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NASA NTRS1974

Numerical calculations of velocity and pressure distribution around oscillating airfoils

An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

Bratanow, T.↗

NASA NTRS1994

Research on Orbital Plasma-Electrodynamics (ROPE)

Since the development of probe theory by Langmuir and Blodgett, the problem of current collection by a charged spherically or cylindrically symmetric body has been investigated by a number of authors. This paper overviews the development of a fully three-dimensional particle simulation code which can be used to understand the physics of current collection in three dimensions and can be used to analyze data resulting from the future tethered satellite system (TSS). According to the TSS configurations, two types of particle simulation models were constructed: a simple particle simulation (SIPS) and a super particle simulation (SUPS). The models study the electron transient response and its asymptotic behavior around a three dimensional, highly biased satellite. The potential distribution surrounding the satellite is determined by solving Laplace's equation in the SIPS model and by solving Poisson's equation in the SUPS model. Thus, the potential distribution in space is independent of the density distribution of the particles in the SUPS model but it does depend on the density distribution of the particles in the SUPS model. The evolution of the potential distribution in the SUPS model is described. When the spherical satellite is charged to a highly positive potential and immersed in a plasma with a uniform magnetic field, the formation of an electron torus in the equatorial plane (the plane in perpendicular to the magnetic field) and elongation of the torus along the magnetic field are found in both the SIPS and the SUPS models but the shape of the torus is different. The areas of high potential that exist in the polar regions in the SUPS model exaggerate the elongation of the electron torus along the magnetic field. The current collected by the satellite for different magentic field strengths is investigated in both models. Due to the nonlinear effects present in SUPS, the oscillating phenomenon of the current collection curve during the first 10 plasma periods can be seen (this does not appear in SIPS). From the parametric studies, it appears that the oscillating phenomenon of the current collection curve occurs only when the magnetic field strength is less than 0.2 gauss for the present model.

Wu, S. T.↗

NASA NTRS1991

Structured background grids for generation of unstructured grids by advancing front method

A new method of background grid construction is introduced for generation of unstructured tetrahedral grids using the advancing-front technique. Unlike the conventional triangular/tetrahedral background grids which are difficult to construct and usually inadequate in performance, the new method exploits the simplicity of uniform Cartesian meshes and provides grids of better quality. The approach is analogous to solving a steady-state heat conduction problem with discrete heat sources. The spacing parameters of grid points are distributed over the nodes of a Cartesian background grid by interpolating from a few prescribed sources and solving a Poisson equation. To increase the control over the grid point distribution, a directional clustering approach is used. The new method is convenient to use and provides better grid quality and flexibility. Sample results are presented to demonstrate the power of the method.

Pirzadeh, Shahyar↗

DOE OSTI2022

Variable resolution Poisson-disk sampling for meshing discrete fracture networks

Here, we present the near-Maximal Algorithm for Poisson-disk Sampling (nMAPS) to generate point distributions for variable resolution Delaunay triangular and tetrahedral meshes in two and three-dimensions, respectively. nMAPS consists of two principal stages. In the first stage, an initial point distribution is produced using a cell-based rejection algorithm. In the second stage, holes in the sample are detected using an efficient background grid and filled in to obtain a near-maximal covering. Extensive testing shows that nMAPS generates a variable resolution mesh in linear run time with the number of accepted points. We demonstrate nMAPS capabilities by meshing three-dimensional discrete fracture networks (DFN) and the surrounding volume. The discretized boundaries of the fractures, which are represented as planar polygons, are used as the seed of 2D-nMAPS to produce a conforming Delaunay triangulation. The combined mesh of the DFN is used as the seed for 3D-nMAPS, which produces conforming Delaunay tetrahedra surrounding the network. Under a set of conditions that naturally arise in maximal Poisson-disk samples and are satisfied by nMAPS, the two-dimensional Delaunay triangulations are guaranteed to only have well-behaved triangular faces. While nMAPS does not provide triangulation quality bounds in more than two dimensions, we found that low-quality tetrahedra in 3D are infrequent, can be readily detected and removed, and a high-quality balanced mesh is produced.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

The composition of cosmic rays near the Bend (10 to the 15th power eV) from a study of muons in air showers at sea level

The distribution of muons near shower cores was studied at sea level at Fermilab using the E594 neutrino detector to sample the muon with E testing 3 GeV. These data are compared with detailed Monte Carlo simulations to derive conclusions about the composition of cosmic rays near the bend in the all particle spectrum. Monte Carlo simulations generating extensive air showers (EAS) with primary energy in excess of 50 TeV are described. Each shower record contains details of the electron lateral distribution and the muon and hadron lateral distributions as a function of energy, at the observation level of 100g/cm. The number of detected electrons and muons in each case was determined by a Poisson fluctuation of the number incident. The resultant predicted distribution of muons, electrons, the rate events are compared to those observed. Preliminary results on the rate favor a heavy primary dominated cosmic ray spectrum in energy range 50 to 1000 TeV.

