at RHIC and LHC are investigated in the fireball model with Tsallis thermodynamics. We assume that the rapidity axis is populated with fireballs following q-Gaussian distribution and the charged particles follow the Tsallis distribution in the fireball. We also extend the fireball model to asymmetric collision systems, i.e. d + Au collisions at $\sqrt{{s}_{\mathrm{N}\mathrm{N}}}=200$ GeV and p + Pb collisions at $\sqrt{{s}_{\mathrm{N}\mathrm{N}}}=5.02$ TeV, by taking into account the asymmetric geometry configuration. The model can fit the experimental data well for all the collision systems and centralities investigated. The collision energy and centrality dependence of the model parameters for the symmetric (asymmetric) collision system, i.e. the central position y 0 (y 0a , y 0A ) and its width σ (σ a , σ A ) of the fireball distribution, are also investigated and discussed. Furthermore, our results suggest that the fireball model with Tsallis thermodynamics can be used as a universal framework for the pseudorapidity distributions of charged particles in high energy collisions at RHIC and LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Modelling the flux distribution function of the extragalactic gamma-ray background from dark matter annihilation

The one-point function (i.e., the isotropic flux distribution) is a complementary method to (anisotropic) two-point correlations in searches for a gamma-ray dark matter annihilation signature. Using analytical models of structure formation and dark matter halo properties, we compute the gamma-ray flux distribution due to annihilations in extragalactic dark matter halos, as it would be observed by the Fermi Large Area Telescope. Combining the central limit theorem and Monte Carlo sampling, we show that the flux distribution takes the form of a narrow Gaussian of 'diffuse' light, with an 'unresolved point source' power-law tail as a result of bright halos. We argue that this background due to dark matter constitutes an irreducible and significant background component for point-source annihilation searches with galaxy clusters and dwarf spheroidal galaxies, modifying the predicted signal-to-noise ratio. A study of astrophysical backgrounds to this signal reveals that the shape of the total gamma-ray flux distribution is very sensitive to the contribution of a dark matter component, allowing us to forecast promising one-point upper limits on the annihilation cross-section. We show that by using the flux distribution at only one energy bin, one can probe the canonical cross-section required for explaining the relic density, for dark matter of masses around tens of GeV.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Implications of different income distributions for future residential energy demand in the U.S.

Abstract Future income distribution will affect energy demand and its interactions with various societal priorities. Most future model simulations assume a single average consumer and thus miss this important demand determinant. We quantify long-term implications of alternative future income distributions for state-level residential energy demand, investment, greenhouse gas, and pollutant emission patterns in the United States (U.S.) by incorporating income quintiles into the residential energy sector of the Global Change Analysis Model with 50-state disaggregation. We find that if the income distribution within each U.S. state becomes more egalitarian than present, what means that the difference on income between the richest and poorest decreases over time, residential energy demand could be 10% (4%–14% across states) higher in 2100. This increase of residential energy demand will directly reduce energy poverty, with a very modest increment on economywide CO 2 emissions (1%–2%). On the other hand, if U.S. states transition to a less equitable income distribution than present, with the difference between richest and poorest increasing over time, residential energy demand could be 19% (12%–26% across states) lower. While this study focuses on a single sector, we conclude that to improve understanding of synergies and tradeoffs across multiple societal goals such as energy access, emissions, and investments, future model simulations should explicitly consider subregional income distribution impacts.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2014

THE MASS DISTRIBUTION OF COMPANIONS TO LOW-MASS WHITE DWARFS

Measuring the masses of companions to single-line spectroscopic binary stars is (in general) not possible because of the unknown orbital plane inclination. Even when the mass of the visible star can be measured, only a lower limit can be placed on the mass of the unseen companion. However, since these inclination angles should be isotropically distributed, for a large enough, unbiased sample, the companion mass distribution can be deconvolved from the distribution of observables. In this work, we construct a hierarchical probabilistic model to infer properties of unseen companion stars given observations of the orbital period and projected radial velocity of the primary star. We apply this model to three mock samples of low-mass white dwarfs (LMWDs; M ≲ 0.45 M {sub ☉}) and a sample of post-common-envelope binaries. We use a mixture of two Gaussians to model the WD and neutron star (NS) companion mass distributions. Our model successfully recovers the initial parameters of these test data sets. We then apply our model to 55 WDs in the extremely low-mass (ELM) WD Survey. Our maximum a posteriori model for the WD companion population has a mean mass μ{sub WD} = 0.74 M {sub ☉}, with a standard deviation σ{sub WD} = 0.24 M {sub ☉}. Our model constrains the NS companion fraction f {sub NS} to be <16% at 68% confidence. We make samples from the posterior distribution publicly available so that future observational efforts may compute the NS probability for newly discovered LMWDs.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Quasiparton distributions in massive QED2: Toward quantum computation

