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At least 163 records · Page 9

Investigating the ecological fallacy through sampling distributions constructed from finite populations

Correlation coefficients and linear regression values computed from group averages can differ from correlation coefficients and linear regression values computed using individual scores. This observation known as the ecological fallacy often assumes that all the individual scores are available from a population. In many situations, one must use a sample from the larger population. In such cases, the computed correlation coefficient and linear regression values will depend on the sample that is chosen and the underlying sampling distribution. The sampling distribution of correlation coefficients and linear regression values for group averages will be identical to the sampling distribution for individuals for normally distributed variables for random samples drawn from infinitely large continuous distributions. However, data that is acquired in practice is often acquired when sampling without replacement from a finite population. Our objective is to demonstrate through Monte Carlo simulations that the sampling distributions for correlation and linear regression will also be similar for individuals and group averages when sampling without replacement from normally distributed variables. These simulations suggest that when a random sample from a population is selected, the correlation coefficients and linear regression values computed from individual scores will not be more accurate in estimating the entire population values compared to samples when group averages are used as long as the sample size is the same.

97 MATHEMATICS AND COMPUTING↗

Distributed Wind Guidebook: Agricultural Producers and Rural Small Business Owners

Distributed wind energy technologies generate clean, carbon-free power close to the point of consumption (i.e., close to people and their energy needs). Distributed wind energy can help individuals, farms, businesses, and communities meet their unique goals, such as reducing impacts on climate change, decreasing electricity bills, boosting energy independence or autonomy from the electric grid, and enhancing grid reliability and resilience. This guidebook is designed to support you in (1) deciding if distributed wind energy is right for you, (2) installing a proven wind turbine technology by working with a reputable installer, and (3) setting up your project for success through its lifetime. The information in this guidebook is tailored to rural small businesses and agricultural producers who are interested in exploring distributed wind energy to meet their electricity, resilience, financial, and environmental goals. You will find gray boxes with key topics, definitions, and considerations throughout the guidebook. The report has been adapted from the Distributed Wind Guidebook, which offers a comprehensive view on core aspects of deploying distributed wind energy technologies. In comparison, this edition of the guidebook is designed to offer a more succinct and tailored guidebook for rural small businesses and agricultural producers. For additional detail on any topic presented within this edition, readers are advised to reference the original version of the Distributed Wind Guidebook.

17 WIND ENERGY↗

Bridging the Gap on Data and Analysis for Distribution System Planning: Information That Utilities Can Provide Regulators, State Energy Offices and Other Stakeholders

Electric utilities conduct planning annually to ensure their distribution system meets technical standards, policies, and regulations; addresses forecasted grid conditions; satisfies customer needs; and advances utility priorities. The plan identifies grid deficiencies, analyzes potential solutions, and prioritizes capital investments and other expenditures. About 20 U.S. states and jurisdictions require regulated utilities to file some type of distribution system plan with the public utility commission for review. Requirements for sharing distribution system data and analyses vary widely, from few specific requirements to a detailed list of information that must be provided. While utilities conduct extensive analysis to develop distribution system plans, in most jurisdictions regulators and stakeholders do not know what data are available and how the utility uses the data in planning and investing. This report aims to bridge the gap by increasing understanding of the types of data and analyses utilities employ to develop distribution system plans and how the information affects their decision-making. The report describes information that states and stakeholders can ask for related to 11 data categories: -Forecasting loads and distributed energy resources (DERs) -Scenario analysis -Worst-performing circuits -Asset management strategy -Hosting capacity analysis -Value of DERs -Grid needs assessment -Cost-effectiveness framework for investments -Distribution system investment strategy and implementation -Geotargeted programs -Non-wires alternatives procurements.

