Search NASA⌕ Search

SEARCH · Search NASA

Results for “normal 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.

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

At least 883 records · Page 49

THE INFLUENCE OF PICK-UP IONS ON SPACE PLASMA DISTRIBUTIONS

The addition and incorporation of highly ordered distributions of pickup ions can increase the ordering of space plasmas, decreasing their entropy, and driving them away from equilibrium. In this study, we present a model for describing the entropy decrease of heliospheric plasmas caused by the pick-up ions and their highly ordered arrangement. We consider a plasma flow consisting of two proton populations: (1) a solar wind distribution that is in quasi-equilibrium and (2) a spherical shell distribution of pick-up protons. Because all protons are indistinguishable, they equally share a hybrid state, where the hybrid probability distribution is given by the normalized sum of the distributions of the solar wind and pick-up protons. We derive an analytical formulation of the thickness of the pick-up proton shell distribution. Then we show that the entropy of the hybrid state depends on a dimensionless fluctuation number, {Theta}, which is a measure of the organizing role of pick-up protons. This number characterizes and compares two types of fluctuations, the thermal motion of solar wind protons and the bounded motion of pick-up protons that forms the spherical shell distribution. We find that the entropy variation between the hybrid and original states is proportional to the negative logarithm of {Theta}. When the two competing fluctuations balance each other, {Theta} {approx} 1, the pick-up protons have no effect on the entropy of solar wind protons. Remarkably, while sunward of the termination shock pick-up ions act to slightly increase entropy, throughout the inner heliosheath their effect is to decrease the entropy dramatically.

79 ASTRONOMY AND ASTROPHYSICS↗

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗

A comparative review of radiation aerosol models

Aerosol characteristics to be introduced into a set of models within a framework of a Standard Radiation Atmosphere (SRA) are reviewed, and a reconciliation of the Toon and Pollack (TP) global model with the SRA models is attempted. Among the topics discussed are physical and radiative characteristics, radiation aerosol models, albedo for single scattering, and phase function and spectral variation of extinction. Size distribution models are also covered, inclusive the Junge power law, and the modified gamma-, log normal-, and zold-distribution. Recommendations include modifying the SRA profile VI to resemble the Elterman profile modified in the TP model, improving discontinuity at the tropopause level for all SRA models, and retaining the same log-normal size distribution for all SRA components.

Lenoble, J.↗

Initial and Final State Interaction Effects in Small-x Quark Distributions

We study the initial and final state interaction effects in the transverse momentum dependent parton distributions in the small-x saturation region. In particular, we discuss the quark distributions in the semi-inclusive deep inelastic scattering, Drell-Yan lepton pair production and dijet-correlation processes in pA collisions. We calculate the quark distributions in the scalar-QED model and then extend to the color glass condensate formalism in QCD. The quark distributions are found universal between the DIS and Drell-Yan processes. On the other hand, the quark distribution from the qq'-->qq' channel contribution to the dijet-correlation process is not universal. However, we find that it can be related to the quark distribution in DIS process by a convolution with the normalized unintegrated gluon distribution in the CGC formalism in the large Nc limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Zooming in on the progenitors of superluminous supernovae with the HST

We present Hubble Space Telescope (HST) rest-frame ultraviolet imaging of the host galaxies of 16 hydrogen-poor superluminous supernovae (SLSNe), including 11 events from the Pan-STARRS Medium Deep Survey. Taking advantage of the superb angular resolution of HST, we characterize the galaxies’ morphological properties, sizes, and star formation rate (SFR) densities. We determine the supernova (SN) locations within the host galaxies through precise astrometric matching and measure physical and host-normalized offsets as well as the SN positions within the cumulative distribution of UV light pixel brightness. We find that the host galaxies of H-poor SLSNe are irregular, compact dwarf galaxies, with a median half-light radius of just 0.9 kpc. The UV-derived SFR densities are high (〈Σ{sub SFR}〉≃0.1M{sub ⊙} yr{sup −1} kpc{sup −2}), suggesting that SLSNe form in overdense environments. Their locations trace the UV light of their host galaxies, with a distribution intermediate between that of long-duration gamma-ray bursts (LGRBs; which are strongly clustered on the brightest regions of their hosts) and a uniform distribution (characteristic of normal core-collapse SNe), though cannot be statistically distinguished from either with the current sample size. Taken together, this strengthens the picture that SLSN progenitors require different conditions than those of ordinary core-collapse SNe to form and that they explode in broadly similar galaxies as do LGRBs. If the tendency for SLSNe to be less clustered on the brightest regions than are LGRBs is confirmed by a larger sample, this would indicate a different, potentially lower-mass progenitor for SLSNe than LRGBs.

