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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Free vibrations of delaminated beams

Free vibration of laminated composite beams is studied. The effect of interply delaminations on natural frequencies and mode shapes is evaluated both analytically and experimentally. The equation of motion and associated boundary conditions are derived for the free vibration of a composite beam with a delamination of arbitrary size and location. A generalized variational principle is used to formulate the equation of motion, taking into account the interlaminar stress concentration at the crack-tips. This is accomplished by introducing a 'crack function' into the beam's compatibility relations. This function has its maximum value at the crack tip and decays exponentially in the longitudinal direction. The rate of exponential decay is determined by a least-square fit with the experimental results. The effect of coupling between longitudinal vibration and bending vibration is considered in the present study. This coupling effect is found to significantly affect the natural frequencies and mode shapes of the delaminated beam.

Shen, M.-H. H.↗
NASA NTRS1996

Dynamic Light Scattering From Colloidal Gels

We present a brief, preliminary account of the interpretation of dynamic light scattering from fractal colloidal gels. For small scattering angles, and for high initial colloid particle volume fractions, the correlation functions exhibit arrested decay, reflecting the non-ergodic nature of these systems and allowing us to directly determine the elastic modulus of the gels. For smaller initial volume fractions, the correlation functions decay completely. In all cases, the initial decay is not exponential, but is instead described by a stretched exponential. We summarize the principles of a model that accounts for these data and discuss the scaling behavior of the measured parameters.

Krall, A. H.↗
NASA NTRS2013

Hubble Space Telescope Hx Imaging of Star-forming Galaxies at z approximately equal to 1-1.5: Evolution in the Size and Luminosity of Giant H II Regions

We present Hubble Space Telescope/Wide Field Camera 3 narrow-band imaging of the Hα emission in a sample of eight gravitationally lensed galaxies at z = 1-1.5. The magnification caused by the foreground clusters enables us to obtain a median source plane spatial resolution of 360 pc, as well as providing magnifications in flux ranging from approximately 10× to approximately 50×. This enables us to identify resolved star-forming HII regions at this epoch and therefore study their Hα luminosity distributions for comparisons with equivalent samples at z approximately 2 and in the local Universe. We find evolution in the both luminosity and surface brightness of HII regions with redshift. The distribution of clump properties can be quantified with an HII region luminosity function, which can be fit by a power law with an exponential break at some cut-off, and we find that the cut-off evolves with redshift. We therefore conclude that 'clumpy' galaxies are seen at high redshift because of the evolution of the cut-off mass; the galaxies themselves follow similar scaling relations to those at z = 0, but their HII regions are larger and brighter and thus appear as clumps which dominate the morphology of the galaxy. A simple theoretical argument based on gas collapsing on scales of the Jeans mass in a marginally unstable disc shows that the clumpy morphologies of high-z galaxies are driven by the competing effects of higher gas fractions causing perturbations on larger scales, partially compensated by higher epicyclic frequencies which stabilize the disc.

H imaging↗
NASA NTRS2017

Autonomous Task Management and Decision Support Tools

For some time aircraft manufacturers and researchers have been pursuing mechanisms for reducing crew workload and providing better decision support to the pilots, especially during non-normal situations. Some previous attempts to develop task managers or pilot decision support tools have not resulted in robust and fully functional systems. However, the increasing sophistication of sensors and automated reasoners, and the exponential surge in the amount of digital data that is now available create a ripe environment for the development of a robust, dynamic, task manager and decision support tool that is context sensitive and integrates information from a wide array of on-board and off aircraft sourcesa tool that monitors systems and the overall flight situation, anticipates information needs, prioritizes tasks appropriately, keeps pilots well informed, and is nimble and able to adapt to changing circumstances. This presentation will discuss the many significant challenges and issues associated with the development and functionality of such a system for use on the aircraft flight deck.

