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Results for “Multiples of uniform random distribution”

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.

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15 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Reconstructing parent microstructures in martensitic and pearlitic Ti-Cu

Evaluating the microstructural evolution of parent phases has long been a challenge in metals with a partial or complete solid state transformation. Most parent microstructure evolution has to be inferred from the product microstructure, with some information permanently lost. Parent microstructure reconstructions relying on orientation relationships and EBSD data are a useful tool to overcome this challenge, though much background knowledge is required to do so. Here, this work introduces a reconstruction process for a eutectoid composition Ti-Cu binary alloy to evaluate the high temperature β-Ti phase from martensitic and pearlitic product microstructures. Martensitic microstructures were accurately reconstructed, enabling elucidation of β-Ti grain size and texture, and the employed script included for scientific reference. Pearlitic microstructures did not reconstruct effectively with the current process. However, new insight into the interfacial crystallographic orientations of pearlitic Ti-Cu microstructures was gleaned via this analysis, and future investigations of interest are discussed accordingly. Ultimately, these findings demonstrate tools widely implemented on conventional titanium and ferrous alloys can also be applied to understand parent microstructures in Ti-Cu and other alloys of emerging interest. This is especially of use as new manufacturing processes for such materials require understanding how parent phase microstructures respond to new, novel material processing such as AM.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Application of the locally self-consistent embedding approach to the Anderson model with non-uniform random distributions

Highlights: • Typical Medium Theory (TMT) for the Anderson Localization. • Locally Self-Consistent Multiple Scattering Method (LSMS) for Random Disordered Systems. • Linear Scaling Computational Method for Random Disordered Systems. We apply the recently developed embedding scheme for the locally self-consistent method to random disorder electrons systems. The method is based on the locally self-consistent multiple scattering theory and the typical medium theory. The locally self-consistent multiple scattering theory divides a system into many small designated local interaction zones. The subsystem within each local interaction zone is embedded in a self-consistent field from the typical medium theory. This approximation allows the study of random systems with large numbers of sites. We present results for the three dimensional Anderson model with different random disorder potential distributions. Using the typical density of states as an indicator of Anderson localization, we find that the method can capture the localization for commonly studied disorder potentials. These include the uniform distribution, the Gaussian distribution, and even the unbounded Cauchy distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Fast GPU-Based Generation of Large Graph Networks From Degree Distributions

Synthetically generated, large graph networks serve as useful proxies to real-world networks for many graph-based applications. The ability to generate such networks helps overcome several limitations of real-world networks regarding their number, availability, and access. Here, we present the design, implementation, and performance study of a novel network generator that can produce very large graph networks conforming to any desired degree distribution. The generator is designed and implemented for efficient execution on modern graphics processing units (GPUs). Given an array of desired vertex degrees and number of vertices for each desired degree, our algorithm generates the edges of a random graph that satisfies the input degree distribution. Multiple runtime variants are implemented and tested: 1) a uniform static work assignment using a fixed thread launch scheme, 2) a load-balanced static work assignment also with fixed thread launch but with cost-aware task-to-thread mapping, and 3) a dynamic scheme with multiple GPU kernels asynchronously launched from the CPU. The generation is tested on a range of popular networks such as Twitter and Facebook, representing different scales and skews in degree distributions. Results show that, using our algorithm on a single modern GPU (NVIDIA Volta V100), it is possible to generate large-scale graph networks at rates exceeding 50 billion edges per second for a 69 billion-edge network. GPU profiling confirms high utilization and low branching divergence of our implementation from small to large network sizes. For networks with scattered distributions, we provide a coarsening method that further increases the GPU-based generation speed by up to a factor of 4 on tested input networks with over 45 billion edges.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Direct numerical simulation of open-channel flow over a heterogeneous particle bed at low relative submergence

