Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Probability density 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 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

The Plasma Environment at Mercury

Mercury is the least explored terrestrial planet, and the one subjected to the highest flux of solar radiation in the heliosphere. Its highly dynamic, miniature magnetosphere contains ions from the exosphere and solar wind, and at times may allow solar wind ions to directly impact the planet's surface. Together these features create a plasma environment that shares many features with, but is nonetheless very different from, that of Earth. The first in situ measurements of plasma ions in the Mercury space environment were made only recently, by the Fast Imaging Plasma Spectrometer (FIPS) during the MESSENGER spacecraft's three flybys of the planet in 2008-2009 as the probe was en route to insertion into orbit about Mercury earlier this year. Here. we present analysis of flyby and early orbital mission data with novel techniques that address the particular challenges inherent in these measurements. First. spacecraft structures and sensor orientation limit the FIPS field of view and allow only partial sampling of velocity distribution functions. We use a software model of FIPS sampling in velocity space to explore these effects and recover bulk parameters under certain assumptions. Second, the low densities found in the Mercury magnetosphere result in a relatively low signal-to-noise ratio for many ions. To address this issue, we apply a kernel density spread function to guide removal of background counts according to a background-signature probability map. We then assign individual counts to particular ion species with a time-of-flight forward model, taking into account energy losses in the carbon foil and other physical behavior of ions within the instrument. Using these methods, we have derived bulk plasma properties and heavy ion composition and evaluated them in the context of the Mercury magnetosphere.

Raines, James M.↗
NASA NTRS1972

Measurement of the light-field amplitude-correlation function through joint photon-count distributions.

When an amplitude-stabilized He-Ne laser beam is scattered by a rotating ground glass with small surface inhomogeneities, the probability density of the instantaneous scattered-wave amplitude is Gaussian. In this paper, we suggest the use of the joint photon-count probability distribution to measure the absolute value of the electric-field amplitude-correlation function for random Gaussian light fields, and report the results of an experiment in which the Gaussian field is produced by scattering a light beam through a rotating ground glass. This procedure offers an alternative to other conventional methods, such as self-beating spectroscopy and irradiance-correlation techniques. The correlation time of the scattered-field amplitude in the present experiment has been measured with an accuracy of approximately 0.8%.

Furcinitti, P.↗
DOE OSTI2025

The impact of nickel concentration and stacking fault energy on deformation mechanisms in high-purity austenitic Fe-Cr-Ni alloys

Understanding how composition affects deformation mechanisms in austenitic stainless steels is essential for developing accurate predictive models of stress-induced failures and stress corrosion cracking. Nickel (Ni), an element classified as a critical element, plays a crucial role in these processes. It is important to examine how Ni concentration influences stacking fault energy (SFE) and, consequently, the deformation mechanisms of austenitic stainless steels. However, in commercial stainless steels, the effects of other alloying elements and impurities can obscure Ni's role, complicating efforts to isolate its impact. Here, in this study, we use two high-purity Fe-Cr-Ni alloys to investigate how Ni concentration and SFE interact to alter deformation mechanisms and induce martensitic transformation. By combining in situ synchrotron X-ray diffraction (XRD) tensile testing and post-mortem electron microscopy with density functional theory simulations, we gain precise insights into these phenomena. We find that the Fe18Cr10Ni (wt%) alloy, with its low SFE, exhibits higher stacking fault probability, deformation-induced martensitic transformation, and a lesser increase in dislocation density with plastic strain. In contrast, the Fe18Cr14Ni (wt%) alloy, with its higher SFE, shows enhanced deformation twinning and greater dislocation density with increasing strain. These findings from high-purity ternary alloys provide valuable insights that can guide the search for alternative elements to replace Ni while achieving similar effects on phase stability and deformation behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Real-time scattering in Ising field theory using matrix product states

