SEARCH · Search NASA

Results for “Methods:statistical”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,405 records · Page 78

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Performance evaluation of cosmic ray muon trajectory estimation algorithms

Muons, being elementary particles with minimal interaction with nuclear materials and abundant at sea level, have sparked interest in utilizing them for imaging various applications, such as mining [Borselli et al., Sci. Rep. 12, 22329 (2022)], volcano imaging [Nagamine et al., Nucl. Instrum. Meth. A, 356, 585(1995)], and underground tunnel detection [Guardincerri et al., Pure Appl. Geophys. 174, 2133 (2017)]. Recently, their use in nuclear nonproliferation and safeguard verification has gained attention, particularly in cargo screening for nuclear waste smuggling [Baesso et al., J. Instrum. 9, C10041 (2014)], source localization [L. J. Schultz et al., Nucl. Instrum. Meth. A 519, 687 (2004)], and locating nuclear fuel debris in reactors [Borozdin et al., Phys. Rev. Let. 109, 152501 (2012)]. However, the resolution of muon image reconstruction techniques is limited due to multiple Coulomb scattering (MCS) within the target object. To achieve robust muon tomography, it is crucial to develop efficient and flexible physics-based algorithms that can model the MCS process accurately and estimate the most probable trajectory of muons as they pass through the target object. To address this limitation, in this study, a novel algorithmic approach utilizing the Bayesian probability theory and Gaussian approximation of MCS is chosen. Different energy levels, materials, and target sizes were considered in the evaluations. The results demonstrate that the Generalized Muon Trajectory Estimation (GMTE) algorithm offers significant improvements over currently used algorithms. Across all test scenarios, the GMTE algorithm demonstrated ~50% and 38% increase in precision compared to Straight Line Path (SLP) and Point of Closest Approach (PoCA) algorithms, respectively. Furthermore, it exhibited 10%–35% and 10%–15% increases in muon flux utilization for high and medium Z materials, respectively, compared to the PoCA algorithm. In conclusion, the extensive simulations confirm the enhanced performance and efficiency of the GMTE algorithm, offering improved resolution and reduced measurement time for cosmic ray muon imaging compared to the current SLP and PoCA algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Optimizing time integration for accurate recovery of shockwave interface location in radiography

We present simulations and experiments of time integrated radiographic imaging of a moving 1D shock wave front and a quantitative method for determining the statistical error in locating the shock front as a function of integration time and noise in the radiograph. We discuss the trade-off between increasing motion blur, which leads to decreased shock front location certainty, and increasing signal-to-noise, which leads to improved image quality with increasing integration time. We find an optimum integration time between a short integration time, where noise limits the error, and a long integration time, where motion blurring limits the error. This methodology can be used to tune experimental configurations to obtain the highest quality radiograph for a given experimental configuration.

Bremsstrahlung↗

DOE OSTI2012

ADAPTIVE OPTICS IMAGES OF KEPLER OBJECTS OF INTEREST

All transiting planets are at risk of contamination by blends with nearby, unresolved stars. Blends dilute the transit signal, causing the planet to appear smaller than it really is, or produce a false-positive detection when the target star is blended with eclipsing binary stars. This paper reports on high spatial-resolution adaptive optics images of 90 Kepler planetary candidates. Companion stars are detected as close as 0.''1 from the target star. Images were taken in the near-infrared (J and Ks bands) with ARIES on the MMT and PHARO on the Palomar Hale 200 inch telescope. Most objects (60%) have at least one star within 6'' separation and a magnitude difference of 9. Eighteen objects (20%) have at least one companion within 2'' of the target star; six companions (7%) are closer than 0.''5. Most of these companions were previously unknown, and the associated planetary candidates should receive additional scrutiny. Limits are placed on the presence of additional companions for every system observed, which can be used to validate planets statistically using the BLENDER method. Validation is particularly critical for low-mass, potentially Earth-like worlds, which are not detectable with current-generation radial velocity techniques. High-resolution images are thus a crucial component of any transit follow-up program.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

CONSTRAINING SUB-PARSEC BINARY SUPERMASSIVE BLACK HOLES IN QUASARS WITH MULTI-EPOCH SPECTROSCOPY. I. THE GENERAL QUASAR POPULATION

