Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “probability generating 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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Hail risk model for solar collectors

This report presents the results of a study assessing the probability of solar arrays being struck by hailstones of various sizes as a function of geographic location and service life. The study complements parallel studies of solar array sensitivity to hail damage, the final objective being an estimate of the most cost effective level for solar array hail protection. A key element of this study involves the generation of a statistical model describing the probability of impact by hailstones of various sizes and estimating the mean time between hits.

Gonzalez, C.↗
DOE OSTI2025

Generative AI models for learning flow maps of stochastic dynamical systems in bounded domains

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approach that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Our ML model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a training-free diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. Here, the performance of the proposed approach is demonstrated via three test cases: a one-dimensional simplified problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional problem of interest to magnetically confined fusion plasmas.

Bounded domains↗
NASA NTRS2010

Analytic Development of a Reference Profile for the First Entry in a Skip Atmospheric Entry

This note shows that a feasible reference drag profile for the first entry portion of a skip entry can be generated as a polynomial expression of the velocity. The coefficients of that polynomial are found through the resolution of a system composed of m + 1 equations, where m is the degree of the drag polynomial. It has been shown that a minimum of five equations (m = 4) are required to establish the range and the initial and final conditions on velocity and flight path angle. It has been shown that at least one constraint on the trajectory can be imposed through the addition of one extra equation in the system, which must be accompanied by the increase in the degree of the drag polynomial. In order to simplify the resolution of the system of equations, the drag was considered as being a probability density function of the velocity, with the velocity as a distribution function of the drag. Combining this notion with the introduction of empirically derived constants, it has been shown that the system of equations required to generate the drag profile can be successfully reduced to a system of linear algebraic equations. For completeness, the resulting drag profiles have been flown using the feedback linearization method of differential geometric control as a guidance law with the error dynamics of a second order homogeneous equation in the form of a damped oscillator. Satisfactory results were achieved when the gains in the error dynamics were changed at a certain point along the trajectory that is dependent on the velocity and the curvature of the drag as a function of the velocity. Future work should study the capacity to update the drag profile in flight when dispersions are introduced. Also, future studies should attempt to link the first entry, as presented and controlled in this note, with a more standard control concept for the second entry, such as the Apollo entry guidance, to try to assess the overall skip entry performance. A guidance law that includes an integral feedback term, as is the case in the actual Space Shuttle entry guidance and as is proposed in Ref 29, could be tried in future studies to assess whether its use results in an improvement of the tracking performance, and to evaluate the design needs when determining the control gains.

Garcia-Llama, Eduardo↗
NASA NTRS1977

Short-term variations of the galactic cosmic ray intensity - 1964-1967

A statistical analysis of time variations in ground-level nucleonic cosmic-ray intensity for the interval from 1964 to 1967 is presented which incorporates synoptic observations of the solar white-light corona as well as indices of photospheric and chromospheric activity. Correlation analysis of solar activity and short-term modulation reveals that all indices vary significantly on time scales near the solar rotation period and that the correlation function exhibits a quasi-sinusoidal variation that maximizes near zero lag. It is found that 27-day variations of the indices were most pronounced in 1966-1967, that recurrent cosmic-ray depressions occurred in conjunction with observed solar-wind disturbances, and that two categories of interplanetary disturbance are sufficient to account for the large recurrent cosmic-ray depressions in 1966-1967. It is suggested that flare-generated shocks were the main source of these recurrent cosmic-ray variations and that the contribution of corotating cosmic-ray disturbances to the observed recurrent modulation was probably very small. This hypothesis is tested against the correlation functions of solar and cosmic-ray indices.