We study scattering in Ising field theory (IFT) using matrix product states and the time-dependent variational principle. IFT is a one-parameter family of strongly coupled nonintegrable quantum field theories in 1+1 dimensions, interpolating between massive free fermion theory and Zamolodchikov's integrable massive 𝐸 8 theory. Particles in IFT may scatter either elastically or inelastically. In the postcollision wave function, particle tracks from all final-state channels occur in superposition; processes of interest can be isolated by projecting the wave function onto definite particle sectors, or by evaluating energy density correlation functions. Using numerical simulations we determine the time delay of elastic scattering and the probability of inelastic particle production as a function of collision energy. We also study the mass and width of the lightest resonance near the 𝐸 8 point in detail. Close to both the free fermion and 𝐸 8 theories, our results for both elastic and inelastic scattering are in good agreement with expectations from form-factor perturbation theory. Using numerical computations to go beyond the regime accessible by perturbation theory, we find that the high-energy behavior of the two-to-two particle scattering probability in IFT is consistent with a conjecture of Zamolodchikov. Our results demonstrate the efficacy of tensor-network methods for simulating the real-time dynamics of strongly coupled quantum field theories in 1+1 dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1979

Quasi-periodic structure of a turbulent jet

The instantaneous near field pressure fluctuations of an axisymmetric subsonic jet were measured by using a longitudinal and an azimuthal microphone arrays in order to qualitatively determine the behaviors of the quasi-periodic structure within the flow. Statistical analysis is used to explain the characteristic of the pressure signals. In addition to the information obtained by forming the power spectral density, auto- and cross-correlation functions, two types of signals are extracted through a conditional probability analysis to represent the quasi-periodic and the random fine structures within the turbulent jet. The quasi-periodic structure first appears as a rolling up of the mixing layer flow within one nozzle diameter downstream of the exit, then becomes fully developed at approximately 3 nozzle diameters downstream with a preferred Strouhal number range 0.3-0.4, and finally disappears beyond the end of potential core. This behavior is also reflected in the variation of the convection velocity.

Maestrello, L.↗
NASA NTRS1982

Radar scattering laws for the lunar surface

Bistatic radar observations of quasi-specular scatter from the lunar surface at 13 and 116 cm wavelengths have been expressed in terms of probability densities of the underlying surface slope distributions. These show best agreement with a Hagfors scattering function, although other forms having predominantly Gaussian or exponential characteristics also occur. Estimates of root mean square (rms) surface slope derived from these function range from 4 deg rms in maria to at least 8 deg rms in highlands. These are values appropriate to 25 m horizontal scales and represent averages over tens of square kilometers of surface area. The effective scattering roughness varies with wavelength, most strongly in maria, where its behavior is consistent with that expected from an immature, i.e., unsaturated cratered surface. There is very little variation in scattering roughness with wavelength in highlands area.

Simpson, R. A.↗
NASA NTRS1992

Nonclassical and nonlocal effects in the interference of light

Although we tend to think of optical interference as a classical wave phenomenon, recent experiments have revealed a number of effects that are not describable in classical terms. This is particularly true of interference effects involving the detection of a photon pair. We shall refer to them as fourth order interference, on the grounds that the joint probability density for the detection of one photon at r sub 1 at time t and another r sub 2 at time t is proportional to the fourth order correlation function of the field. This probability is readily measured when two photodetectors are positioned at r sub 1 and r sub 2 and the signals from the two detectors are fed to a coincidence counter that registers 'simultaneous' detections by the two detectors in coincidence. The topics covered include: fourth order interference measurements; the Franson experiment; and experimental test of the de Broglie guided wave theory.

Mandel, L.↗
NASA NTRS2013

Unit-Sphere Anisotropic Multiaxial Stochastic-Strength Model Probability Density Distribution for the Orientation of Critical Flaws

Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software

Nemeth, Noel↗
DOE OSTI2021

Beyond the universal Dyson singularity for 1-D chains with hopping disorder

We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder, where the hopping terms are chosen randomly. This model exhibits a well-known singularity at the band center both in the density of states and localization length. If the probability distribution of the hopping terms is well-behaved, then the singularities exhibit universal behavior, the functional form of which was first discovered by Freeman Dyson in the context of a chain of classical harmonic oscillators. We show here that this universal form can be violated in a tunable manner if the hopping elements are chosen from a divergent probability distribution. We also demonstrate a connection between a breakdown of universality in this quantum problem and an analogous scenario in the classical domain — that of random walks and diffusion with anomalous exponents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quantifying the Long‐Range Coupling of Electronic Properties in Proteins with ab initio Molecular Dynamics**