79 ASTRONOMY AND ASTROPHYSICS↗

Analysis of field size distributions, LACIE test sites 5029, 5033, and 5039, Anhwei Province, People's Republic of China

A study was made of the field size distributions for LACIE test sites 5029, 5033, and 5039, People's Republic of China. Field lengths and widths were measured from LANDSAT imagery, and field area was statistically modeled. Field size parameters have log-normal or Poisson frequency distributions. These were normalized to the Gaussian distribution and theoretical population curves were made. When compared to fields in other areas of the same country measured in the previous study, field lengths and widths in the three LACIE test sites were 2 to 3 times smaller and areas were smaller by an order of magnitude.

Podwysocki, M. H.↗

Quantifying the evidence for dark matter in CoGeNT data

We perform an independent analysis of data from the CoGeNT direct detection experiment to quantify the evidence for dark matter recoils. We critically re-examine the assumptions that enter the analysis, focusing specifically on the separation of bulk and surface events, the latter of which constitute a large background. This separation is performed using the event rise-time, with the surface events being slower on average. We fit the rise-time distributions for the bulk and surface events with a log-normal and Pareto distribution (which gives a better fit to the tail in the bulk population at high rise-times) and account for the energy-dependence of the bulk fraction using a cubic spline. Using Bayesian and frequentist techniques and additionally investigating the effect of varying the rise-time cut, the bulk background spectrum and bin-sizes, we conclude that the CoGeNT data show a preference for light dark matter recoils at less than 1σ.

79 ASTRONOMY AND ASTROPHYSICS↗

Property Improvement in CZT via Modeling and Processing Innovations . Te-particles in vertical gradient freeze CZT: Size and Spatial Distributions and Constitutional Supercooling

A section of a vertical gradient freeze CZT boule approximately 2100-mm 3 with a planar area of 300-mm 2 was prepared and examined using transmitted IR microscopy at various magnifications to determine the three-dimensional spatial and size distributions of Te-particles over large longitudinal and radial length scales. The boule section was approximately 50-mm wide by 60-mm in length by 7-mm thick and was doubly polished for TIR work. Te-particles were imaged through the thickness using extended focal imaging to locate the particles in thickness planes spaced 15-µm apart and then in plane of the image using xy-coordinates of the particle center of mass so that a true three dimensional particle map was assembled for a 1-mm by 45-mm longitudinal strip and for a 1-mm by 50-mm radial strip. Te-particle density distributions were determined as a function of longitudinal and radial positions in these strips, and treating the particles as vertices of a network created a 3D image of the particle spatial distribution. Te-particles exhibited a multi-modal log-normal size density distribution that indicated a slight preference for increasing size with longitudinal growth time, while showing a pronounced cellular network structure throughout the boule that can be correlated to dislocation network sizes in CZT. Higher magnification images revealed a typical Rayleigh-instability pearl string morphology with large and small satellite droplets. This study includes solidification experiments in small crucibles of 30:70 mixtures of Cd:Te to reduce the melting point below 1273 K (1000°C). These solidification experiments were performed over a wide range of cooling rates and clearly demonstrated a growth instability with Te-particle capture that is suggested to be responsible for one of the peaks in the size distribution using size discrimination visualization. The results are discussed with regard to a manifold Te-particle genesis history as 1) Te-particle direct capture from melt-solid growth instabilities, 2) Te-particle formation from dislocation core diffusion and the formation and breakup of Te-tubes, and 3) Te-particle formation due to classical nucleation and growth as precipitates.

36 MATERIALS SCIENCE↗

Information extraction techniques for multispectral scanner data

The applicability of recognition-processing procedures for multispectral scanner data from areas and conditions used for programming the recognition computers to other data from different areas viewed under different measurement conditions was studied. The reflective spectral region approximately 0.3 to 3.0 micrometers is considered. A potential application of such techniques is in conducting area surveys. Work in three general areas is reported: (1) Nature of sources of systematic variation in multispectral scanner radiation signals, (2) An investigation of various techniques for overcoming systematic variations in scanner data; (3) The use of decision rules based upon empirical distributions of scanner signals rather than upon the usually assumed multivariate normal (Gaussian) signal distributions.