Parker, G. D.↗
DOE OSTI2022

Improved Heralded Single-Photon Source with a Photon-Number-Resolving Superconducting Nanowire Detector

Deterministic generation of single photons is essential for many quantum information technologies. A bulk optical nonlinearity emitting a photon pair, where the measurement of one of the photons heralds the presence of the other, is commonly used with the caveat that the single-photon emission rate is constrained due to a trade-off between multiphoton events and pair emission rate. Using an efficient and low noise photon-number-resolving superconducting nanowire detector we herald, in real time, a single photon at telecommunication wavelength. We perform a second-order photon correlation g 2 ( 0 ) measurement of the signal mode conditioned on the measured photon number of the idler mode for various pump powers and demonstrate an improvement of a heralded single-photon source. We develop an analytical model using a phase-space formalism that encompasses all multiphoton effects and relevant imperfections, such as loss and multiple Schmidt modes. We perform a maximum-likelihood fit to test the agreement of the model to the data and extract the best-fit mean photon number μ of the pair source for each pump power. A maximum reduction of 0.118 ± 0.012 in the photon g 2 ( 0 ) correlation function at μ = 0.327 ± 0.007 is obtained, indicating a strong suppression of multiphoton emissions. For a fixed g 2 ( 0 ) = 7 × 10 − 3 , we increase the single pair generation probability by 25%. Our experiment, built using fiber-coupled and off-the-shelf components, delineates a path to engineering ideal sources of single photons.

Davis, Samantha I.↗
NASA NTRS1983

Waves observed upstream of interplanetary shocks

The properties of the waves that are present upstream of interplanetary, collisionless, quasi-parallel shocks are described. Two types of such waves have been detected, a higher frequency whistler mode wave and a lower frequency fast mode MHD wave. Both are typically circular or elliptically polarized right-hand waves which propagate along the ambient magnetic field with a 15 deg angle cone. The high frequency waves have sufficient group velocities to outrun the shock, and may be generated by cyclotron resonance with 100 eV to 1 keV shock electrons. The lower frequency waves must be generated locally by particles upstream of the shock, probably by 1-10 keV ions flowing away from the shock. Distinct changes in the spectra of upstream waves as a function of distance from the shock have been noted.

Tsurutani, B. T.↗
NASA NTRS1985

Correcting for particle counting bias error in turbulent flow

An ideal seeding device is proposed generating particles that exactly follow the flow out are still a major source of error, i.e., with a particle counting bias wherein the probability of measuring velocity is a function of velocity. The error in the measured mean can be as much as 25%. Many schemes have been put forward to correct for this error, but there is not universal agreement as to the acceptability of any one method. In particular it is sometimes difficult to know if the assumptions required in the analysis are fulfilled by any particular flow measurement system. To check various correction mechanisms in an ideal way and to gain some insight into how to correct with the fewest initial assumptions, a computer simulation is constructed to simulate laser anemometer measurements in a turbulent flow. That simulator and the results of its use are discussed.

Edwards, R. V.↗
NASA NTRS2000

A simulator for evaluating methods for the detection of lesion-deficit associations

Although much has been learned about the functional organization of the human brain through lesion-deficit analysis, the variety of statistical and image-processing methods developed for this purpose precludes a closed-form analysis of the statistical power of these systems. Therefore, we developed a lesion-deficit simulator (LDS), which generates artificial subjects, each of which consists of a set of functional deficits, and a brain image with lesions; the deficits and lesions conform to predefined distributions. We used probability distributions to model the number, sizes, and spatial distribution of lesions, to model the structure-function associations, and to model registration error. We used the LDS to evaluate, as examples, the effects of the complexities and strengths of lesion-deficit associations, and of registration error, on the power of lesion-deficit analysis. We measured the numbers of recovered associations from these simulated data, as a function of the number of subjects analyzed, the strengths and number of associations in the statistical model, the number of structures associated with a particular function, and the prior probabilities of structures being abnormal. The number of subjects required to recover the simulated lesion-deficit associations was found to have an inverse relationship to the strength of associations, and to the smallest probability in the structure-function model. The number of structures associated with a particular function (i.e., the complexity of associations) had a much greater effect on the performance of the analysis method than did the total number of associations. We also found that registration error of 5 mm or less reduces the number of associations discovered by approximately 13% compared to perfect registration. The LDS provides a flexible framework for evaluating many aspects of lesion-deficit analysis.

