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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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NASA NTRS1995

Estimation of attitude sensor timetag biases

This paper presents an extended Kalman filter for estimating attitude sensor timing errors. Spacecraft attitude is determined by finding the mean rotation from a set of reference vectors in inertial space to the corresponding observed vectors in the body frame. Any timing errors in the observations can lead to attitude errors if either the spacecraft is rotating or the reference vectors themselves vary with time. The state vector here consists of the attitude quaternion, timetag biases, and, optionally, gyro drift rate biases. The filter models the timetags as random walk processes: their expectation values propagate as constants and white noise contributes to their covariance. Thus, this filter is applicable to cases where the true timing errors are constant or slowly varying. The observability of the state vector is studied first through an examination of the algebraic observability condition and then through several examples with simulated star tracker timing errors. The examples use both simulated and actual flight data from the Extreme Ultraviolet Explorer (EUVE). The flight data come from times when EUVE had a constant rotation rate, while the simulated data feature large angle attitude maneuvers. The tests include cases with timetag errors on one or two sensors, both constant and time-varying, and with and without gyro bias errors. Due to EUVE's sensor geometry, the observability of the state vector is severely limited when the spacecraft rotation rate is constant. In the absence of attitude maneuvers, the state elements are highly correlated, and the state estimate is unreliable. The estimates are particularly sensitive to filter mistuning in this case. The EUVE geometry, though, is a degenerate case having coplanar sensors and rotation vector. Observability is much improved and the filter performs well when the rate is either varying or noncoplanar with the sensors, as during a slew. Even with bad geometry and constant rates, if gyro biases are independently known, the timetag error for a single sensor can be accurately estimated as long as its boresight is not too close to the spacecraft rotation axis.

Sedlak, J.↗

NASA NTRS2023

Does the way we do science foster discovery?

Freedom to explore the unknown is key to scientific discovery. Maximizing modern individualistic measures of scientific productivity like citations and number of publications may impede the progress of science as a whole.

discovery↗

NASA NTRS1983

Stochastic models for atomic clocks

For the atomic clocks used in the National Bureau of Standards Time Scales, an adequate model is the superposition of white FM, random walk FM, and linear frequency drift for times longer than about one minute. The model was tested on several clocks using maximum likelihood techniques for parameter estimation and the residuals were acceptably random. Conventional diagnostics indicate that additional model elements contribute no significant improvement to the model even at the expense of the added model complexity.

Barnes, J. A.↗

DOE OSTI2025

Random Walks With Tweedie: A Unified View of Score-Based Diffusion Models [In the Spotlight]

We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals—particularly natural images—and often play a role in state-of-the-art algorithms for inverse problems in image processing. While these algorithms are often surprisingly simple, the theory behind them is not, and multiple complex theoretical justifications exist in the literature. Here, in this study, we provide a simple and largely self-contained theoretical justification for score-based diffusion models that is targeted towards the signal processing community. This approach leads to generic algorithmic templates for training and generating samples with diffusion models. We show that several influential diffusion models correspond to particular choices within these templates and demonstrate that alternative, more straightforward algorithmic choices can provide comparable results. This approach has the added benefit of enabling conditional sampling without any likelihood approximation.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2012

Using Markov Models of Fault Growth Physics and Environmental Stresses to Optimize Control Actions

A generalized Markov chain representation of fault dynamics is presented for the case that available modeling of fault growth physics and future environmental stresses can be represented by two independent stochastic process models. A contrived but representatively challenging example will be presented and analyzed, in which uncertainty in the modeling of fault growth physics is represented by a uniformly distributed dice throwing process, and a discrete random walk is used to represent uncertain modeling of future exogenous loading demands to be placed on the system. A finite horizon dynamic programming algorithm is used to solve for an optimal control policy over a finite time window for the case that stochastic models representing physics of failure and future environmental stresses are known, and the states of both stochastic processes are observable by implemented control routines. The fundamental limitations of optimization performed in the presence of uncertain modeling information are examined by comparing the outcomes obtained from simulations of an optimizing control policy with the outcomes that would be achievable if all modeling uncertainties were removed from the system.

Bole, Brian↗

NASA NTRS1984

A theoretical and experimental study of turbulent evaporating sprays

Measurements and analysis limited to the dilute portions of turbulent evaporating sprays, injected into a still air environment were completed. Mean and fluctuating velocities and Reynolds stress were measured in the continuous phase. Liquid phase measurements included liquid mass fluxes, drop sizes and drop size and velocity correlation. Initial conditions needed for model evaluation were measured at a location as close to the injector exit as possible. The test sprays showed significant effects of slip and turbulent dispersion of the discrete phase. The measurements were used to evaluate three typical models of these processes: (1) a locally homogeneous flow (LHF) model, where slip between the phases were neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of drop dispersion by turbulence were ignored; and (3) a stochastic separated flow (SSF) model, where effects of interphase slip and turbulent dispersion were considered using random-walk computations for drop motion. For all three models, a k-epsilon model as used to find the properties of the continuous phase. The LHF and DSF models did not provide very satisfactory predictions for the present measurements. In contrast, the SSF model performed reasonably well--with no modifications in the prescription of eddy properties from its original calibration.