Abstract The delicate interplay of covalent and non‐covalent interactions in proteins is inherently quantum mechanical and highly dynamic in nature. To directly interrogate the evolving nature of the electronic structure of proteins, we carry out 100‐ps‐scale ab initio molecular dynamics simulations of three representative small proteins with range‐separated hybrid density functional theory. We quantify the nature and length‐scale of the coupling of residue‐specific charge probability distributions in these proteins. While some nonpolar residues exhibit expectedly narrow charge distributions, most polar and charged residues exhibit broad, multimodal distributions. Even for nonpolar residues, we observe sequence‐specific deviations corresponding to charge accumulation or depletion that would be challenging to capture in a fixed charge force field. We quantify the effect of residue‐residue interactions on charge distributions first with linear cross‐correlations. We then show how additional insight can be gained from evaluating the mutual information of charge distributions. We show that a significant number of residues couple most strongly with residues that are distant in both sequence and space over a range of secondary structures including α‐helical, β‐sheet, disulfide bridging, and lasso motifs. The mutual information analysis is necessary to capture coupling between some polar and charged residues that would be otherwise missed.

Yang, Zhongyue↗
DOE OSTI2020

Closing the Gap Between Experiment and Theory: Reactive Scattering of HCl from Au(111)

Accurate simulation of molecules reacting on metal surfaces, which can help in improving heterogeneous catalysts, remains out of reach for several reactions. For example, a large disagreement between theory and experiment for HCl reacting on Au(111) still remains, despite many efforts. In this work, the dissociative chemisorption of HCl on Au(111) is investigated with a recently developed MGGA density functional (MS-RPBEl) and a high-dimensional neural network potential. Additionally, previous experimental sticking probabilities are re-examined. A considerably improved agreement between experiment and theory is obtained, although theory still overestimates experimental sticking probabilities by a factor of 2-7 at the highest incidence energy. Computed and measured vibrational transition probabilities are also in improved agreement. Several dynamical effects such as angular steering and energy transfer from the molecule to the surface are found to play an important role.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Atomistic models of In and Ga diffusion in Cu(In,Ga)Se 2

To improve the performance of Cu(In,Ga)Se 2 thin-film photovoltaic devices, a robust understanding of the dominant diffusion pathways of the alloy species In and Ga is needed. Here, the most probable defect complexes and mechanisms for In and Ga diffusion are identified with the aid of density functional theory. The binding energies and migration barriers for these complexes are calculated in bulk CuInSe 2 and CuGaSe 2 . Analytic models and kinetic lattice Monte Carlo simulations are employed to predict the diffusivity of In and Ga under variations in composition and temperature. Here, we find that a model based on coulombic interactions between group III antisites and vacancies on the Cu-sublattice produces results that match well with experiment.

14 SOLAR ENERGY↗
NASA NTRS1972

The resolution of point sources of light as analyzed by quantum detection theory

The resolvability of point sources of incoherent light is analyzed by quantum detection theory in terms of two hypothesis-testing problems. In the first, the observer must decide whether there are two sources of equal radiant power at given locations, or whether there is only one source of twice the power located midway between them. In the second problem, either one, but not both, of two point sources is radiating, and the observer must decide which it is. The decisions are based on optimum processing of the electromagnetic field at the aperture of an optical instrument. In both problems the density operators of the field under the two hypotheses do not commute. The error probabilities, determined as functions of the separation of the points and the mean number of received photons, characterize the ultimate resolvability of the sources.

Helstrom, C. W.↗
NASA NTRS1973

Resolution of point sources of light as analyzed by quantum detection theory.

The resolvability of point sources of incoherent thermal light is analyzed by quantum detection theory in terms of two hypothesis-testing problems. In the first, the observer must decide whether there are two sources of equal radiant power at given locations, or whether there is only one source of twice the power located midway between them. In the second problem, either one, but not both, of two point sources is radiating, and the observer must decide which it is. The decisions are based on optimum processing of the electromagnetic field at the aperture of an optical instrument. In both problems the density operators of the field under the two hypotheses do not commute. The error probabilities, determined as functions of the separation of the points and the mean number of received photons, characterize the ultimate resolvability of the sources.