NASA Program Biomedical Research and Countermeasur↗
NASA NTRS2019

Evaluating Precipitation Features and Rainfall Characteristics in a Multi-scale Modeling Framework

Cloud and precipitation systems over the tropics and subtropics are simulated with a multi-scale modeling framework (MMF) and compared against the TRMM radar precipitation features (RPFs) product. A methodology, in close analogy to the TRMM RPFs, is developed to analyze simulated cloud precipitating structures from the embedded two-dimensional cloud-resolving models (CRMs) within an MMF. Despite the two-dimensionality of the CRMs, the simulated RPFs population distribution, and horizontal and vertical structure are in good agreement with TRMM observations. However, some deficits are also found in the model simulations. The model tends to overestimate mean convective precipitation rates for RPFs with a size less than 100 km, contributing to the excessive precipitation biases in the warm pool and western Pacific, western and northern India Ocean, and eastern Pacific commonly found in most MMFs. For large features with a size greater than 150 km, both convective and stratiform rain rates are underestimated. The distribution of maximum radar echo top heights as a function of RPF size is well simulated except the model tends to underestimate the occurrence frequency of maximum heights greater than 15 km. The maximum echo top heights for convective cells embedded within large RPFs with a size greater than 150 km are also underestimated. The cyclic lateral boundary with a limited model domain generates artificial occurrences for RPFs with a size close to the model domain size, producing a significant contribution to the total rainfall due to their sizes. This cyclic lateral boundary effect can be easily identified and quantified in both probability and cumulative distribution functions of RPFs. The geophysical distribution of the population of the largest RPFs in the control experiment shows they are mainly located in the Subtropics but also partially contribute to the common MMF biases of excessive precipitation in the Tropics. Sensitivity experiments using CRMs with different domain sizes and different grid spacings show larger domains (higher resolution) tend to shift the RPFs distribution to large (small) sizes. The cyclic lateral boundary biases increase as CRM domain size decreases. The impacts of model horizontal and vertical resolution on simulated convective systems are also investigated.

Chern, Jiun-Dar↗
DOE OSTI2022

Stable High‐Conductivity Ethylenedioxythiophene Polymers via Borane‐Adduct Doping

Efficient doping of polymer semiconductors is required for high conductivity and efficient thermoelectric performance. Lewis acids, e.g., B(C 6 F 5 ) 3 , have been widely employed as dopants, but the mechanism is not fully understood. 1:1 “Wheland type” or zwitterionic complexes of B(C 6 F 5 ) 3 are created with small conjugated molecules 3,6-bis(5-(7-(5-methylthiophen-2-yl)-2,3-dihydrothieno[3,4-b][1,4]dioxin-5-yl)thiophen-2-yl)-2,5-dioctyl-2,5-dihydropyrrolo[3,4-c]pyrrole-1,4-dione [oligo_DPP(EDOT) 2 ] and 3,6-bis(5''-methyl-[2,2':5',2''-terthiophen]-5-yl)-2,5-dioctyl-2,5-dihydropyrrolo[3,4-c]pyrrole-1,4-dione [oligo_DPP(Th) 2 ]. Using a wide variety of experimental and computational approaches, the doping ability of these Wheland Complexes with B(C 6 F 5 ) 3 are characterized for five novel diketopyrrolopyrrole-ethylenedioxythiophene (DPP-EDOT)-based conjugated polymers. The electrical properties are a strong function of the specific conjugated molecule constituting the adduct, rather than acidic protons generated via hydrolysis of B(C 6 F 5 ) 3 , serving as the oxidant. It is highly probable that certain repeat units/segments form adduct structures in p -type conjugated polymers which act as intermediates for conjugated polymer doping. Electronic and optical properties are consistent with the increase in hole-donating ability of polymers with their cumulative donor strengths. The doped film of polymer (DPP(EDOT) 2 -(EDOT) 2 ) exhibits exceptionally good thermal and air-storage stability. The highest conductivities, ≈300 and ≈200 S cm -1 , are achieved for DPP(EDOT) 2 -(EDOT) 2 doped with B(C 6 F 5 ) 3 and its Wheland complexes.