decision support↗
DOE OSTI2025

Simplifying activations with linear approximations in neural networks

A key step in Neural Networks is activation. Among the different types of activation functions, sigmoid, tanh, and others involve the usage of exponents for calculation. From a hardware perspective, exponential implementation implies the usage of Taylor series or repeated methods involving many addition, multiplication, and division steps, and as a result are power-hungry and consume many clock cycles. We implement a piecewise linear approximation of the sigmoid function as a replacement for standard sigmoid activation libraries. This approach provides a practical alternative by leveraging piecewise segmentation, which simplifies hardware implementation and improves computational efficiency. In this paper, we detail piecewise functions that can be implemented using linear approximations and their implications for overall model accuracy and performance gain. Our results show that for the DenseNet, ResNet, and GoogLeNet architectures, the piecewise linear approximation of the sigmoid function provides faster execution times compared to the standard TensorFlow sigmoid implementation while maintaining comparable accuracy. Specifically, for MNIST with DenseNet, accuracy reaches 99.91% (Piecewise) vs. 99.97% (Base) with up to 1.31x speedup in execution time. For CIFAR-10 with DenseNet, accuracy improves to 98.97% (Piecewise) vs. 99.40% (Base) while achieving 1.24x faster execution. Similarly, for CIFAR-100 with DenseNet, the accuracy is 97.93% (Piecewise) vs. 98.39% (Base), with a 1.18x execution time reduction. These results confirm the proposed method’s capability to efficiently process large-scale datasets and computationally demanding tasks, offering a practical means to accelerate deep learning models, including LSTMs, without compromising accuracy.

Activation function↗
NASA NTRS1981

Observations of the ionization states of energetic particles accelerated in solar flares

Results of a survey of ten solar flare particle events, in which the ionization states and spectra of 0.3 to 2.4 MeV/nuc He, C, O and Fe were measured, are reported. He+ was present in all events (He+/He++ approximately 0.1 to 0.25), and the mean ionization states of C, O and Fe are high. The distribution functions of He+, He++ and heavier elements are well represented by simple exponentials of the particle speed times its rigidity to a power n, where n is between O and 1, and equal e-folding values. Results are consistent with a model whereby ions are accelerated in the corona by multi-dimensional shocks out of a population taken from both hot and cold coronal regions.

Gloeckler, G.↗
NASA NTRS1980

Distribution function representation of energy spectra of H, He, C, O and Fe in corotating particle streams

From an analysis of nine corotating events observed near 1 AU during the 1974-1976 solar minimum, the spectral parameters for H, He, C, O and Fe and relative abundances of these elements and of Ne, Mg, Si, and S-Ca were determined. The distribution functions of H, He, O and Fe are well represented by an exponential in particle speed over the energy range of the measurements from 0.3 to 5 MeV/nucleon. The composition resembles that of the solar corona, particularly in the O/C ratio which is 0.95 + or - 0.19, and the He/H and He/Ne ratios are similar to the respective ratios in the solar wind. The results are consistent with interplanetary statistical acceleration of these particles out of the high-energy tail of the high-speed solar wind.

Gloeckler, G.↗
NASA NTRS1981

On the acceleration of thermal coronal ions by flare induced shock waves

The energy spectra of solar flare ions are calculated by assuming that the process which accelerates solar wind ions to MeV/ nucleon energies in the interplanetary corotating interaction region (CIR) also occurs in flare induced magnetosonic fast-mode (MFM) shocks in the corona. Solar wind ions are considered to be accelerated to MeV/nucleon energies by wave-particle interactions in the shock front and the downstream flow, being compressed between upstream and downstream magnetic field irregularities, and then accelerated by the shock drift acceleration mechanism. The energy spectra of the accelerated ions is calculated from the number of shock encounters as a function of the post- and preacceleration energies. A best fit by an exponential in momentum is determined for ions in the 50 MeV to a few GeV range, and from 20-80 MeV by a suitable power law in kinetic energy with a mean spectral index. Comparisons with observed solar protons show good agreement.