Goodman, J. A.↗

NASA NTRS1982

A Poisson process approximation for generalized K-5 confidence regions

One-sided confidence regions for continuous cumulative distribution functions are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. To avoid tedious computation of confidence levels and critical values, an approximation based on the Poisson process is introduced. This aproximation provides a conservative confidence region; moreover, the approximation error decreases monotonically to 0 as sample size increases. Critical values necessary for implementation are given. Applications are made to the areas of risk analysis, investment modeling, reliability assessment, and analysis of fault tolerant systems.

Arsham, H.↗

NASA NTRS1991

The effect of model uncertainty on some optimal routing problems

The effect of model uncertainties on optimal routing in a system of parallel queues is examined. The uncertainty arises in modeling the service time distribution for the customers (jobs, packets) to be served. For a Poisson arrival process and Bernoulli routing, the optimal mean system delay generally depends on the variance of this distribution. However, as the input traffic load approaches the system capacity the optimal routing assignment and corresponding mean system delay are shown to converge to a variance-invariant point. The implications of these results are examined in the context of gradient-based routing algorithms. An example of a model-independent algorithm using online gradient estimation is also included.

Mohanty, Bibhu↗

DOE OSTI2022

Chandra measurements of gas homogeneity and turbulence at intermediate radii in the Perseus Cluster

ABSTRACT We present a Chandra study of surface brightness fluctuations in the diffuse intracluster medium of the Perseus Cluster. Our study utilizes deep, archival imaging of the cluster core as well as a new mosaic of 29 short $\, 5\,$-ks observations extending in eight different directions out to radii of $r_{500} \sim 2.2\, r_{2500}$. Under the assumption that the distribution of densities at a given radius is log-normally distributed, two important quantities can be derived from the width of the log-normal density distribution on a given spatial scale: the density bias, that is equal to the square root of the clumping factor C; and the one-component turbulent velocity, vk,1D. We forward-model all contributions to the measured surface brightness, including astrophysical and particle background components, and account for the Poisson nature of the measured signal. Measuring the distribution of surface brightness fluctuations in 1 arcmin2 regions, spanning the radial range $0.3\rm {-}2.2\, r_{2500}$ ($7.8\rm {-}57.3\,$ arcmin), we find a small to moderate average density bias of around $3{{\ \rm per\ cent}}$ at radii below $1.6\, r_{2500}$. We also infer an average turbulent velocity at these radii of V1D < 400 km s−1. Direct confirmation of our results on turbulent velocities inferred from surface brightness fluctuations should be possible using the X-ray calorimeter spectrometers to be flown aboard the XRISM and Athena observatories.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

A new portable random number generator wrapper library

Random number generator is an important component of many scientific projects. Many projects are written using programming models (like OpenMP and SYCL) to target different architectures. However, some programming models do not provide a random number generator. In this work, we introduce our random number generator wrapper. It is a header-only library that supports three distributions of random numbers: uniform, normal, and poisson. On the GPU backend, it wraps the cuRAND and rocRAND library, and supports various random number engines. It also wraps random123, a counterbased random number generator, on both CPU and GPU. With this library, we can generate random numbers with a few lines of code and target both GPU and multi-thread CPU with the same code. We also investigate the performance and scalability of this wrapper on different architectures with different engines and the number of cores.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

Star counts from the Hubble Space Telescope Snapshot Survey. I - Galactic models

We report a photometric study of stars from 450 fields at high Galactic latitudes that were observed in the Hubble Space Telescope Snapshot Survey to an average limiting apparent magnitude of V = 21.4. There are 166 fields that contain quasars selected in radio, X-ray, and color-excess surveys. This sample of 273 stars is free of selection bias with respect to the density of stars. To within the Poisson errors, the total counts and magnitude distribution of this unbiased sample are in agreement with the Bahcall-Soneira model (Bahcall, 1986). The angular distribution of the faint stars favors, at the 2 sigma level, a somewhat steeper disk luminosity function and a smaller spheroid main-sequence normalization than given by the model. The sample does not have enough statistical power to distinguish between the two-component Bahcall-Soneira model and the three-component model first proposed by Gilmore and Reid (1983), which contains a thick disk. The statistical power of the survey would increase about 15-fold if colors were obtained for the stars: the data probe the main sequences of the disk, thick disk, and spheroid. Models with and without a thick disk could then be distinguished at the 6 sigma level. The HST Snapshot Survey includes an additional 284 fields, 279 of which are centered on quasars that were selected by objective-prism surveys. These 279 fields are expected to show and do exhibit bias against bright stars, making them unsuitable for testing Galactic models.