36 MATERIALS SCIENCE↗
NASA NTRS2019

Effect of Latitude Bias in Entry Angle on Ground Casualty Risk from Naturally Decaying Space Objects

An improvement to the long-term estimation of ground casualties from naturally decaying space objects is the refinement to the distribution of entry angle at the entry interface as a function of latitude. Previous analyses were based on an assumed "small angle," typically -0.1°, and entry interface at the equator. This study expands on work by Bacon and Matney that indicated there is significant latitude bias in the location of reentries, compared to prior assumptions of equal temporal probability. A new model has been developed, which describes the distribution of entry angle as a function of orbital inclination and argument of latitude. This model has been used to generate inputs for ODPO’s certified reentry survivability software, Object Reentry Survival Analysis Tool (ORSAT). These new results are compared with the prior standard model to assess the magnitude of the effects on reentry casualty risk.

Ostrom, Chris L.↗
NASA NTRS2011

Step-by-Step Simulation of Radiation Chemistry Using Green Functions for Diffusion-Influenced Reactions

Radiolytic species are formed approximately 1 ps after the passage of ionizing radiation through matter. After their formation, they diffuse and chemically react with other radiolytic species and neighboring biological molecules, leading to various oxidative damage. Therefore, the simulation of radiation chemistry is of considerable importance to understand how radiolytic species damage biological molecules [1]. The step-by-step simulation of chemical reactions is difficult, because the radiolytic species are distributed non-homogeneously in the medium. Consequently, computational approaches based on Green functions for diffusion-influenced reactions should be used [2]. Recently, Green functions for more complex type of reactions have been published [3-4]. We have developed exact random variate generators of these Green functions [5], which will allow us to use them in radiation chemistry codes. Moreover, simulating chemistry using the Green functions is which is computationally very demanding, because the probabilities of reactions between each pair of particles should be evaluated at each timestep [2]. This kind of problem is well adapted for General Purpose Graphic Processing Units (GPGPU), which can handle a large number of similar calculations simultaneously. These new developments will allow us to include more complex reactions in chemistry codes, and to improve the calculation time. This code should be of importance to link radiation track structure simulations and DNA damage models.

Plante, Ianik↗
DOE OSTI2022

Retrieval of the molecular orientation distribution from atom-pair angular distributions

Imaging laser-induced rotational dynamics is an important and active field due to its applications in capturing reactions in the molecular frame and in molecular imaging. Experimental measurement of the molecular orientation distribution, as a function of the Euler angles, has only been demonstrated for special cases when the detectable signal is generated along the molecular symmetry axis. Here we developed the general theory that maps the probability density distribution of the molecular orientation to the atom-pair angular distributions for nonlinear molecules. With the theory, the molecular orientation distribution can be retrieved from the measured atom-pair angular distribution, which we demonstrate experimentally using ultrafast electron diffractive imaging of impulsively aligned trifluoro-iodomethane molecules. Here, the retrieved molecular orientation distribution is in good agreement with direct numerical simulations of the time-dependent Schrodinger equation using the experimental conditions. Unlike the existing retrieval methods, the retrieval method does not require solving Schrodinger equation, works for any alignment method, and is in principle applicable to asymmetric top molecules.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Correlation energy of the uniform electron gas determined by ground-state conditional probability density functional theory