In this article, this study investigates turbulent open-channel flows over beds of irregularly arranged particles, using direct numerical simulations at a friction Reynolds number of Re T = 300⁠. Two distinct cases are examined: a polydisperse bed (P800) composed of multiple layers of randomly distributed spheres of varying sizes, and a monodisperse bed (M1015) formed by a random distribution of uniform sized spheres, with a bottommost single layer of varied-sized particles to introduce realistic randomness. Our investigation unveils a rich network of low- and high-speed streaks within the flow field, exhibiting distinctive behaviors in different bed configurations. The P800 case presents a poorly organized flow pattern induced by the varied particle sizes and arrangements, while the M1015 case shows a more regular flow pattern, marked by larger streaks. We also observe that total wall shear stress is substantially influenced by surface roughness-induced drag, extending beyond the effects documented in existing studies of open-channel flows. The present study reveals intricate secondary flow patterns over irregular particle beds. Large-scale circulations are discerned around particle crests in the P800 case and localized circulations with increased turbulence in the M1015 case. Furthermore, analysis of Reynolds stress tensor components indicates that roughness disrupts coherent turbulent eddies, consequently mitigating peak stress. We quantify correlations between drag force and local fluid velocity fluctuations. Notably, a larger deviation in drag is observed in the P800 case compared to M1015, accentuating the influence of particle size and distribution on fluid–particle interactions.

42 ENGINEERING↗
NASA NTRS1992

Kanerva's sparse distributed memory with multiple hamming thresholds

If the stored input patterns of Kanerva's Sparse Distributed Memory (SDM) are highly correlated, utilization of the storage capacity is very low compared to the case of uniformly distributed random input patterns. We consider a variation of SDM that has a better storage capacity utilization for correlated input patterns. This approach uses a separate selection threshold for each physical storage address or hard location. The selection of the hard locations for reading or writing can be done in parallel of which SDM implementations can benefit.

Pohja, Seppo↗
NASA NTRS2006

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Pohorille, Andrew↗
NASA NTRS1971

Uniform random number generators

Methods are presented for the generation of random numbers with uniform and normal distributions. Subprogram listings of Fortran generators for the Univac 1108, SDS 930, and CDC 3200 digital computers are also included. The generators are of the mixed multiplicative type, and the mathematical method employed is that of Marsaglia and Bray.

Farr, W. R.↗
NASA NTRS2005

Performance Analysis of Direct-Sequence Code-Division Multiple-Access Communications with Asymmetric Quadrature Phase-Shift-Keying Modulation

This article considers a quaternary direct-sequence code-division multiple-access (DS-CDMA) communication system with asymmetric quadrature phase-shift-keying (AQPSK) modulation for unequal error protection (UEP) capability. Both time synchronous and asynchronous cases are investigated. An expression for the probability distribution of the multiple-access interference is derived. The exact bit-error performance and the approximate performance using a Gaussian approximation and random signature sequences are evaluated by extending the techniques used for uniform quadrature phase-shift-keying (QPSK) and binary phase-shift-keying (BPSK) DS-CDMA systems. Finally, a general system model with unequal user power and the near-far problem is considered and analyzed. The results show that, for a system with UEP capability, the less protected data bits are more sensitive to the near-far effect that occurs in a multiple-access environment than are the more protected bits.

Wang, C.-W.↗
NASA NTRS1996

Gravitational Effects on Closed-Cellular-Foam Microstructure

Polyurethane foam has been produced in low gravity for the first time. The cause and distribution of different void or pore sizes are elucidated from direct comparison of unit-gravity and low-gravity samples. Low gravity is found to increase the pore roundness by 17% and reduce the void size by 50%. The standard deviation for pores becomes narrower (a more homogeneous foam is produced) in low gravity. Both a Gaussian and a Weibull model fail to describe the statistical distribution of void areas, and hence the governing dynamics do not combine small voids in either a uniform or a dependent fashion to make larger voids. Instead, the void areas follow an exponential law, which effectively randomizes the production of void sizes in a nondependent fashion consistent more with single nucleation than with multiple or combining events.

