Search NASA⌕ Search

SEARCH · Search NASA

Results for “Probability Distribution Function”

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.

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

At least 847 records · Page 47

Status of vibrational structure in {sup 62}Ni

Measurements consisting of {gamma}-ray excitation functions and angular distributions were performed using the (n,n{sup '{gamma}}) reaction on {sup 62}Ni. The excitation function data allowed us to check the consistency of the placement of transitions in the level scheme. From {gamma}-ray angular distributions, the lifetimes of levels up to {approx}3.8 MeV in excitation energy were extracted with the Doppler-shift attenuation method. The experimentally deduced values of reduced transition probabilities were compared with the predictions of the quadrupole vibrator model and with large-scale shell model calculations in the fp shell configuration space. Two-phonon states were found to exist with some notable deviation from the predictions of the quadrupole vibrator model, but no evidence for the existence of three-phonon states could be established. Z=28 proton core excitations played a major role in understanding the observed structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Geometric characterization and simulation of planar layered elastomeric fibrous biomaterials

Many important biomaterials are composed of multiple layers of networked fibers. While there is a growing interest in modeling and simulation of the mechanical response of these biomaterials, a theoretical foundation for such simulations has yet to be firmly established. Moreover, correctly identifying and matching key geometric features is a critically important first step for performing reliable mechanical simulations. This paper addresses these issues in two ways. First, using methods of geometric probability, we develop theoretical estimates for the mean linear and areal fiber intersection densities for 2-D fibrous networks. These densities are expressed in terms of the fiber density and the orientation distribution function, both of which are relatively easy-to-measure properties. Secondly, we develop a random walk algorithm for geometric simulation of 2-D fibrous networks which can accurately reproduce the prescribed fiber density and orientation distribution function. Furthermore, the linear and areal fiber intersection densities obtained with the algorithm are in agreement with the theoretical estimates. Both theoretical and computational results are compared with those obtained by post-processing of scanning electron microscope images of actual scaffolds. These comparisons reveal difficulties inherent to resolving fine details of multilayered fibrous networks. Finally, the methods provided herein can provide a rational means to define and generate key geometric features from experimentally measured or prescribed scaffold structural data.

36 MATERIALS SCIENCE↗

Determination of the collisional energy transfer distribution responsible for the collision-induced dissociation of NO 2 with Ar

Collisional energy transfer is an essential aspect of chemical reactivity and maintenance of thermal equilibrium. We report the shape (energy-dependence) of the collisional energy transfer probability function for collisions of vibrationally excited NO 2 entrained in a molecular beam and photoexcited to within 40 cm -1 of its dissociation threshold. The internally excited molecules undergo collisions with Ar atoms in a crossed beam apparatus. Dissociative collisions rapidly produce the NO(J) fragment, which is observed by velocity-mapped ion imaging and REMPI techniques. The measured collisional energy transfer function is obtained via energy conservation and is compared with the results of classical trajectory calculations. Good agreement between the theory and experiment is found for collisions that transfer small amounts of energy, but the theory predicts a higher likelihood of energetic collisions than is observed experimentally. We explore possible explanations for this discrepancy in the dynamics of the collision excitation process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A scoping study of far-SOL main-wall protection limiters for steady-state operation of compact pilot plant tokamaks

We present a novel method for handling steady-state heat fluxes incident on the main wall of pilot plant-scale magnetic fusion devices, based on the utilization of protection limiters in the far scrape-off layer (SOL). This method helps avoid large plasma-wall gaps, without excessively compromising blanket performance. We present an optimization algorithm for determining the appropriate size and scale of these protection limiters given (1) probability distributions of SOL plasma parameters and (2) assumed risk tolerance. As part of this optimization, we have developed an analytic description of parallel heat fluxes across limiter shadows, and an objective cost function (the ‘Far-SOL Marginal Cost’) to quantify the impact that different main-wall thermal management design choices have on reactor capital cost. Applying the model to a midscale fusion pilot plant concept shows that making use of far-SOL protection limiters can reduce capital costs on the order of $500 M, relative to naively increasing the plasma-wall gap. Our analysis demonstrates that the far-SOL power decay length is the highest-leverage plasma assumption for thermal loading of the first wall, and the primary cost driver for main wall thermal management. The relative cost efficiency of protection limiters increases as assumptions on the far-SOL heat flux become more pessimistic. The concepts described in this paper motivate the further development of far-SOL protection limiters as part of larger efforts to design economical core-edge-wall compatible solutions for a fusion pilot plant.