Decker, R. B.↗
NASA NTRS1984

A model of the radiative properties of the El Chichon stratospheric aerosol layer

An accurate multiple-scattering model has been employed to examine the effect of an aerosol layer at 25 mb, corresponding to the El Chichon observations, on the reflection, transmission and absorption of radiation by the stratosphere as a function of latitude, optical thickness and aerosol size distribution. Results are presented and parameterized for each of two wavelength intervals in the shortwave region and 17 wavelength intervals in the longwave region for three models of the aerosol size distribution. They include one model representing the unperturbed stratospheric aerosol plus two models based on measurements of the El Chichon aerosol size distribution. In addition to models of the radiative properties of the aerosol layer, a simple model of the latitudinal distribution of aerosol optical thickness as a function of time is developed, based on diffusive transport in latitude and exponential decay in time. These parameterizations for solar and infrared radiation, together with the dispersion model, permit climate models to account for the evolution of an aerosol size distribution from post-volcanic conditions to background conditions.

King, M. D.↗
NASA NTRS1989

Analytic solution for vertical launch into orbit

An approximate analytic solution is presented for the motion and heating of nonlifting spacecraft launched vertically for ascending flight through the atmosphere into earth orbit. The solution is based on Chapman's Z-function transformation of the equations of motion with the assumption of an exponential atmosphere. The transformed equations have been modified to include the effects of thrusting with mass loss. It is assumed that the vehicle negotiates a gravity turn during ascent so that the thrust vector is aligned in the flight-path direction. Numerical results are presented to document the analytic solution and provide evidence of the useful information generated by it.

Boltz, Frederick W.↗
NASA NTRS2006

Skeletal Recovery Following Long-Duration Spaceflight Missions as Determined by Preflight and Postflight DXA Scans of 45 Crew Members

Introduction: The loss of bone mineral in astronauts during spaceflight has been investigated throughout the more than 40 years of bone research in space. Consequently, it is a medical requirement at NASA that changes in bone mass be monitored in crew members by measurements of bone mineral density (BMD) with dual-energy x-ray absorptiometry (DXA). This report is the first to evaluate medical data to address the recovery of bone mineral that is lost during spaceflight. Methods: DXA scans are performed before and after flight in astronauts who serve on long-duration missions (4-6 months) to ensure that medical standards for flight certification are met, to evaluate the effects of spaceflight and to monitor the restoration to preflight BMD status after return to Earth. Through cooperative agreements with the Russian Space Agency, the Bone and Mineral Lab at NASA Johnson Space Center (Houston, TX), also had access to BMD data from cosmonauts who had flown on long-duration missions yielding data from a total of 45 individual crew members. Changes in BMD (between 56 different sets of pre- and postflight measurements) were plotted as a function of time (days after landing); plotted data were fitted to an exponential mathematical model that determined i) BMD change at day 0 after landing and ii) the number of days after which 50% of the lost bone was recovered ("Recovery Half-Life"). These fits were performed for BMD of the lumbar spine, trochanter, pelvis, femoral neck and calcaneus. Results: In sum, averaged losses of bone mineral after spaceflight ranged between 2-9% for sites in the axial and appendicular skeleton. The fitted postflight BMD values predicted a 50% recovery of bone loss for all sites within 9 months.

Sibonga, J. D.↗
NASA NTRS2011

Shuttle Risk Progression: Use of the Shuttle Probabilistic Risk Assessment (PRA) to Show Reliability Growth