Gould, A.↗

NASA NTRS1995

MMPP Traffic Generator for the Testing of the SCAR 2 Fast Packet Switch

A prototype MWP Traffic Generator (TG) has been designed for testing of the COMSAT-supplied SCAR II Fast Packet Switch. By generating packets distributed according to a Markov-Modulated Poisson Process (MMPP) model. it allows the assessment of the switch performance under traffic conditions that are more realistic than could be generated using the COMSAT-supplied Traffic Generator Module. The MMPP model is widely believed to model accurately real-world superimposed voice and data communications traffic. The TG was designed to be as much as possible of a "drop-in" replacement for the COMSAT Traffic Generator Module. The latter fit on two Altera EPM7256EGC 192-pin CPLDs and produced traffic for one switch input port. No board changes are necessary because it has been partitioned to use the existing board traces. The TG, consisting of parts "TGDATPROC" and "TGRAMCTL" must merely be reprogrammed into the Altera devices of the same name. However, the 040 controller software must be modified to provide TG initialization data. This data will be given in Section II.

Chren, William A., Jr.↗

NASA NTRS2000

Photon-Counting Microlaser Rangers, Transponders, and Altimeters

Unlike current manned systems, NASA's next generation SLR2000 Satellite Laser Ranging (SLR) station is fully autonomous. eye-safe, relatively compact and inexpensive. and, during daytime tracking operates at signal-to-noise ratios several orders of magnitude below unity. Tiny, passively Q-switched microlasers generate ultra-short pulses with output energies on the order of 100 micron-J at few kHz rates to achieve mm-level ranging precision to satellite altitudes of 20,000 km. Special ranging receivers, combined with Poisson statistical analysis of the received photon distribution, enable the system to rapidly and reliably identify and extract the single photon laser echoes from the solar background. The enhanced rate of return, combined with a uniform signal strength, can actually drive down both systematic and random range errors. The new SLR2000 technology has already spawned exciting new applications. Compact microlaser altimeters, capable of mapping the surface of a planet or other celestial body at multikilohertz rates, is one such application, and a high altitude, airborne version is currently being developed under NASA's Instrument Incubator Program. Interplanetary microlaser transponders would be capable of performing decimeter ranging or subnanosecond time transfer to spacecraft throughout the inner Solar System. resulting in improved knowledge of planetary motions and liberations and enhanced General Relativity experiments.

Degnan, John J.↗

NASA NTRS2010

Probabilistic Assessment of Cancer Risk from Solar Particle Events

For long duration missions outside of the protection of the Earth s magnetic field, space radiation presents significant health risks including cancer mortality. Space radiation consists of solar particle events (SPEs), comprised largely of medium energy protons (less than several hundred MeV); and galactic cosmic ray (GCR), which include high energy protons and heavy ions. While the frequency distribution of SPEs depends strongly upon the phase within the solar activity cycle, the individual SPE occurrences themselves are random in nature. We estimated the probability of SPE occurrence using a non-homogeneous Poisson model to fit the historical database of proton measurements. Distributions of particle fluences of SPEs for a specified mission period were simulated ranging from its 5 th to 95th percentile to assess the cancer risk distribution. Spectral variability of SPEs was also examined, because the detailed energy spectra of protons are important especially at high energy levels for assessing the cancer risk associated with energetic particles for large events. We estimated the overall cumulative probability of GCR environment for a specified mission period using a solar modulation model for the temporal characterization of the GCR environment represented by the deceleration potential (^). Probabilistic assessment of cancer fatal risk was calculated for various periods of lunar and Mars missions. This probabilistic approach to risk assessment from space radiation is in support of mission design and operational planning for future manned space exploration missions. In future work, this probabilistic approach to the space radiation will be combined with a probabilistic approach to the radiobiological factors that contribute to the uncertainties in projecting cancer risks.

Kim, Myung-Hee Y.↗

DOE OSTI2022

Exponential Escape Rate of Filamentary Incubation in Mott Spiking Neurons

Mott materials such as vanadium oxides, when subject to a strong applied voltage, present an inhomogeneous insulator-to-metal transition with formation of metallic filaments within the insulating bulk. This property is enabling the development of compact and power-efficient neuromorphic devices known as Mott neurons. However, the nature of the transition has not been fully understood yet, as it may be attributed to different effects, including Joule self-heating and hot-carrier injection. Moreover, the experimental determination of the threshold voltage needed to induce the transition has proven to be challenging, as the transition becomes increasingly unpredictable when the threshold is approached. The physical understanding of these issues would not only deepen our understanding of Mott insulators, but would also be an important step toward the realization of neuromorphic devices based on such materials. In this work we use numerical simulations based on the Mott resistor network model to study the nature of the filament incubation and formation process. Here, we show that both electronic and thermal effects, in the form of current density focusing and Joule self-heating, respectively, contribute to the filamentary incubation and growth. Remarkably, we find that the percolation of the metallic filaments near the threshold is intrinsically stochastic, qualitatively similar to the familiar Arrhenius activated behavior and to the stochastic firing of biological neurons. More precisely, we characterize the filament percolation as a Poisson point process, which has the same probability distribution as mathematical models of neuronal firing with an exponential escape rate. Finally, we support the numerical simulation results by performing experiments in VO 2 that are in agreement with the exponential escape rate behavior. Thus, we establish a functionality of Mott insulators that opens a path toward implementing neuromorphic hardware with quantum materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Poisson Equation for a (General) Homogeneous d-Dimensional Ellipsoid with Applications to Beam Envelope Tracking