Malila, W. A.↗

A study of lunar impact crater size-distributions

In view of the discrepancies in published crater frequency data, effects modifying production size distributions of impact craters are discussed. The resulting criteria are applied to the determination of the size distributions of unmodified impact crater populations in selected lunar regions of different ages. The measured cumulative crater frequencies are used to obtain a general calibration size distribution curve by a normalization procedure. Deviations of measured size distributions from the calibration distribution are strongly suggestive of the existence of processes having modified the primary impact crater population.

Neukum, G.↗

Probabilistic structural analysis of a truss typical for space station

A three-bay, space, cantilever truss is probabilistically evaluated using the computer code NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) to identify and quantify the uncertainties and respective sensitivities associated with corresponding uncertainties in the primitive variables (structural, material, and loads parameters) that defines the truss. The distribution of each of these primitive variables is described in terms of one of several available distributions such as the Weibull, exponential, normal, log-normal, etc. The cumulative distribution function (CDF's) for the response functions considered and sensitivities associated with the primitive variables for given response are investigated. These sensitivities help in determining the dominating primitive variables for that response.

Pai, Shantaram S.↗

Normal tissue dose conformality measures to guide radiotherapy fractionation decisions

Purpose: To determine conditions under which hypofractionation could be favorable for a normal tissue--even if tumor [{alpha}/{beta}] exceeds the normal tissue's [{alpha}/{beta}]. Methods: The hypofractionation sufficiency condition (HSC) for an organ is defined as a dose conformality constraint such that, if satisfied, a family of tumor control probability isoeffective fractionation schemes will show decreasing normal tissue complication probability with decreasing number of fractions. Results: In the extended equivalent uniform dose (EUD) model [obtained by replacing dose with linear quadratic (LQ) 2 Gy equivalent dose], the HSC for a normal organ is proven to be satisfied if a suitably weighted average of the relative dose [hypofractionation sufficiency index (HSI)] is less than the ratio of normal tissue to tumor [{alpha}/{beta}]. The HSI is determined solely by dose distribution and the normal tissue volume factor, ''a.'' If the HSC is satisfied for every normal tissue of concern, then there is a therapeutic gain with hypofractionation. The corresponding multifractionation sufficiency condition (therapeutic gain with increasing number of fractions) and multifractionation sufficiency index (MSI) are also derived. A sample clinical case is presented. Conclusions: Within the context of the LQ/EUD models, conformality measures (HSI and MSI) can be used to inform fractionation decisions.

60 APPLIED LIFE SCIENCES↗

Normalizing flows for domain adaptation when identifying Λ hyperon events

Here this study focuses on the application of a normalizing flow as a method of domain adaptation when classifying physics data. Normalizing flows offer a way to transform data points between two different distributions. The present study investigates a novel method of transforming latent representations of physics data to a normal distribution and then to a physics distribution again. The final distribution models a simulated distribution. After being transformed, the data can be classified by a neural network trained on labeled simulation data. The present study succeeds in training two normalizing flows that can transform between data (or simulation) and a Gaussian distribution.

47 OTHER INSTRUMENTATION↗

Bayesian mixture model approach to quantifying the empirical nuclear saturation point

The equation of state (EOS) in the limit of infinite symmetric nuclear matter exhibits an equilibrium density, $n_0 \approx 0.16 \, \mathrm{fm}^{-3}$, at which the pressure vanishes and the energy per particle attains its minimum, $E_0 \approx -16 \, \mathrm{MeV}$. Although not directly measurable, the nuclear saturation point $(n_0,E_0)$ can be extrapolated by density functional theory (DFT), providing tight constraints for microscopic interactions derived from chiral effective field theory (EFT). However, when considering several DFT predictions for $(n_0,E_0)$ from Skyrme and Relativistic Mean Field (RMF) models together, a discrepancy between these model classes emerges at high confidence levels that each model prediction's uncertainty cannot explain. How can we leverage these DFT constraints to rigorously benchmark nuclear saturation properties of chiral interactions? To address this question, we present a Bayesian mixture model that combines multiple DFT predictions for $(n_0,E_0)$ using an efficient conjugate prior approach. The inferred posterior distribution for the saturation point's mean and covariance matrix follows a Normal-inverse-Wishart class, resulting in posterior predictives in the form of correlated, bivariate $t$-distributions. The DFT uncertainty reports are then used to mix these posteriors using an ordinary Monte Carlo approach. At the 95\% credibility level, we estimate $n_0 \approx 0.157 \pm 0.010 \, \mathrm{fm}^{-3}$ and $E_0 \approx -15.97 \pm 0.40 \, \mathrm{MeV}$ for the marginal (univariate) $t$-distributions. Combined with chiral EFT calculations of the pure neutron matter EOS, we obtain bivariate normal distributions for the nuclear symmetry energy and its slope parameter evaluated at $n_0$: $S_v \approx 32.0 \pm 1.1 \, \mathrm{MeV}$ and $L\approx 52.6\pm 8.1 \, \mathrm{MeV}$ (95\%), respectively. Furthermore, our Bayesian framework is publicly available, so practitioners can readily use and extend our results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Optimizing Service Restoration in Distribution Systems With Uncertain Repair Time and Demand