We perform a systematic search for sub-parsec binary supermassive black holes (BHs) in normal broad-line quasars at z < 0.8, using multi-epoch Sloan Digital Sky Survey (SDSS) spectroscopy of the broad Hβ line. Our working model is that (1) one and only one of the two BHs in the binary is active; (2) the active BH dynamically dominates its own broad-line region (BLR) in the binary system, so that the mean velocity of the BLR reflects the mean velocity of its host BH; (3) the inactive companion BH is orbiting at a distance of a few R{sub BLR}, where R{sub BLR} ∼ 0.01-0.1 pc is the BLR size. We search for the expected line-of-sight acceleration of the broad-line velocity from binary orbital motion by cross-correlating SDSS spectra from two epochs separated by up to several years in the quasar rest frame. Out of ∼700 pairs of spectra for which we have good measurements of the velocity shift between two epochs (1σ error ∼40 km s{sup –1}), we detect 28 systems with significant velocity shifts in broad Hβ, among which 7 are the best candidates for the hypothesized binaries, 4 are most likely due to broad-line variability in single BHs, and the rest are ambiguous. Continued spectroscopic observations of these candidates will easily strengthen or disprove these claims. We use the distribution of the observed accelerations (mostly non-detections) to place constraints on the abundance of such binary systems among the general quasar population. Excess variance in the velocity shift is inferred for observations separated by longer than 0.4 yr (quasar rest frame). Attributing all the excess to binary motion would imply that most of the quasars in this sample must be in binaries, that the inactive BH must be on average more massive than the active one, and that the binary separation is at most a few times the size of the BLR. However, if this excess variance is partly or largely due to long-term broad-line variability, the requirement of a large population of close binaries is much weakened or even disfavored for massive companions. Future time-domain spectroscopic surveys of normal quasars can provide vital prior information on the structure function of stochastic velocity shifts induced by broad-line variability in single BHs. Such surveys with improved spectral quality, increased time baseline, and more epochs can greatly improve the statistical constraints of this method on the general binary population in broad-line quasars, further shrink the allowed binary parameter space, and detect true sub-parsec binaries.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Architecture of Kepler's multi-transiting systems. II. New investigations with twice as many candidates

We report on the orbital architectures of Kepler systems having multiple-planet candidates identified in the analysis of data from the first six quarters of Kepler data and reported by Batalha et al. (2013). These data show 899 transiting planet candidates in 365 multiple-planet systems and provide a powerful means to study the statistical properties of planetary systems. Using a generic mass-radius relationship, we find that only two pairs of planets in these candidate systems (out of 761 pairs total) appear to be on Hill-unstable orbits, indicating ∼96% of the candidate planetary systems are correctly interpreted as true systems. We find that planet pairs show little statistical preference to be near mean-motion resonances. We identify an asymmetry in the distribution of period ratios near first-order resonances (e.g., 2:1, 3:2), with an excess of planet pairs lying wide of resonance and relatively few lying narrow of resonance. Finally, based upon the transit duration ratios of adjacent planets in each system, we find that the interior planet tends to have a smaller transit impact parameter than the exterior planet does. This finding suggests that the mode of the mutual inclinations of planetary orbital planes is in the range 1.°0-2.°2, for the packed systems of small planets probed by these observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

RECONSTRUCTING THE SHAPE OF THE CORRELATION FUNCTION

We develop an estimator for the correlation function which, in the ensemble average, returns the shape of the correlation function, even for signals that have significant correlations on the scale of the survey region. Our estimator is general and works in any number of dimensions. We develop versions of the estimator for both diffuse and discrete signals. As an application, we apply them to Monte Carlo simulations of X-ray background measurements. These include a realistic, spatially inhomogeneous population of spurious detector events. We discuss applying the estimator to the averaging of correlation functions evaluated on several small fields, and to other cosmological applications.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

The Completed SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: N-body Mock Challenge for Galaxy Clustering Measurements

We develop a series of N-body data challenges, functional to the final analysis of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 (DR16) galaxy sample. The challenges are primarily based on high-fidelity catalogues constructed from the Outer Rim simulation - a large box size realization (3h(-1) Gpc) characterized by an unprecedented combination of volume and mass resolution, down to 1.85 x 10(9) h(-1)M(circle dot). We generate synthetic galaxy mocks by populating Outer Rim haloes with a variety of halo occupation distribution (HOD) schemes of increasing complexity, spanning different redshift intervals. We then assess the performance of three complementary redshift space distortion (RSD) models in configuration and Fourier space, adopted for the analysis of the complete DR16 eBOSS sample of Luminous Red Galaxies (LRG5). We find all the methods mutually consistent, with comparable systematic errors on the Alcock-Paczynski parameters and the growth of structure, and robust to different HOD prescriptions - thus validating the robustness of the models and the pipelines used for the baryon acoustic oscillation (BAO) and full shape clustering analysis. In particular, all the techniques are able to recover and alpha(11) to within 0.9 per cent, and f sigma(8) to within 1.5 per cent. As a by-product of our work, we are also able to gain interesting insights on the galaxy-halo connection. Our study is relevant for the final eBOSS DR16 'consensus cosmology', as the systematic error budget is informed by testing the results of analyses against these high-resolution mocks. In addition, it is also useful for future large-volume surveys, since similar mock-making techniques and systematic corrections can be readily extended to model for instance the Dark Energy Spectroscopic Instrument (DESI) galaxy sample.