We analyze the quasiparton distributions of the lightest 𝜂′ meson in massive two-dimensional quantum electrodynamics (QED2) by exact diagonalization. The Hamiltonian and boost operators are mapped onto spin qubits in a spatial lattice with open boundary conditions. The lowest excited state in the exact diagonalization is shown to interpolate continuously between an anomalous 𝜂′ state at strong coupling, and a nonanomalous heavy meson at weak coupling, with a cusp at the critical point. The boosted 𝜂′ state follows relativistic kinematics but with large deviations in the luminal limit. The spatial quasiparton distribution function and amplitude for the 𝜂′ state are computed numerically for increasing rapidity both at strong and weak coupling, and compared to the exact light front results. The numerical results from the boosted form of the spatial parton distributions, compare fairly with the inverse Fourier transformation of the luminal parton distributions, derived in the lowest Fock space approximation. Our analysis points out some of the limitations facing the current lattice program for the parton distributions.

Lattice field theory↗

DOE OSTI2019

Modeling of Grid-Forming Inverters for Transient Stability Simulations of an all Inverter-based Distribution System

Existing models of grid-forming inverters are typically three-phase electromagnetic models and positive sequence electromechanical models. Both of them are not suitable for dynamic simulations of large scale three-phase unbalanced distribution systems. In order to investigate grid-forming inverters’ impact on the transient stability of large scale three-phase unbalanced distribution systems, a dynamic model of a grid-forming inverter is developed and implemented in an open-source GridLAB-D simulation environment. The advantage of this method is that it can be extended to full-size three-phase unbalanced distribution systems. Simulation results of an all grid-forming inverter-based modified version of IEEE 123-node distribution system verify the capability of grid-forming inverters to maintain the transient stability of a resilient distribution system.

Grid-forming, Inverter, Distribution System, Trans↗

DOE OSTI2017

A Hierarchical Modeling for Reactive Power Optimization With Joint Transmission and Distribution Networks by Curve Fitting

Here, in order to solve the reactive power optimization with joint transmission and distribution networks, a hierarchical modeling method is proposed in this paper. It allows the reactive power optimization of transmission and distribution networks to be performed separately, leading to a master–slave structure and improves traditional centralized modeling methods by alleviating the big data problem in a control center. Specifically, the transmission-distribution-network coordination issue of the hierarchical modeling method is investigated. First, a curve-fitting approach is developed to provide a cost function of the slave model for the master model, which reflects the impacts of each slave model. Second, the transmission and distribution networks are decoupled at feeder buses, and all the distribution networks are coordinated by the master reactive power optimization model to achieve the global optimality. Finally, numerical results on two test systems verify the effectiveness of the proposed hierarchical modeling and curve-fitting methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Evaluation of Distributed Power Apportioning with Net Load Management Engine in Microgrids Using Power Hardware-in-the-Loop Simulation

This article presents the performance evaluation of ratio consensus-based distributed power apportioning engine along with centralized net load management (NLM) engine that ensures viable and stable operation of an islanded microgrid. Managing net load variability in a microgrid with high penetrations of uncertain renewable generation and ever-changing load demands is a crucial need in order to ensure viable and stable operation of the microgrid. Centralized “dispatch-rule”-based and/or multi-agent-based distributed control of distributed energy resources (DERs) in microgrid are well accepted for microgrid by adapting ANSI/ISA-95-based hierarchical control architecture. In the application where microgrid network has large geographical span with multiple DERs dispersed in the network, high penetration of uncertain renewable energy resources, and ever-changing load demands, a judicious selection of techniques/solutions for managing net-load resources for maintaining viability and stability is required. With this motivation, this article proposes a novel solution to mitigate the challenges by incorporating a mixed centralized NLM engine and distributed power apportioning control of DERs and loads. A power-hardware-in-the-loop (PHIL) -based experiment is conducted with the centralized NLM engine and the distributed power apportioning engine along with two commercial inverters. The experimental results validates the efficacy of the proposed method in ensuring viability and stability of a microgrid.

hardware-in-the-loop simulation↗

DOE OSTI2023

Distributed Energy Resource-Cognizant Upgrade Paths to the Traditional Restoration Strategy of Utilities for Improved Load Restoration

Climate change has resulted in increasingly impactful and more frequent occurrences of extreme weather events. This trend poses a significant challenge for distribution utilities and system operators to ensure that there is uninterrupted power supply to critical loads in their networks under fault scenarios; however, currently, utilities deploying the automated fault location, isolation and restoration (FLISR) function in their advanced distribution management system (ADMS) do not take into account the available generation and load-modification capabilities of distributed energy resources present in the disconnected network due to an upstream isolated fault. This results in the network reconfiguration and restoration to result in sub-optimal load restoration. Therefore, this paper presents two approaches that can upgrade the existing FLISR capabilities of distribution utilities to significantly increase the restoration of critical loads. The performance of the proposed approaches is evaluated on a numerical model of a real distribution feeder in Georgia, USA.