24 POWER TRANSMISSION AND DISTRIBUTION↗

State Requirements for Electric Distribution System Planning

Utilities have conducted distribution planning since they first began building and operating electricity systems. But filing these plans for regulatory and stakeholder review is a relatively recent phenomenon. This report summarizes legislative and regulatory requirements for regulated electric utilities to file some type of distribution system plan in 20 U.S. jurisdictions. Some plans focus on expedited cost recovery for certain types of distribution system improvements; other plans focus on investments for grid modernization or distributed energy resources. Increasingly, states are adopting requirements for Integrated Distribution Plans. Such plans provide holistic grid investment strategies that address state and local policies and increasing complexity at the grid edge. The report covers the following topics for distribution system plans, highlighting advanced practices: -State goals and objectives -Procedural requirements -Forecasting loads and distributed energy resources -Hosting capacity analysis -Baseline information requirements -Grid modernization strategy -Grid needs assessment -Non-wires solutions -Reliability and resilience analyses -Stakeholder engagement -Equity -Pilots -Coordination with other planning processes The report includes links to legislation; regulatory requirements, proceedings, and orders; and filed utility plans. The U.S. Department of Energy’s Office of Electricity provided funding support.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Implementing Distributed Operations: A Comparison of Two Deep Space Missions

Two very different deep space exploration missions--Mars Exploration Rover and Cassini--have made use of distributed operations for their science teams. In the case of MER, the distributed operations capability was implemented only after the prime mission was completed, as the rovers continued to operate well in excess of their expected mission lifetimes; Cassini, designed for a mission of more than ten years, had planned for distributed operations from its inception. The rapid command turnaround timeline of MER, as well as many of the operations features implemented to support it, have proven to be conducive to distributed operations. These features include: a single science team leader during the tactical operations timeline, highly integrated science and engineering teams, processes and file structures designed to permit multiple team members to work in parallel to deliver sequencing products, web-based spacecraft status and planning reports for team-wide access, and near-elimination of paper products from the operations process. Additionally, MER has benefited from the initial co-location of its entire operations team, and from having a single Principal Investigator, while Cassini operations have had to reconcile multiple science teams distributed from before launch. Cassini has faced greater challenges in implementing effective distributed operations. Because extensive early planning is required to capture science opportunities on its tour and because sequence development takes significantly longer than sequence execution, multiple teams are contributing to multiple sequences concurrently. The complexity of integrating inputs from multiple teams is exacerbated by spacecraft operability issues and resource contention among the teams, each of which has their own Principal Investigator. Finally, much of the technology that MER has exploited to facilitate distributed operations was not available when the Cassini ground system was designed, although later adoption of web-based and telecommunication tools has been critical to the success of Cassini operations.

Cassini Mission↗

Uniform secondary current distribution at disk electrodes under Tafel kinetics enabled by concentric current-shielding rings

Non-uniform secondary current distribution at rotating disk electrodes (RDE) is a common problem when using resistive electrolyte media or large applied currents. In a recent publication, we have shown that auxiliary electrodes such as the ring of a rotating ring disk electrode (RRDE) can help suppress current non-uniformities at the disk enabling reliable electroanalytical measurements. However, this previous work considered linear kinetics where current distribution non-uniformities were moderate. In the present contribution, we consider current distribution non-uniformities encountered under Tafel kinetics. We show, for the case of 2,5-dihydroxy-1,4-benzoquinone (DHBQ) reduction, that optimally chosen ring conditions serve to provide effective shielding at the disk edge rendering the overall disk current distribution to be uniform. Numerical modeling and scaling analysis (using the Wagner number) are presented to aid a user in determining the optimal ring current density for achieving uniform disk current distribution under Tafel kinetics. This approach is especially useful when studying soluble-soluble redox transitions for which, unlike deposit distribution in electrodeposition, the current distribution non-uniformity is not visually apparent.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Proton Cyclotron Waves and Pickup Ion Ring Distribution Instabilities Upstream of Mars

Proton cyclotron waves (PCWs) upstream of Mars are thought to be associated with the instabilities of pickup ions. The instabilities of pickup ions of ring distributions have larger maximum growth rates compared with beam distributions. However, observations revealed a notably‐reduced occurrence rate of PCWs for pickup ions of ring distributions. Linear instability analysis and a corresponding two‐dimensional particle‐in‐cell (PIC) simulation are performed to investigate the instabilities of pickup ion ring distributions upstream of Mars. Linear instability analysis indicates that a pickup ion ring distribution is unstable to the ion cyclotron, ion Bernstein, and mirror instabilities. The corresponding PIC simulation confirms the linear analysis results and further demonstrates that the pickup ions are scattered toward an isotropic shell distribution by the waves excited. Interestingly, the saturation energy of the waves is much lower than that driven by a corresponding pickup ion beam distribution, and mirror waves eventually dominate the system.