Design under uncertainty↗

Superior model for fault tolerance computation in designing nano-sized circuit systems

As CMOS technology scales nano-metrically, reliability turns out to be a decisive subject in the design methodology of nano-sized circuit systems. As a result, several computational approaches have been developed to compute and evaluate reliability of desired nano-electronic circuits. The process of computing reliability becomes very troublesome and time consuming as the computational complexity build ups with the desired circuit size. Therefore, being able to measure reliability instantly and superiorly is fast becoming necessary in designing modern logic integrated circuits. For this purpose, the paper firstly looks into the development of an automated reliability evaluation tool based on the generalization of Probabilistic Gate Model (PGM) and Boolean Difference-based Error Calculator (BDEC) models. The Matlab-based tool allows users to significantly speed-up the task of reliability analysis for very large number of nano-electronic circuits. Secondly, by using the developed automated tool, the paper explores into a comparative study involving reliability computation and evaluation by PGM and, BDEC models for different implementations of same functionality circuits. Based on the reliability analysis, BDEC gives exact and transparent reliability measures, but as the complexity of the same functionality circuits with respect to gate error increases, reliability measure by BDEC tends to be lower than the reliability measure by PGM. The lesser reliability measure by BDEC is well explained in this paper using distribution of different signal input patterns overtime for same functionality circuits. Simulation results conclude that the reliability measure by BDEC depends not only on faulty gates but it also depends on circuit topology, probability of input signals being one or zero and also probability of error on signal lines.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Improved approximations of non-Gaussian probability, force, and energy of a single polymer chain

The mechanical behavior of polymers such as their probability density function (PDF), strain energy, and entropic force, has long been described by the non-Gaussian statistical model. Non-Gaussian models are often approximated by the Kuhn-Grün (KG) distribution function, which is derived from the first-order approximation of the complex Rayleigh's exact Fourier integral distribution. Furthermore, the KG function is widely accepted in polymer physics, where the non-Gaussian theory is often used to describe energy of the chains with various flexibility ratios. However, the KG function is shown to be relevant only for long chains and becomes extremely inaccurate for chains with fewer than 40 segments. In comparison to the KG model, other approximations of the non-Gaussian statistical model are often less accurate, and those with higher accuracy are usually too complex to be implemented in large-scale simulations. Here a new accurate approximation of the non-Gaussian PDF, entropic force, and strain energy of a single chain subsequently is developed to describe the mechanics of a polymer chain. With a similar level of complexity, the presented approximations of non-Gaussian PDF, strain energy, and entropic force are at least 10 times more accurate than KG approximations and thus are an excellent alternative option to be used in micromechanical constitutive models.

42 ENGINEERING↗

A Logarithmic Bayesian Approach to Quantum Error Detection

We consider the problem of continuous quantum error correction from a Bayesian perspective, proposing a pair of digital filters using logarithmic probabilities that are able to achieve near-optimal performance on a three-qubit bit-flip code, while still being reasonable to implement on low-latency hardware. These practical filters are approximations of an optimal filter that we derive explicitly for finite time steps, in contrast with previous work that has relied on stochastic differential equations such as the Wonham filter. By utilizing logarithmic probabilities, we are able to eliminate the need for explicit normalization and can reduce the Gaussian noise distribution to a simple quadratic expression. The state transitions induced by the bit-flip errors are modeled using a Markov chain, which for log-probabilities must be evaluated using a LogSumExp function. We develop the two versions of our filter by constraining this LogSumExp to have either one or two inputs, which favors either simplicity or accuracy, respectively. Using simulated data, we demonstrate that the single-term and two-term filters are able to significantly outperform both a double threshold scheme and a linearized version of the Wonham filter in tests of error detection under a wide variety of error rates and time steps.

97 MATHEMATICS AND COMPUTING↗

Crystal Plasticity Modeling and Experimental Validation with an Orientation Distribution Function for Ti-7Al Alloy

An orientation distribution function based model is used for micromechanical modeling of the titanium-aluminum alloys, Ti-0 wt % Al and Ti-7 wt % Al, which are in demand for many aerospace applications. This probability descriptor based modeling approach is different than crystal plasticity finite element techniques since it computes the averaged material properties using upper bound averaging. A rate-independent single-crystal plasticity model is implemented to compute the effect of macroscopic strain on the polycrystal. An optimization problem is defined for calibrating the basal, prismatic, pyramidal slip system and twin parameters using the available tension and compression experimental data. The crystal plasticity parameters of Ti-7 wt % Al are not studied extensively in literature, and therefore the optimization results for the crystal plasticity model realization produce unique data, which will be beneficial to future studies in the field. The sensitivities of the slip and twin parameters to the design objectives are also investigated to identify the most critical slip system parameters. Using the optimum design parameters, the microstructural textures, during the tension test, are predicted by the crystal plasticity finite element simulations, and compared to the available experimental texture and scanning electron microscope—digital image correlation data.