Helstrom, C. W.↗
NASA NTRS1991

Theoretical temperature-dependent branching ratios and laser thresholds of the 3F4 to 3H6 levels of Tm(3+) in ten garnets

The calculated energy levels, the branching ratios, and the estimated thresholds for thulium operating on the 3F4 to 3H6 transitions are reported. Garnet materials with the general formula A3B2C3O12 are evaluated. Calculations are performed for the A side under the assumption of D2 symmetry. X-ray data available in the literature are used to evaluate the crystal-field components, A sub nm. Even-n components are employed to calculate the crystal-field splittings within the manifold. Thermal occupation factors are determined in a straightforward manner using a Boltzmann distribution for the respective manifolds. Odd-n components are applied to calculate the transition probabilities for electric field transitions. It is determined that the magnetic dipole contributions to the transition probability are comparable to the electric dipole contributions in some cases. Thresholds as a function of the density of thulium atoms are calculated.

Filer, Elizabeth D.↗
NASA NTRS1999

International Space Station (ISS) Meteoroid/Orbital Debris Shielding

Design practices to provide protection for International Space Station (ISS) crew and critical equipment from meteoroid and orbital debris (M/OD) Impacts have been developed. Damage modes and failure criteria are defined for each spacecraft system. Hypervolocity Impact -1 - and analyses are used to develop ballistic limit equations (BLEs) for each exposed spacecraft system. BLEs define Impact particle sizes that result in threshold failure of a particular spacecraft system as a function of Impact velocity, angles and particle density. The BUMPER computer code Is used to determine the probability of no penetration (PNP) that falls the spacecraft shielding based on NASA standard meteoroid/debris models, a spacecraft geometry model, and the BLEs. BUMPER results are used to verify spacecraft shielding requirements Low-weight, high-performance shielding alternatives have been developed at the NASA Johnson Space Center (JSC) Hypervelocity Impact Technology Facility (HITF) to meet spacecraft protection requirements.

Christiansen, Eric L.↗
DOE OSTI2020

A method to fuse multiphysics waveforms and improve predictive explosion detection: theory, experiment and performance

Natural and human-made sources of transient energy often emit multiple geophysical signatures that include mechanical and electromagnetic waveforms. We present a constructive method to fuse and evaluate statistics that we derive from such multiphysics waveforms that improves our capability to detect small, near-ground explosions over similar methods that consume single signature waveforms. Our method advances Fisher's Combined Probability Test (Fisher's Method) to operate under both hypotheses of a binary test on noisy data and provide researchers with the density functions required to forecast the ability of Fisher's Method to screen fused explosion signatures from noise. We apply this method against 12 d, multisignature explosion and noise records to show (1) that a fused multiphysics waveform statistic that combines radio, acoustic and seismic waveform data can identify explosions roughly 0.8 magnitude units lower than an acoustic emission, STA/LTA detector for the same detection probability and (2) that we can quantitatively predict how this fused, multiphysics statistic performs with Fisher's Method. Our work thereby offers a baseline method for predictive waveform fusion that supports multiphenomenological explosion monitoring (multiPEM) and is applicable to any binary testing problem in observational geophysics.

58 GEOSCIENCES↗
DOE OSTI2025

Facet-dependent structure and dissociation of water at pristine IrO 2 /water interfaces

Understanding the microscopic structure of water at metal oxide interfaces is crucial for advancing electrocatalysis. IrO 2 , specifically, has shown exceptional activity for electrochemical water oxidation, but we currently lack a fundamental understanding of how the surface structure of IrO 2 impacts water reactivity. In this work, we developed a machine learning potential trained to first-principles accuracy for modeling IrO 2 /water interfaces across different facets: (110), (100), (101), and (001). Using extensive machine learning molecular dynamics simulations, we investigated the spontaneous dissociation of water molecules at these interfaces. Our results reveal a distinct dissociation probability trend: (110) > (100) ≈ (101) > (001), which we attribute primarily to the reaction thermodynamics of surface water dissociation. A strong correlation is observed between the surface Ir–O bond distances and the dissociation probabilities, highlighting the role of surface geometry in modulating reactivity. As a consequence, the interfacial solvation structures and hydrogen bonding environments are dynamically tuned by the varying water dissociation capabilities across facets. This work elucidates how water dissociation energetics depend on surface orientation and interfacial structure, offering atomistic insights into manipulating reaction chemistry at electrocatalytic interfaces.

organic↗