79 ASTRONOMY AND ASTROPHYSICS↗

A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions

Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

97 MATHEMATICS AND COMPUTING↗

Comments on the continuity of distribution functions obtained by superposition.

Assuming that Y is a nonnegative random variable independent of the differential process X(t), attention is given to the question of whether or not the superposition X(Y) can have a continuous probability distribution. If the process has continuous distributions, then the superposition is continuous if and only if P/Y = 0/ = 0. If the process has discontinuous distributions and no trend, then no superposition can have continuous distribution. If the process has discontinuous distributions and nonzero trend, then the superposition onto a random epoch has continuous distribution if and only if Y has continuous distribution.

Huff, B. W.↗

Electron pitch angle distributions throughout the magnetosphere as observed on Ogo 5.

A survey of the equatorial pitch angle distributions of energetic electrons is provided for all local times out to radial distances of 20 earth radii on the night side of the earth and to the magnetopause on the day side of the earth. In much of the inner magnetosphere and in the outer magnetosphere on the day side of the earth, the normal loss cone distribution prevails. The effects of drift shell splitting - i.e., the appearance of pitch angle distributions with minimums at 90 deg, called butterfly distributions - become apparent in the early afternoon magnetosphere at extended distances, and the distribution is observed in to 5.5 earth radii in the nighttime magnetosphere. Inside about 9 earth radii the pitch angle effects are quite energy-dependent. Beyond about 9 earth radii in the premidnight magnetosphere during quiet times the butterfly distribution is often observed. It is shown that these electrons cannot survive a drift to dawn without being considerably modified. The role of substorm activity in modifying these distributions is identified.

West, H. I., Jr.↗

The distribution of maximum temperatures of coronal active region loops

The emission measure distribution across the range 4.5 log T 6.5 was derived for several coronal active regions by combining EUV line fluxes with broadband X-ray fluxes. The distributions of the maximum temperature was then derived using a numerical model. It is shown that the emission measure distribution can be represented over the full range 5.6 log Tm 6.5 by the superposition of simple loop models, if the models incorporate a substantial rise in their individual emission measure distributions near the maximum temperature. The unresolved loops may have substantial area ratios, since it is this ratio that fixes the extent of the rise in the emission measure distribution. Since the bulk of the emission measure is then contributed from the loop tops, the distribution of maximum temperatures has approximately the same shape as does the integrated emission measure distributions. The EUV and X-ray data used were obtained by from two separate experiments on ATM/Skylab.

Mayfield, E. B.↗

Problem solving in a distributed environment

Distributed problem solving is anayzed as a blend of two disciplines: (1) problem solving and ai; and (2) distributed systems (monitoring). It may be necessary to distribute because the application itself is one of managing distributed resources (e.g., distributed sensor net) and communication delays preclude centralized processing, or it may be desirable to distribute because a single computational engine may not satisfy the needs of a given task. In addition, considerations of reliability may dictate distribution. Examples of multi-process language environment are given.

Rashid, R. F.↗

Centralized versus distributed propulsion

The functions and requirements of auxiliary propulsion systems are reviewed. None of the three major tasks (attitude control, stationkeeping, and shape control) can be performed by a collection of thrusters at a single central location. If a centralized system is defined as a collection of separated clusters, made up of the minimum number of propulsion units, then such a system can provide attitude control and stationkeeping for most vehicles. A distributed propulsion system is characterized by more numerous propulsion units in a regularly distributed arrangement. Various proposed large space systems are reviewed and it is concluded that centralized auxiliary propulsion is best suited to vehicles with a relatively rigid core. These vehicles may carry a number of flexible or movable appendages. A second group, consisting of one or more large flexible flat plates, may need distributed propulsion for shape control. There is a third group, consisting of vehicles built up from multiple shuttle launches, which may be forced into a distributed system because of the need to add additional propulsion units as the vehicles grow. The effects of distributed propulsion on a beam-like structure were examined. The deflection of the structure under both translational and rotational thrusts is shown as a function of the number of equally spaced thrusters. When two thrusters only are used it is shown that location is an important parameter. The possibility of using distributed propulsion to achieve minimum overall system weight is also examined. Finally, an examination of the active damping by distributed propulsion is described.