36 MATERIALS SCIENCE↗

Burst wait time simulation of CALIBAN reactor at delayed super-critical state

In the past, the super prompt critical wait time probability distribution was measured on CALIBAN fast burst reactor [4]. Afterwards, these experiments were simulated with a very good agreement by solving the non-extinction probability equation [5]. Recently, the burst wait time probability distribution has been measured at CEA-Valduc on CALIBAN at different delayed super-critical states [6]. However, in the delayed super-critical case the non-extinction probability does not give access to the wait time distribution. In this case it is necessary to compute the time dependent evolution of the full neutron count number probability distribution. In this paper we present the point model deterministic method used to calculate the probability distribution of the wait time before a prescribed count level taking into account prompt neutrons and delayed neutron precursors. This method is based on the solution of the time dependent adjoint Kolmogorov master equations for the number of detections using the generating function methodology [8,9,10] and inverse discrete Fourier transforms. The obtained results are then compared to the measurements and Monte-Carlo calculations based on the algorithm presented in [7]. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Recovering non-Maxwellian particle velocity distribution functions from collective Thomson-scattered spectra

Collective optical Thomson scattering (TS) is a diagnostic commonly used to characterize plasma parameters. These parameters are typically extracted by a fitting algorithm that minimizes the difference between a measured scattered spectrum and an analytic spectrum calculated from the velocity distribution function (VDF) of the plasma. However, most existing TS analysis algorithms assume that the VDFs are Maxwellian, and applying an algorithm that makes this assumption does not accurately extract the plasma parameters of a non-Maxwellian plasma due to the effect of non-Maxwellian deviations on the TS spectra. We present new open-source numerical tools for forward modeling analytic spectra from arbitrary VDFs and show that these tools are able to more accurately extract plasma parameters from synthetic TS spectra generated by non-Maxwellian VDFs compared to standard TS algorithms. Estimated posterior probability distributions of fits to synthetic spectra for a variety of example non-Maxwellian VDFs are used to determine uncertainties in the extracted plasma parameters and show that correlations between parameters can significantly affect the accuracy of fits in plasmas with non-Maxwellian VDFs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Determination of laser damage initiation probability and growth on fused silica scratches

Current methods for the manufacture of optical components inevitably leaves a variety of sub-surface imperfections including scratches of varying lengths and widths on even the finest finishes. It has recently been determined that these finishing imperfections are responsible for the majority of laser-induced damage for fluences typically used in ICF class lasers. We have developed methods of engineering subscale parts with a distribution of scratches mimicking those found on full scale fused silica parts. This much higher density of scratches provides a platform to measure low damage initiation probabilities sufficient to describe damage on large scale optics. In this work, damage probability per unit scratch length was characterized as a function of initial scratch width and post fabrication processing including acid-based etch mitigation processes. The susceptibility of damage initiation density along scratches was found to be strongly affected by the post etching material removal and initial scratch width. We have developed an automated processing procedure to document the damage initiations per width and per length of theses scratches. We show here how these tools can be employed to provide predictions of the performance of full size optics in laser systems operating at 351 nm. In addition we use these tools to measure the growth rate of a damage site initiated along a scratch and compare this to the growth measured on an isolated damage site.

42 ENGINEERING↗

Analysis of the approximations applied in the continuum-distorted-wave-eikonal-initial-state theory for the evaluation of ionization cross sections: Post-prior discrepancy, axial symmetry, and ion-ion interaction