Noever, David A.↗
DOE OSTI2020

Sub-micrometer random-pyramid texturing of silicon solar wafers with excellent surface passivation and low reflectance

Select emerging solar cell technologies, ranging from very narrow screen-printed fingers to perovskite/silicon tandems, would benefit from a reduction of the height of the standard pyramidal texture of monocrystalline silicon wafers to below 1 μm. However, fabricating such small surface features usually compromises the requisite low reflectance and high passivation quality. Through systematic design of experiments, we demonstrate that conventional alkaline-based wet-chemical etching processes can be tuned to produce dense, spatially homogeneous, and uniformly sized sub-micrometer pyramids. Precise texture size can be further controlled by adding potassium silicate to the texturing solution to effectively slow the pyramid growth rate and promote nucleation. With pyramid size distribution data—extracted from multiple atomic force microscopy images across each wafer—we demonstrate 16 nanotextures with average pyramid sizes ranging from 62 to 512 nm, with the largest having only 0.3% of its pyramids taller than 1 μm. Six of the nanotextures exhibit light trapping and surface defect densities comparable to state-of-the-art microtextured wafers. In conclusion, the best nanotexture achieved an AM1.5G-weighted reflectance of 11.8% and a minority-carrier lifetime of 3.4 ms after passivation with amorphous silicon, demonstrating that smaller textures need not deteriorate solar cell performance.

14 SOLAR ENERGY↗
DOE OSTI2022

Deterministic Linear Time for Maximal Poisson‐Disk Sampling using Chocks without Rejection or Approximation

Abstract We show how to sample uniformly within the three‐sided region bounded by a circle, a radial ray, and a tangent, called a “chock.” By dividing a 2D planar rectangle into a background grid, and subtracting Poisson disks from grid squares, we are able to represent the available region for samples exactly using triangles and chocks. Uniform random samples are generated from chock areas precisely without rejection sampling. This provides the first implemented algorithm for precise maximal Poisson‐disk sampling in deterministic linear time. We prove O(n · M(b) log b), where n is the number of samples, b is the bits of numerical precision and M is the cost of multiplication. Prior methods have higher time complexity, take expected time, are non‐maximal, and/or are not Poisson‐disk distributions in the most precise mathematical sense. We fill this theoretical lacuna.

Mitchell, Scott A.↗
DOE OSTI2026

Two datasets are better than one: method of double moments for 3D reconstruction in cryo-EM

Cryo-electron microscopy is a powerful imaging technique for reconstructing three-dimensional molecular structures from noisy tomographic projection images of randomly oriented particles. We introduce a new data fusion framework, termed the method of double moments, which reconstructs molecular structures from two instances of the second-order moment of projection images obtained under distinct orientation distributions: one uniform, the other non-uniform and unknown. We prove that these moments generically uniquely determine the underlying structure, up to a global rotation and reflection, and we develop a convex-relaxation-based algorithm that achieves accurate recovery using only second-order statistics. Our results demonstrate the advantage of collecting and modeling multiple datasets under different experimental conditions, illustrating that leveraging dataset diversity can substantially enhance reconstruction quality in computational imaging tasks.

Kam’s method↗
DOE OSTI2025

Comparing three generations of D-Wave quantum annealers for minor embedded combinatorial optimization problems

Abstract Quantum annealing (QA) is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. QA in the transverse Ising model, implemented on D-Wave quantum processing units, are available as cloud computing resources. In this study we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-hard discrete combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently quadratic unconstrained binary optimization, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly variable, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size 52, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid-search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples, chain break proportions, and time-to-solution for the maximum clique problem instances. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