Clark, J. P.↗

Characteristics of electron velocity distribution functions in the solar wind derived from the Helios plasma experiment

The details of the shapes of three typical electron distribution functions observed by the Helios 1 and 2 probes in the solar wind between 0.3 AU and 1 AU are analyzed and compared with theoretical predictions. These are (1) a distribution function with a narrow 'strahl' (narrow beam), which is extremely anisotropic and skewed with respect to the magnetic field direction at particle energies above 100 eV; (2) a distribution function with a broad 'strahl', less anisotropic and skewed; and (3) a nearly isotropic distribution function. For each distribution function, a sudden change in the slope was discerned, separating the 'core' at lower energies from the 'halo' at higher energies. The most obvious differences of the analyzed electron distribution functions were observed at energies above 50-100 eV. The possible origins for the observed features of the distribution functions are discussed.

Pilipp, W. G.↗

On the distribution of sunspot cycle periods

A comparison is made between the observed distribution of sunspot cycle periods and distributions based on uniform, normal, and bimodal distributions. The bimodal distribution, composed of short-period and long-period cycles, is found to best describe the observed distribution. Compared to the normal distribution for the most reliably determined cycles (cycles 8-20), the bimodal distribution has a residual (sum of squares of differences) that is about 86 percent smaller. Means for short-period and long-period cycles are estimated to be 122 + or - 4 months and 140 + or - 5 months, respectively.

Wilson, Robert M.↗

The weight distribution and randomness of linear codes

Finding the weight distributions of block codes is a problem of theoretical and practical interest. Yet the weight distributions of most block codes are still unknown except for a few classes of block codes. Here, by using the inclusion and exclusion principle, an explicit formula is derived which enumerates the complete weight distribution of an (n,k,d) linear code using a partially known weight distribution. This expression is analogous to the Pless power-moment identities - a system of equations relating the weight distribution of a linear code to the weight distribution of its dual code. Also, an approximate formula for the weight distribution of most linear (n,k,d) codes is derived. It is shown that for a given linear (n,k,d) code over GF(q), the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q = q(-)(n-k) as u becomes large. A relationship between the randomness of a linear block code and the minimum distance of its dual code is given, and it is shown that most linear block codes with rigid algebraic and combinatorial structure also display certain random properties which make them similar to random codes with no structure at all.

Cheung, K.-M.↗

Distribution function of continuously created newborn and pickup ions in outer cometary exospheres

The time evolution of the distribution function of newborn ions in the solar wind is investigated using a quasi-linear-type diffusion equation. The initial distribution is taken to be a ring beam, which is approximated by delta function in pitch angle and velocity, and it is assumed that the ions are created at a constant rate with a similar distribution. A long-time asymptotic form of ion distribution is obtained, which is a mixture of newborn ions and ions generated throughout the entire process. It is shown that the time asymptotic distribution function exists even in the presence of a continuous ionization process. The stability of the long-time asymptotic distribution was examined for the case of parallel propagation, and the results show that the distribution function can be unstable to low-frequency hydromagnetic waves. The results of the analysis were found to agree with recent satellite observations.

Gaffey, J. D., Jr.↗

Quantitative characterization of spatial distribution of particles in materials: Application to materials processing

Most engineering materials contain second phase particles or fibers which serve to reinforce the matrix phase. The effect of reinforcements on material properties is usually analyzed in terms of the average volume fraction and spacing of reinforcements, quantities which are global microstructural characteristics. However, material properties can also depend on local microstructural characteristics; for example, on how uniformly the reinforcing phase is distributed in the material. The analysis method will then be applied to a materials processing problem to discover how processing parameters can be selected to maximize redistribution of the reinforcing phase during processing. Several mathematical analysis methods could be adapted to the problem of characterizing the distribution of particles in materials. A tessellation-based method was selected. In the first phase of the investigation, a software package was written to automate the analysis. Typical results are shown. The analysis technique allows the degree to which particles are clustered together, the size and spacing of particle clusters, and the particle density in clusters to be found. The analysis methods were applied to computer-generated distributions and to a few real particle-containing materials. Methods for analyzing a nonuniform particle distribution in a material can be applied to two broad classes of materials science problems: understanding how the resulting particle distribution affects properties. The analysis method described is applied to a materials processing problem: how to select extrusion conditions to maximize the redistribution of reinforcing particles that are initially nonuniformly distributed. In addition, the tessellation-based method to analyze star distributions in spiral galaxies was adapted, illustrating the diverse types of problems to which the analysis method can be applied.

Parse, J. B.↗