It is important to the Space Shuttle Program (SSP), as well as future manned spaceflight programs, to understand the early mission risk and progression of risk as the program gains insights into the integrated vehicle through flight. The risk progression is important to the SSP as part of the documentation of lessons learned. The risk progression is important to future programs to understand reliability growth and the first flight risk. This analysis uses the knowledge gained from 30 years of operational flights and the current Shuttle PRA to calculate the risk of Loss of Crew and Vehicle (LOCV) at significant milestones beginning with the first flight. Key flights were evaluated based upon historical events and significant re-designs. The results indicated that the Shuttle risk tends to follow a step function as opposed to following a traditional reliability growth pattern where risk exponentially improves with each flight. In addition, it shows that risk can increase due to trading safety margin for increased performance or due to external events. Due to the risk drivers not being addressed, the risk did not improve appreciably during the first 25 flights. It was only after significant events occurred such as Challenger and Columbia, where the risk drivers were apparent, that risk was significantly improved. In addition, this paper will show that the SSP has reduced the risk of LOCV by almost an order of magnitude. It is easy to look back afte r 30 years and point to risks that are now obvious, however; the key is to use this knowledge to benefit other programs which are in their infancy stages. One lesson learned from the SSP is understanding risk drivers are essential in order to considerably reduce risk. This will enable the new program to focus time and resources on identifying and reducing the significant risks. A comprehensive PRA, similar to that of the Shuttle PRA, is an effective tool quantifying risk drivers if support from all of the stakeholders is given.

Hamlin, Teri L.↗
DOE OSTI2025

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↗
DOE OSTI2025

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [Zhang et al., Enabling long-range exploration in minimization of multimodal functions, UAI 2021], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by deterministic oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. Here, we also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justifying the advantage of using moderate or large smoothing radii with the method. Furthermore, if the noise level decays to zero when approaching the global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based methods in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

Tran, Hoang [Oak Ridge National Laboratory (ORNL),↗
NASA NTRS2006

What Happens to bone health during and after spaceflight?

Weightless conditions of space flight accelerate bone loss. There are no reports to date that address whether the bone that is lost during spaceflight could ever be recovered. Spaceinduced bone loss in astronauts is evaluated at the Johnson Space Center (JSC) by measurement of bone mineral density (BMD) by Dual-energy x-ray absorptiometry (DXA) scans. Astronauts are routinely scanned preflight and at various time points postflight (greater than or equal to Return+2 days). Two sets of BMD data were used to model spaceflight-induced loss and skeletal recovery in crewmembers following long-duration spaceflight missions (4-6 months). Group I was from astronauts (n=7) who were systematically scanned at multiple time points during the postflight period as part of a research protocol to investigate skeletal recovery. Group II came from a total of 49 sets of preflight and postflight data obtained by different protocols. These data were from 39 different crewmembers some of whom served on multiple flights. Changes in BMD (between pre- and postflight BMD) were plotted as a function of time (days-after-landing); plotted data were fitted to an exponential equation which enabled estimations of i) BMD change at day 0 after landing and ii) the number of days by which 50% of the lost bone is recovered (half-life). These fits were performed for BMD of the lumbar spine, trochanter, pelvis, femoral neck and calcaneus. There was consistency between the models for BMD recovery. Based upon the exponential model of BMD restoration, recovery following long-duration missions appears to be substantially complete in crewmembers within 36 months following return to Earth.

Sibonga, Jean D.↗
NASA NTRS2008

Damage Propagation Modeling for Aircraft Engine Prognostics

This paper describes how damage propagation can be modeled within the modules of aircraft gas turbine engines. To that end, response surfaces of all sensors are generated via a thermo-dynamical simulation model for the engine as a function of variations of flow and efficiency of the modules of interest. An exponential rate of change for flow and efficiency loss was imposed for each data set, starting at a randomly chosen initial deterioration set point. The rate of change of the flow and efficiency denotes an otherwise unspecified fault with increasingly worsening effect. The rates of change of the faults were constrained to an upper threshold but were otherwise chosen randomly. Damage propagation was allowed to continue until a failure criterion was reached. A health index was defined as the minimum of several superimposed operational margins at any given time instant and the failure criterion is reached when health index reaches zero. Output of the model was the time series (cycles) of sensed measurements typically available from aircraft gas turbine engines. The data generated were used as challenge data for the Prognostics and Health Management (PHM) data competition at PHM 08.

Saxena, Abhinav↗
NASA NTRS2011

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.

Solakiewicz, Richard↗