cosmology: theory, large-scale structure of Univer↗

DOE OSTI2021

Using action space clustering to constrain the recent accretion history of Milky Way-like galaxies

ABSTRACT In the currently favoured cosmological paradigm galaxies form hierarchically through the accretion of satellites. Since a satellite is less massive than the host, its stars occupy a smaller volume in action space. Actions are conserved when the potential of the host halo changes adiabatically, so stars from an accreted satellite would remain clustered in action space as the host evolves. In this paper, we identify recently disrupted accreted satellites in three Milky Way-like disc galaxies from the cosmological baryonic FIRE-2 simulations by tracking satellites through simulation snapshots. We try to recover these satellites by applying the cluster analysis algorithm Enlink to the orbital actions of accreted star particles in the z = 0 snapshot. Even with completely error-free mock data we find that only 35 per cent (14/39) satellites are well recovered while the rest (25/39) are poorly recovered (i.e. either contaminated or split up). Most (10/14 ∼70 per cent) of the well-recovered satellites have infall times <7.1 Gyr ago and total mass >4 × 108M⊙ (stellar mass more than 1.2 × 106 M⊙, although our upper mass limit is likely to be resolution dependent). Since cosmological simulations predict that stellar haloes include a population of in situ stars, we test our ability to recover satellites when the data include 10–50 per cent in situ contamination. We find that most previously well-recovered satellites stay well recovered even with 50 per cent contamination. With the wealth of 6D phase space data becoming available we expect that cluster analysis in action space will be useful in identifying the majority of recently accreted and moderately massive satellites in the Milky Way.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

AbacusHOD : a highly efficient extended multitracer HOD framework and its application to BOSS and eBOSS data

ABSTRACT We introduce the AbacusHOD model and present two applications of AbacusHOD and the AbacusSummit simulations to observations. AbacusHOD is a Halo Occupation Distribution (HOD) framework written in Python that is particle-based, multitracer, highly generalized, and highly efficient. It is designed specifically with multitracer/cosmology analyses for next-generation large-scale structure surveys in mind, and takes advantage of the volume and precision offered by the new state-of-the-art AbacusSummit cosmological simulations. The model is also highly customizable and should be broadly applicable to any upcoming surveys and a diverse range of cosmological analyses. In this paper, we demonstrate the capabilities of the AbacusHOD framework through two example applications. The first example demonstrates the high efficiency and the large HOD extension feature set through an analysis of full-shape redshift-space clustering of BOSS galaxies at intermediate to small scales ($\lt 30\, h^{-1}$ Mpc), assessing the necessity of introducing secondary galaxy biases (assembly bias). We find strong evidence for using halo environment instead of concentration to trace secondary galaxy bias, a result which also leads to a moderate reduction in the ‘lensing is low’ tension. The second example demonstrates the multitracer capabilities of the AbacusHOD package through an analysis of the extended Baryon Oscillation Spectroscopic Survey cross-correlation measurements between three different galaxy tracers: luminous red galaxies, emission-line galaxies, and quasi-stellar objects. We expect the AbacusHOD framework, in combination with the AbacusSummit simulation suite, to play an important role in a simulation-based analysis of the upcoming Dark Energy Spectroscopic Instrument data sets.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Measuring the thermal and ionization state of the low- z IGM using likelihood free inference