Theoretical studies of the radar properties of the icy Galilean moons of Jupiter

The icy Galilean satellites of Jupiter - Europa, Ganymede, and Callisto - have unusual radar scattering properties compared with those of the terrestrial planets or Earth's Moon. There are three main features of the data that distinguish these targets: (1) the radar cross-section normalized by the geometrical cross-section is an order of magnitude larger than that of any terrestrial planet; (2) the reflected power is almost evenly distributed between two orthogonal polarizations with more power being returned in the same circular polarization as was transmitted whereas virtually all of the power returned from the terrestrial planets is contained in the opposite circular polarization to the one that was transmitted; and (3) the echo power spectra have a broad shape indicating a nearly uniformly radar-bright surface in contrast to the spectra from the terrestrial planets that contain a strong quasi-specular component from the vicinity of the sub-radar point and very little reflected power from the rest of the surface. The normalized radar cross-sections decrease as the areal water ice coverage decreases from Europa to Ganymede to Callisto. Recently, radar echoes from the polar caps of Mars and Mercury, and from Saturn's satellite Titan imply similarly strong cross-sections and have classically unexpected polarization properties and it is also thought that this is due to the presence of ice on the surface. A model called the radar glory model is analyzed and it is shown that the main features of the radar echoes calculated from this model agree well with the observations from all three icy Galilean satellites. This model involves long radar paths in the ice below the surface and special structures in which the refractive index decreases abruptly at a hemispherical boundary. It is not known whether such structures exist or how they could be created, but possible scenarios can be imagined such as the formation of an impact crater followed by deposition of a frost layer followed by a resurfacing event in which a layer of solid ice is placed above the layer of frost. Regardless of the exact geophysical processes required to create such structures, the superior ability of this model to account for all of the important observations with very few adjustable parameters and with no ad hoc assumptions is a compelling argument in support of at least the electromagnetic model. The key features of the electromagnetic model are multiple subsurface scattering events, total internal reflection, and a low degree of randomness imposed on a deterministic geometry that strongly favors backscattering.

Eshleman, Von R.↗
NASA NTRS2017

Evaluation of Satellite Remote Sensing Albedo Retrievals over the Ablation Area of the Southwestern Greenland Ice Sheet

MODerate resolution Imaging Spectroradiometer (MODIS) albedo products have been validated over spatially uniform, snow-covered areas of the Greenland ice sheet (GrIS) using the so-called single 'point-to-pixel' method. This study expands on this methodology by applying a 'multiple-point-to-pixel' method and examination of spatial autocorrelation (here using semivariogram analysis) by using in situ observations, high-resolution World- View-2 (WV-2) surface reflectances, and MODIS Collection V006 daily blue-sky albedo over a spatially heterogeneous surfaces in the lower ablation zone in southwest Greenland. Our results using 232 ground-based samples within two MODIS pixels, one being more spatial heterogeneous than the other, show little difference in accuracy among narrow and broad band albedos (except for Band 2). Within the more homogenous pixel area, in situ and MODIS albedos were very close (error varied from −4% to +7%) and within the range of ASD standard errors. The semivariogram analysis revealed that the minimum observational footprint needed for a spatially representative sample is 30 m. In contrast, over the more spatially heterogeneous surface pixel, a minimum footprint size was not quantifiable due to spatial autocorrelation, and far exceeds the effective resolution of the MODIS retrievals. Over the high spatial heterogeneity surface pixel, MODIS is lower than ground measurements by 4-7%, partly due to a known in situ undersampling of darker surfaces that often are impassable by foot (e.g., meltwater features and shadowing effects over crevasses). Despite the sampling issue, our analysis errors are very close to the stated general accuracy of the MODIS product of 5%. Thus, our study suggests that the MODIS albedo product performs well in a very heterogeneous, low-albedo, area of the ice sheet ablation zone. Furthermore, we demonstrate that single 'point-to-pixel' methods alone are insufficient in characterizing and validating the variation of surface albedo displayed in the lower ablation area. This is true because the distribution of in situ data deviations from MODIS albedo show a substantial range, with the average values for the 10th and 90th percentiles being −0.30 and 0.43 across all bands. Thus, if only single point is taken for ground validation, and is randomly selected from either distribution tails, the error would appear to be considerable. Given the need for multiple in-situ points, concurrent albedo measurements derived from existing AWSs, (low-flying vehicles (airborne or unmanned) and high-resolution imagery (WV-2)) are needed to resolve high sub-pixel variability in the ablation zone, and thus, further improve our characterization of Greenland's surface albedo.

Ablation zone↗