Conditional-probability density functional theory (CP-DFT) is a formally exact method for finding correlation energies from Kohn-Sham DFT without evaluating an explicit energy functional. We present details on how to generate accurate exchange-correlation energies for the ground-state uniform gas. We also use the exchange hole in a CP antiparallel spin calculation to extract the high-density limit. We give a highly accurate analytic solution to the Thomas-Fermi model for this problem, showing its performance relative to Kohn-Sham and may be useful at high temperatures. We explore several approximations to the CP potential. Furthermore, results are compared to accurate parameterizations for both exchange-correlation energies and holes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Derivation of the Future Time Equation for Analog, Non-Multiplying Monte Carlo Simulation

The expected computational time required to simulate a particle from a point in phase space through a Monte Carlo history, termed the expected future time, is found by solving the Future Time Equation (FTE). The expected future time may be useful when generating variance reduction parameters for a Monte Carlo simulation with a method such as Consistent Adjoint Driven Importance Sampling (CADIS). This report presents a detailed derivation of the Future Time Probability Density Function (FTPDF) and FTE for neutral particle Monte Carlo transport to aid future researchers. For simplicity, this derivation only considers analog transport in non-multiplying media.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1993

PDF approach for turbulent scalar field: Some recent developments

The probability density function (PDF) method has been proven a very useful approach in turbulence research. It has been particularly effective in simulating turbulent reacting flows and in studying some detailed statistical properties generated by a turbulent field There are, however, some important questions that have yet to be answered in PDF studies. Our efforts in the past year have been focused on two areas. First, a simple mixing model suitable for Monte Carlo simulations has been developed based on the mapping closure. Secondly, the mechanism of turbulent transport has been analyzed in order to understand the recently observed abnormal PDF's of turbulent temperature fields generated by linear heat sources.

Gao, Feng↗
NASA NTRS2003

Determination of Rolling-Element Fatigue Life From Computer Generated Bearing Tests

Two types of rolling-element bearings representing radial loaded and thrust loaded bearings were used for this study. Three hundred forty (340) virtual bearing sets totaling 31400 bearings were randomly assembled and tested by Monte Carlo (random) number generation. The Monte Carlo results were compared with endurance data from 51 bearing sets comprising 5321 bearings. A simple algebraic relation was established for the upper and lower L(sub 10) life limits as function of number of bearings failed for any bearing geometry. There is a fifty percent (50 percent) probability that the resultant bearing life will be less than that calculated. The maximum and minimum variation between the bearing resultant life and the calculated life correlate with the 90-percent confidence limits for a Weibull slope of 1.5. The calculated lives for bearings using a load-life exponent p of 4 for ball bearings and 5 for roller bearings correlated with the Monte Carlo generated bearing lives and the bearing data. STLE life factors for bearing steel and processing provide a reasonable accounting for differences between bearing life data and calculated life. Variations in Weibull slope from the Monte Carlo testing and bearing data correlated. There was excellent agreement between percent of individual components failed from Monte Carlo simulation and that predicted.

Vlcek, Brian L.↗
DOE OSTI2025

Refining fast calorimeter simulations with a Schrödinger Bridge

Machine learning-based simulations, especially calorimeter simulations, are promising tools for approximating the precision of classical high energy physics simulations with a fraction of the generation time. Nearly all methods proposed so far learn neural networks that map a random variable with a known probability density, like a Gaussian, to realistic-looking events. In many cases, physics events are not close to Gaussian and so these neural networks have to learn a highly complex function. We study an alternative approach: Schrödinger bridge Quality Improvement via Refinement of Existing Lightweight Simulations (SQuIRELS). SQuIRELS leverages the power of diffusion-based neural networks and Schrödinger bridges to map between samples where the probability density is not known explicitly. We apply SQuIRELS to the task of refining a classical fast simulation to approximate a full classical simulation. On simulated calorimeter events, we find that SQuIRELS is able to reproduce highly non-trivial features of the full simulation with a fraction of the generation time.

Calorimeter methods↗