This note describes the solution of the free-space Poisson equation in the interior of a $d$-dimensional homogeneous ellipsoid, and the associated space charge fields. An explicit formula (\ref{Sformula}) is provided that relates the $d\times d$ matrix describing the space charge (quadratic) potential to the $d\times d$ covariance matrix of the ellipsoid. For the cases $d=2$ and $d=3$, this result is used to determine the linear map corresponding to a space charge kick, that may be used to push the beam $6\times 6$ covariance matrix during envelope tracking. The treatment of upright ellipsoids for $d=2$ and $d=3$ is well-represented in the literature. However, the approach taken here emphasizes a general ellipsoid with arbitrary correlations in any dimension. The Appendix provides a general solution of the free-space Poisson equation in dimension $d$ for a source distribution with ellipsoidal symmetry.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

Vibrational Power Flow Analysis of Rods and Beams

A new method to model vibrational power flow and predict the resulting energy density levels in uniform rods and beams is investigated. This method models the flow of vibrational power in a manner analogous to the flow of thermal power in a heat conduction problem. The classical displacement solutions for harmonically excited, hysteretically damped rods and beams are used to derive expressions for the vibrational power flow and energy density in the rod and beam. Under certain conditions, the power flow in these two structural elements will be shown to be proportional to the energy density gradient. Using the relationship between power flow and energy density, an energy balance on differential control volumes in the rod and beam leads to a Poisson's equation which models the energy density distribution in the rod and beam. Coupling the energy density and power flow solutions for rods and beams is also discussed. It is shown that the resonant behavior of finite structures complicates the coupling of solutions, especially when the excitations are single frequency inputs. Two coupling formulations are discussed, the first based on the receptance method, and the second on the travelling wave approach used in Statistical Energy Analysis. The receptance method is the more computationally intensive but is capable of analyzing single frequency excitation cases. The traveling wave approach gives a good approximation of the frequency average of energy density and power flow in coupled systems, and thus, is an efficient technique for use with broadband frequency excitation.

Wohlever, James Christopher↗

NASA NTRS1997

Containerless Liquid to Solid Nucleation Pathways in Two Representative Grades of Commercially Available Zirconium

Experimental measurements were conducted to determine the solid metal nucleation pathways of radiatively cooling, molten zirconium spheres of two different commercially available purity grades in a high-vacuum, high-temperature electrostatic levitator. The ensemble distribution of maximum undercooling temperatures was interpreted using Poisson statistics to determine the temperature dependence of the solid metal nucleation rate. For a sample of nominally 99.95% pure zirconium, the results are consistent with heterogeneous solid metal nucleation either on static catalyst particles at least approx. 30 nm diameter or on a surface coating. For a sample of nominally 99% pure zirconium, however, it appears that heterogeneous solid metal nucleation occurred either on a polydispersion of approx. 10 nm (mean diameter) static catalyst particles or on dynamic catalyst particles that precipitated from a solution that became supersaturated as the melt cooled.

Rulison, A. J.↗

NASA NTRS1995

Containerless Liquid to Solid Nucleation Pathways in Two Representative Grades of Commercially Available Zirconium

Experimental measurements were conducted to determine the solid metal nucleation pathways of radiatively cooling, molten zirconium spheres of two different commercially available purity grades in a high-vacuum, high-temperature electrostatic levitator. The ensemble distribution of maximum undercooling temperatures was interpreted using Poisson statistics to determine the temperature dependence of the solid metal nucleation rate. For a sample of nominally 99.95% pure zirconium, the results are consistent with heterogeneous solid metal nucleation either on static catalyst particles at least ~30 nm diameter or on a surface coating. For a sample of nominally 99% pure zirconium, however, it appears that heterogeneous solid metal nucleation occurred either on a polydispersion of ~10 nm (mean diameter) static catalyst particles or on dynamic catalyst particles which precipitated from a solution which became supersaturated as the melt cooled. A quantitative analysis of the compositions of both samples suggests that the catalysts probably consisted of one or more of the following elements: niobium, molybdenum, hafnium, and oxygen.

containerless, nucleation, zirconium↗