This paper proposes a novel method to co-optimize the distribution system operation and repair crew routing for outage restoration after extreme weather events. A two-stage stochastic mixed integer linear program is developed. The first stage is to dispatch the repair crews to the damaged components. The second stage is distribution system restoration using distributed generators, and reconfiguration. We consider demand uncertainty in terms of a truncated normal forecast error distribution, and model the uncertainty of the repair time using a lognormal distribution. A new decomposition approach, combined with the progressive hedging algorithm, is developed for solving large-scale outage management problems in an effective and timely manner. Furthermore, the proposed method is validated on modified IEEE 34- and 8500-bus distribution test systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

D-Guaranteed Discrimination of Statistical Hypotheses: a Review of Results and Unsolved Problems

We compare two sequential d-guaranteed tests and an optimal d-guaranteed test based on a fixed number of observations with respect to the average number of observations within the most accepted practical applications of Bayesian probabilistic models. We consider the sequential “first skipping” test, the sequential locally efficient test based on the score statistic, and the test based on a fixed number of observations that minimizes the necessary sample size. We study various characteristics of these tests connected with the number of observations within three probabilistic models, namely, the normal (ϑ, σ{sup 2}) distribution of the observed random variable and the normal a priori distribution of ϑ with fixed σ{sup 2}; the exponential distribution with the intensity parameter ϑ and the a priori gamma distribution of ϑ; and the Bernoulli sampling with the success probability ϑ and the a priori beta distribution of ϑ. We discuss the connection of the d-posterior approach with the compound decision problem as applied to the analysis of data provided by microchips (when the false discovery rate, or FDR, for short, is treated as the d-risk of the first kind). We present the vast data on characteristics of the mentioned tests obtained by the method of mathematical modeling in several tables. We discuss unsolved problems of the d-guaranteed discrimination of hypotheses with the minimal number of observations and approaches to their solution.

97 MATHEMATICS AND COMPUTING↗

Self-consistent mean-field theory of size distribution narrowing during ramped temperature ion beam synthesis

A simple mathematical argument explains a recently identified route for the ion beam synthesis of nanoclusters with a narrowed size distribution. The key idea is that growth conditions for which the average nanocluster size is increasing rapidly can lead to narrowed size distributions. Modeling candidate processes using a self-consistent, mean-field theory shows that normalized nanocluster size distributions with full-width at half-maximum of 17% of the average can be attained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An elastoplastic finite element study of cylindrical plane-strain contact for steel/steel and Inconel 617/Incoloy 800H undergoing unidirectional sliding

The current work employs a two-dimensional plane strain finite element analysis to investigate the unidirectional sliding contact between a deformable half-cylinder and a deformable flat block. The unidirectional sliding is governed by a displacement-controlled action where the materials of the two contacting bodies are first set to identical steels at 20 ℃ and then to Inconel 617 and Incoloy 800H at 800 ℃. First, a normal interference (indentation) is applied, which is followed by unidirectional sliding. The von Mises stress distribution, plastic strain distribution, junction growth, normal force, tangential force, effective coefficient of friction, and scars on the surface of the block are obtained during the sliding motion. The leading edge of the contacting area and the bulk material under the leading edge experience large von Mises stresses. The large plastic strain is found on the surface of the block, and forms a “pocket” shape under the surface. The junction growth is also investigated, showing the direction of the growth is in the same direction of the tangential force that the weaker material experiences. The forces and the effective coefficient of friction are found to stabilize after a certain sliding distance, and the effective coefficient of friction converges to the coefficient of friction used in the model. Pileup is found on the surface of the block after a sufficient unidirectional sliding distance.

Yang, Huaidong↗