DER↗

DOE OSTI2016

Methods for Dynamic Analysis of Distribution Feeders with High Penetration of PV Generators

An increase in the number of inverter-interfaced photovoltaic (PV) generators on existing distribution feeders affects the design, operation, and control of the distribution systems. Existing distribution system analysis tools are capable of supporting only snapshot and quasi-static analyses. Capturing the dynamic effects of PV generators during the variation in distribution system states is necessary when studying the effects of controller bandwidths, multiple voltage correction devices, and anti-islanding. This work explores the use of dynamic phasors and differential algebraic equations (DAE) for impact analysis of PV generators on the existing distribution feeders.

14 SOLAR ENERGY↗

DOE OSTI2021

Design of Resilient Electric Distribution Systems for Remote Communities: Surgical Load Management using Smart Meters

This paper describes a systematic process of designing resilient electric distribution systems and microgrids using smart meters for surgical load management (SLM) as part of Advanced Metering Infrastructure (AMI). The work focuses on selection approach, integration, and interoperability aspects for AMI in microgrids. SLM is proposed as a granular control methodology for serving selective critical loads across different distribution feeders in the system during extreme events. The surgical load shedding as well as load pick-up provides a robust approach for maximizing critical load served in a resource-constrained electric distribution system or a microgrid. We present the case of a 20 MW islanded microgrid in Cordova, AK, USA, which is the demonstration site for field validation of resilience enhancement technologies for the DOE-funded Grid Modernization project RADIANCE. Cordova microgrid is an islanded distribution grid that provides an environment to prove the approach, and the techniques may also be applicable to other regional distribution systems.

microgrids↗

DOE OSTI2020

Reverse and Forward Engineering of Local Voltage Control in Distribution Networks

The increasing penetration of renewable and distributed energy resources in distribution networks calls for real-time and distributed voltage control. As such, in this paper we investigate local Volt/VAR control with a general class of control functions, and show that the power system dynamics with non-incremental local voltage control can be seen as a distributed algorithm for solving a well-defined optimization problem (reverse engineering). The reverse engineering further reveals a fundamental limitation of the non-incremental voltage control: the convergence condition is restrictive and prevents better voltage regulation at equilibrium. This motivates us to design two incremental local voltage control schemes based on the subgradient and pseudo-gradient algorithms respectively for solving the same optimization problem (forward engineering). The new control schemes decouple the dynamical property from the equilibrium property, and have much less restrictive convergence conditions. This work presents another step towards developing a new foundation—network dynamics as optimization algorithms—for distributed real-time control and optimization of future power networks.

42 ENGINEERING↗

DOE OSTI2021

Clutter Distributions for Tomographic Image Standardization in Ground-Penetrating Radar

Multistatic ground-penetrating radar (GPR) signals can be imaged tomographically to produce 3-D distributions of image intensities. In the absence of objects of interest, these intensities can be considered to be estimates of clutter. These clutter intensities spatially vary over several orders of magnitude and vary across different arrays, which makes a direct comparison of these raw intensities difficult. However, by gathering statistics on these intensities and their spatial variation, a variety of metrics can be determined. In this study, the clutter distribution is found to fit better to a two-parameter Weibull distribution than Gaussian or log-normal distributions. Based on the spatial variation of the two Weibull parameters, scale and shape, more information may be gleaned from these data. How well the GPR array is illuminating various parts of the ground, in depth and cross track, may be determined from the spatial variation of the Weibull scale parameter, which may in turn be used to estimate an effective attenuation coefficient in the soil. The transition in depth from clutter- to noise-limited conditions (which is one possible definition of GPR penetration depth) can be estimated from the spatial variation of the Weibull shape parameter. Lastly, the underlying clutter distributions also provide an opportunity to standardize image intensities to determine when a statistically significant deviation from background (clutter) has occurred, which is convenient for buried threat detection algorithm development that needs to be robust across multiple different arrays.

42 ENGINEERING↗