ABSTRACT We present a new approach to measure the power-law temperature density relationship $T=T_0 (\rho/ \bar{\rho })^{\gamma -1}$ and the UV background photoionization rate $\Gamma _{{{{\rm H\, {\small I}}}}{}}$ of the intergalactic medium (IGM) based on the Voigt profile decomposition of the Ly α forest into a set of discrete absorption lines with Doppler parameter b and the neutral hydrogen column density $N_{\rm H\, {\small I}}$. Previous work demonstrated that the shape of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution is sensitive to the IGM thermal parameters T0 and γ, whereas our new inference algorithm also takes into account the normalization of the distribution, i.e. the line-density dN/dz, and we demonstrate that precise constraints can also be obtained on $\Gamma _{{{{\rm H\, {\small I}}}}{}}$. We use density-estimation likelihood-free inference (DELFI) to emulate the dependence of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution on IGM parameters trained on an ensemble of 624 nyx hydrodynamical simulations at z = 0.1, which we combine with a Gaussian process emulator of the normalization. To demonstrate the efficacy of this approach, we generate hundreds of realizations of realistic mock HST/COS data sets, each comprising 34 quasar sightlines, and forward model the noise and resolution to match the real data. We use this large ensemble of mocks to extensively test our inference and empirically demonstrate that our posterior distributions are robust. Our analysis shows that by applying our new approach to existing Ly α forest spectra at z ≃ 0.1, one can measure the thermal and ionization state of the IGM with very high precision ($\sigma _{\log T_0} \sim 0.08$ dex, σγ ∼ 0.06, and $\sigma _{\log \Gamma _{{{{\rm H\, {\small I}}}}{}}} \sim 0.07$ dex).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Image feature extraction and galaxy classification: a novel and efficient approach with automated machine learning

ABSTRACT In this work, we explore the possibility of applying machine learning methods designed for 1D problems to the task of galaxy image classification. The algorithms used for image classification typically rely on multiple costly steps, such as the point spread function deconvolution and the training and application of complex Convolutional Neural Networks of thousands or even millions of parameters. In our approach, we extract features from the galaxy images by analysing the elliptical isophotes in their light distribution and collect the information in a sequence. The sequences obtained with this method present definite features allowing a direct distinction between galaxy types. Then, we train and classify the sequences with machine learning algorithms, designed through the platform Modulos AutoML. As a demonstration of this method, we use the second public release of the Dark Energy Survey (DES DR2). We show that we are able to successfully distinguish between early-type and late-type galaxies, for images with signal-to-noise ratio greater than 300. This yields an accuracy of $86{{\ \rm per\ cent}}$ for the early-type galaxies and $93{{\ \rm per\ cent}}$ for the late-type galaxies, which is on par with most contemporary automated image classification approaches. The data dimensionality reduction of our novel method implies a significant lowering in computational cost of classification. In the perspective of future data sets obtained with e.g. Euclid and the Vera Rubin Observatory, this work represents a path towards using a well-tested and widely used platform from industry in efficiently tackling galaxy classification problems at the peta-byte scale.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

The high-mass end of the red sequence at z ~ 0.55 from SDSS-III/BOSS: completeness, bimodality and luminosity function

The history of the expanding universe is encoded in the large-scale distribution of galaxies throughout space. By mapping out the three-dimensional locations of millions of galaxies with powerful telescopes, we can directly measure this expansion history. When interpreted using Einstein's theory of gravity, this expansion history lets us infer the contents of the universe, including the amount and nature of "dark energy", an as-yet unexplained energy density associated with the empty vacuum of space. However, to make these measurements and inferences accurately, we must understand and control for a large number of experimental effects. This paper develops a novel method for large cosmological galaxy surveys, and applies it to data from the "BOSS" experiment of the Third Sloan Digital Sky Survey. This method enables an accurate statistical characterization of the "completeness" of the BOSS experiment: the probability that a given galaxy at a given place in the universe is actually detected and successfully measured. It also enables the accurate determination of the underlying demographics of the galaxy population being studied by the experiment. These two ingredients can then be used to make a more accurate comparison between the results of the experiment and the theoretical models that predict the observable effects of dark energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Quality control for community-based sea-ice model development

A new collaborative organization for sea-ice model development, the CICE Consortium, has devised quality control procedures to maintain the integrity of its numerical codes' physical representations, enabling broad participation from the scientific community in the Consortium's open software development environment. Using output from five coupled and uncoupled configurations of the Los Alamos Sea Ice Model, CICE, we formulate quality control methods that exploit common statistical properties of sea-ice thickness, and test for significant changes in model results in a computationally efficient manner. New additions and changes to CICE are graded into four categories, ranging from bit-for-bit amendments to significant, answer-changing upgrades. These modifications are assessed using criteria that account for the high level of autocorrelation in sea-ice time series, along with a quadratic skill metric that searches for hemispheric changes in model answers across an array of different CICE configurations. These metrics also provide objective guidance for assessing new physical representations and code functionality.