When the continuum distorted wave with eikonal initial state (CDW-EIS) [D. S. Crothers and J. F. McCann, J. Phys B 16, 3229 (1983)] theory is applied to the evaluation of ionization cross sections, many additional approximations are assumed. However, usually, the influence of these approximations is not clear. Aiming to estimate them, we compare the differential and total cross sections obtained with diverse approximations for ionization of He atoms by proton impact. We analyze the post-prior discrepancy, which depends on the perturbative Hamiltonian applied in the scattering amplitude. We study the dependence of the cross sections on the description of the initial and final states. For this purpose, we use the 1Z and 5Z variational and numerical Optimized Potential Model (OPM) [J. D. Talman, Comput. Phys. Commun. 54, 85 (1989)] bound states for the initial target state, and for the final target state we set Coulomb waves with proper effective charges or the continuum state of an OPM potential model. The cross sections resulting from OPM post and prior versions are identical and show excellent agreement with experimental data in each case. Nevertheless, the cross section derived by the prior CDW-EIS, 5Z initial wave, and corresponding continuum state gives comparable results, requiring shorter computational work. Then we study the determination of the impact parameter ionization probability from the transition amplitudes, also including an axial symmetry for the ionization process. The hypothesis of this axial symmetry saves an angular integration in the evaluation of the probabilities. We analyze the variation of these probabilities within the post and prior formalisms and mention initial and final states, according to the supposed symmetry. We found that the probabilities derived with the axial symmetry concentrate at a lower impact parameter than the usual ones and are quite sensitive to the approximations used for the CDW-EIS evaluation. Furthermore, these probabilities underestimate distant collisions. In the last section we introduce the projectile-residual ion potential, and we discuss the effect of the diverse approximations on the dependence of the cross section as a function of the projectile scattering angle. We compare the projectile angular distribution resulting from a full Coulomb interaction between the ions with the one obtained by a screened potential, but in the latter case the theoretical distributions underestimate the experimental data. The OPM and 5Z functions give a good description of the experimental data.

74 ATOMIC AND MOLECULAR PHYSICS↗

Statistical characterization of a shock interacting with an inclined gas column

We present a statistical characterization of the interaction between a planar shock and a finite-diameter, cylindrical column of dense gas based on three-dimensional, large-eddy simulation results. In the simulation, the column of gas is initially inclined at an angle $\alpha _0$ with respect to the shock plane. Effects of the initial column angle on the mixing characteristics are examined at Mach number 2.0 for column incline angles $1^\circ$ , $5^\circ$ , $10^\circ$ and $30^\circ$ . Mean velocity profiles show that the column angle affects the gas velocity components in the vertical plane, but not in the spanwise direction. The gas undergoes higher initial upward acceleration at larger initial column incline angles. With time, the gas motion tends to become one-dimensional in the streamwise direction. Initially, velocity fluctuations are most intense within the interior of the column, but concentrate near the column leading edge over time. At high wavenumbers $\kappa$ , the turbulent kinetic energy spectra follow a power-law scaling of $\kappa ^{-1}$ . The structure functions of the mass fraction do not clearly demonstrate power-law scaling except at early times for $\alpha _0=30^\circ$ , manifesting overall trends very similar to those observed in earlier experiments. Probability distributions of the mass fraction show independence of the mean and the standard deviation of the mixed gas on $\alpha _0$ . The column angle was also found to have little effect on the mixing efficiency characterized by the molecular mixedness. Velocity components in the streamwise and transverse directions tend towards a bimodal distribution for larger $\alpha _{0}$ .

42 ENGINEERING↗

Modeling X-ray emission around galaxies

Extended X-ray emission can be studied by spatial surface brightness measurements or by spectral analysis, but the two methods can disagree at low intensity levels. Here we present an improved method for spatial analysis that can be extended to include spectral information simultaneously. We construct a model for the entire image in a given energy band and generate a likelihood function to compare the model to the data. A critical goal is disentangling vignetted and unvignetted backgrounds through their different spatial distributions. Employing either maximum likelihood or Markov Chain Monte Carlo, we can derive probability distributions for the source and background parameters together, or we can fit and subtract the background, leaving the description of the source non-parametric. We calibrate this method against a variety of simulated images, and apply it to Chandra observations of the hot gaseous halo around the elliptical galaxy NGC 720. We follow the emission below a tenth of the background and infer a hot gas mass within 35 kpc of 4-5 × 10{sup 9} M {sub ☉}, with some indication that the profile continues to at least 50 kpc and that it steepens. We derive stronger constraints on the surface brightness profile than previous studies that employed the spectral method, and we show that the density profiles inferred from these studies are in conflict with the observed surface brightness profile. Contrary to a previous claim, we find that the X-ray halo does not contain the full complement of missing baryons within the virial radius.

79 ASTRONOMY AND ASTROPHYSICS↗

Evidence Theory Representations for Properties Associated With Weak Link/Strong Link Systems, Part 2: Failure Time and Failure Temperature

The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems is introduced and illustrated. Article content includes cumulative and complementary cumulative belief, plausibility, and probability for (i) time at which LOAS occurs for a one WL/two SL system, (ii) time at which a two-link system fails, (iii) temperature at which a two-link system fails, and (iv) temperature at which LOAS occurs for a one WL/two SL system. The presented results can be generalized to systems with more than one WL and two SLs.