58 GEOSCIENCES↗

DOE OSTI2021

Low-temperature breakdown of many-body perturbation theory for thermodynamics

It is shown analytically and numerically that the finite-temperature many-body perturbation theory in the grand canonical ensemble has zero radius of convergence at zero temperature when the energy ordering or degree of degeneracy for the ground state changes with the perturbation strength. When the degeneracy of the reference state is partially or fully lifted at the first-order Hirschfelder-Certain degenerate perturbation theory, the grand potential and internal energy diverge as T → 0. Contrary to earlier suggestions of renormalizability by the chemical potential μ, this nonconvergence, first suspected by W. Kohn and J. M. Luttinger, is caused by the nonanalytic nature of the Boltzmann factor e –E/k e T at T = 0, also plaguing the canonical ensemble, which does not involve chemical potential. The finding reveals a fundamental flaw in perturbation theory, which is deeply rooted in the mathematical limitation of power-series expansions and is unlikely to be removed within its framework.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Spectral-partitioned Kohn-Sham density functional theory

Here we introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Transverse Momentum Distributions from Lattice QCD without Wilson Lines

The transverse-momentum-dependent distributions (TMDs), which are defined by gauge-invariant 3D parton correlators with staple-shaped lightlike Wilson lines, can be calculated from quark and gluon correlators fixed in the Coulomb gauge on a Euclidean lattice. These quantities can be expressed gauge invariantly as the correlators of Coulomb-gauge-dressed fields, which reduce to the standard TMD correlators under principal-value prescription in the infinite boost limit. In the framework of large-momentum effective theory, a quasi-TMD defined from such correlators in a large-momentum hadron state can be matched to the TMD via a factorization formula, whose exact form is derived using soft collinear effective theory and verified at one-loop order. Compared to the currently used gauge-invariant correlators, this new method can substantially improve statistical precision and simplify renormalization for the time-reversal-even TMDs, which will greatly enhance the predicative power of lattice QCD in the nonperturbative region.

Effective field theory↗

DOE OSTI2019

Learning-Based Inversion-Free Model-Data Integration to Advance Ecosystem Model Prediction

Ecosystem model prediction is important for understanding ecosystem responses to climate change and for management support. Model prediction and quantification of predictive uncertainty of ecosystems have long been investigated. The traditional workflow, which calibrates models to match observations and then uses the calibrated models for predictions, relies heavily on inverse modeling to constrain uncertain parameters in complex forward models. This inversion-based prediction approach is infeasible for complex models with heterogeneous parameter uncertainties and incapable of rapid integration of streaming and multiple sources of data because of the difficulty and computational cost in the model inversion, which is typically ill-posed and can require hundreds of thousands of expensive forward simulations to be performed iteratively. We propose to circumvent inverse modeling by precomputing an ensemble of unconstrained forward simulations and then using machine learning (ML) methods to learn the statistical relationship between simulated observation and prediction quantities. Once the ML model has learned the relationship, it can be used to make predictions of future system behavior with uncertainty quantification based on observations. The proposed learningbased inversion-free model prediction (LIMP) framework is computationally efficient which only requires a few thousands of fully parallelizable forward simulations. Additionally, LIMP can continually update predictions based on streaming observations from multiple locations and sources without necessarily requiring extra model simulations. In this study, we apply LIMP to a regional terrestrial ecosystem model with 47 parameters for testing, refining, and evaluating the approach. We demonstrate that LIMP can be used for efficient model prediction, rapid data assimilation, and cost-effective experimental design for improving robust predictive understanding of ecosystems.

Lu, Dan↗

DOE OSTI2020

Robust System Separation Strategy Considering Online Wide-Area Coherency Identification and Uncertainties of Renewable Energy Sources

With the fast growth of renewable energy sources (RES), more and more uncertainties are involved and influencing the stable operation of power systems. Controlled islanding is the last measure to prevent power system blackouts, thus this paper aims to propose a novel model of system separation based on Online Coherency Identification and Adjustable Robust Optimization Programming (OCI-AROP) for minimizing load shedding considering the uncertainties of RES. First, Fuzzy C-Means (FCM) clustering method with F-statistics is utilized to identify the coherent generator groups with the frequency data measured by Phasor Measurement Units (PMUs). Then, the OCI-AROP model considering coherent group constraints, connectivity constraints and robustness constraints about RES are presented. Finally, the case studies on IEEE-39 bus system and WECC-179 bus system are employed to demonstrate the effectiveness of the proposed OCI-AROP model, and comparisons among the OCI-AROP model and the other models are also given to show its superiority.

24 POWER TRANSMISSION AND DISTRIBUTION↗