42 ENGINEERING↗

Structure–Activity Relationships in Ether-Functionalized Solid-State Metal–Organic Framework Electrolytes

The structure–property relationships of metal–organic framework (MOF)-based solid-state electrolytes are not well understood. Herein, a systematic investigation of 12 Zr(IV)-based UiO-66 MOFs with varying ether-chain functional groups was carried out to elucidate the critical microscopic interactions that facilitate improved solid-state electrolyte performance. Enhanced sampling molecular dynamics (MD) simulations were employed and revealed a three-tier ion hopping mechanism: linker–linker hopping, linker-counterion hopping, and counterion-counterion hopping. Detailed structural analysis of the MD trajectories revealed that the chemistry and morphology of the linker groups affect the relative stability and population distribution of the electrolyte components, such that crown-ether-based linker groups enhance the probability of extended, low-barrier ion percolation pathways. As a result, we were able to tune the ionic conductivities by rationally manipulating the counterion distributions, linker binding strengths, and the configurational entropy (multivariability of the linkers). The resulting performance of these MOF-based solid-state electrolytes was significantly enhanced, with a methoxy-functionalized framework (UiO-66-L1 100 ) achieving high ionic conductivities of 2.32 × 10 –4 S/cm and 2.07 × 10 –3 S/cm at 30 °C and 90 °C, respectively, an order of magnitude greater than other all-solid-state MOF electrolyte systems. The electrolyte stability was evaluated with LiIn|LPSCl|MOF:LiTFSI|LPSCl|LiIn symmetric cells, showing excellent Li plating/stripping processes for over 2 months.

36 MATERIALS SCIENCE↗

IMPROVING SENSITIVITY TO WEAK PULSATIONS WITH PHOTON PROBABILITY WEIGHTING

All {gamma}-ray telescopes suffer from source confusion due to their inability to focus incident high-energy radiation, and the resulting background contamination can obscure the periodic emission from faint pulsars. In the context of the Fermi Large Area Telescope, we outline enhanced statistical tests for pulsation in which each photon is weighted by its probability to have originated from the candidate pulsar. The probabilities are calculated using the instrument response function and a full spectral model, enabling powerful background rejection. With Monte Carlo methods, we demonstrate that the new tests increase the sensitivity to pulsars by more than 50% under a wide range of conditions. This improvement may appreciably increase the completeness of the sample of radio-loud {gamma}-ray pulsars. Finally, we derive the asymptotic null distribution for the H-test, expanding its domain of validity to arbitrarily complex light curves.

79 ASTRONOMY AND ASTROPHYSICS↗

Closures and Simulation for Thermal Radiation Transport in Stochastic Media with Nonlinear Temperature Dependence

Because of the practical challenge of rendering very complex realistic spatial structures for numerical work, it is common practice to resort to characterizing such media as stochastic mixtures of materials, ideally parametrized with low order statistics such as the mean, variance, and correlation functions of the now random material properties. This enables realizations of the medium to be repeatedly generated and radiation transport computations to, in principle, be performed for a large ensemble of these realizations to obtain a statistically well-characterized radiation field. Statistical post-processing yields desired quantities such as conditional and unconditional mean radiation flux and probability distributions of transmitted radiation. However, such computations prove expensive for all but the simplest stochastic geometries and are most suited for benchmarking approximate models. The most common approximations lead to homogenized media so that transport computations are required only on a single medium realization but by construct provide only limited statistical information on the radiation field. Almost all approximate approaches to this problem attempt to develop equations for low order moments of the radiation intensity (mean, second moment, correlation function) but inevitably encounter a closure problem: the equation for any statistical moment will contain terms depending on unknown higher-order moments. Thus, the challenge shifts to one of developing closure relations that relate the unknown moments to the lower order moments. Under very special conditions, an exact closure can be derived but in general closures are heuristically stated constitutive relations. Also, closure approaches depend on whether the mixing statistics are spatially and/or temporally continuous as in fluctuating turbulent fields, or discontinuous as in randomly mixed solid chunks of material. Thus, unconditional averaging is generally applied in the former case but conditional averaging is more appropriate when the mixing is discontinuous. In this work, the emphasis is on binary statistical mixtures of immiscible fluids as as such the quantities of interest are averages (flux, temperature) conditioned on the material type.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