Solomon, A. S. P.↗

NASA NTRS1985

Monte Carlo lattice models for adsorbed polymer conformation

The adhesion between a polymer film and a metal surface is of great technological interest. However, the prediction of adhesion and wear properties of polymer coated metals is quite difficult because a fundamental understanding of the polymer surface interaction does not yet exist. A computer model for the conformation of a polymer molecule adsorbed on a surface is discussed. The chain conformation is assumed to be described by a partially directed random walk on a three dimensional simple cubic lattice. An attractive surface potential is incorporated into the model through the use of a random walk step probability distribution that is anisotropic in the direction normal to the attractive surface. The effects of variations in potential characteristics are qualitatively included by varying both the degree of anisotropy of the step distribution and the range of the anisotropy. Polymer conformation is characterized by the average end to end distance, average radius of gyration, and average number of chain segments adsorbed on the surface.

Good, B. S.↗

NASA NTRS1983

The structure of evaporating and combusting sprays: Measurements and predictions

The structure of particle-laden jets and nonevaporating and evaporating sprays was measured in order to evaluate models of these processes. Three models are being evaluated: (1) a locally homogeneous flow model, where slip between the phases is neglected and the flow is assumed to be in local thermodynamic equilibrium; (2) a deterministic separated flow model, where slip and finite interphase transport rates are considered but effects of particle/drop dispersion by turbulence and effects of turbulence on interphase transport rates are ignored; and (3) a stochastic separated flow model, where effects of interphase slip, turbulent dispersion and turbulent fluctuations are considered using random sampling for turbulence properties in conjunction with random-walk computations for particle motion. All three models use a k-e-g turbulence model. All testing and data reduction are completed for the particle laden jets. Mean and fluctuating velocities of the continuous phase and mean mixture fraction were measured in the evaporating sprays.

Shuen, J. S.↗

NASA NTRS1983

The structure of particle-laden jets and nonevaporating sprays

Mean and fluctuating gas velocities, liquid mass fluxes and drop sizes were in nonevaporating sprays. These results, as well as existing measurements in solid particle-laden jets, were used to evaluate models of these processes. The following models were considered: (1) a locally homogeneous flow (LHF) model, where slip between the phases was neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of particle dispersion by turbulence were ignored; and (3) a stochastic separated flow (SSF) model, where effects of interphase slip and turbulent dispersion were considered using random-walk computations for particle motion. The LHF and DSF models did not provide very satisfactory predictions over the present data base. In contrast, the SSF model performed reasonably well - including conditions in nonevaporating sprays where enhanced dispersion of particles by turbulence caused the spray to spread more rapidly than single-phase jets for comparable conditions. While these results are encouraging, uncertainties in initial conditions limit the reliability of the evaluation. Current work is seeking to eliminate this deficiency.

Shuen, J. S.↗

NASA NTRS1984

A theoretical and experimental study of turbulent nonevaporating sprays

Measurements and analysis limited to the dilute portions of turbulent nonevaporating sprays injected into a still air environment were completed. Mean and fluctuating velocities and Reynolds stress were measured in the continuous phase. Liquid phase measurements included liquid mass fluxes, drop sizes and drop size and velocity correlation. Initial conditions needed for model evaluation were measured at a location as close to the injector exit as possible. The test sprays showed significant effects of slip and turbulent dispersion of the discrete phase. The measurements were used to evaluate three typical models of these processes: (1) a locally homogenous flow (LHF) model, where slip between the phases were neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of drop dispersion by turbulence were ignored; and (3) a stochastic separated flow (SSF) model, where effects of interphase slip and turbulent dispersion were considered using random-walk computations for drop motion. The LHF and DSF models did not provide very satisfactory predictions for the present measurements. In contrast, the SSF model performed reasonably well with no modifications in the prescription of eddy properties from its original calibration. Some effects of drops on turbulence properties were observed near the dense regions of the sprays.

Solomon, A. S. P.↗

NASA NTRS2009

A Monte-Carlo Model for the Formation of Radiation-induced Chromosomal Aberrations

Purpose: To simulate radiation-induced chromosome aberrations in mammalian cells (e.g., rings, translocations, and dicentrics) and to calculate their frequency distributions following exposure to DNA double strand breaks (DSBs) produced by high-LET ions. Methods: The interphase genome was assumed to be comprised of a collection of 2 kbp rigid-block monomers following the random-walk geometry. Additional details for the modeling of chromosomal structure, such as chromosomal domains and chromosomal loops, were included. A radial energy profile for heavy ion tracks was used to simulate the high-LET pattern of induced DSBs. The induced DSB pattern depended on the ion charge and kinetic energy, but always corresponded to the DSB yield of 25 DSBs/cell/Gy. The sum of all energy contributions from Poisson-distributed particle tracks was taken to account for all possible one-track and multi-track effects. The relevant output of the model was DNA fragments produced by DSBs. The DSBs, or breakpoints, were defined by (x, y, z, l) positions, where x, y, z were the Euclidian coordinates of a DSB, and where l was the relative position along the genome. Results: The code was used to carry out Monte Carlo simulations for DSB rejoinings at low doses. The resulting fragments were analyzed to estimate the frequencies of specific types of chromosomal aberrations. Histograms for relative frequencies of chromosomal aberrations and P.D.F.s (probability density functions) of a given aberration type were produced. The relative frequency of dicentrics to rings was compared to empirical data to calibrate rejoining probabilities. Of particular interest was the predicted distribution of ring sizes, irrespective of their frequencies relative to other aberrations. Simulated ring sizes were . 4 kbp, which are far too small to be observed experimentally (i.e., by microscopy) but which, nevertheless, are conjectured to exist. Other aberrations, for example, inversions, translocations, as well as multi-centrics were also recorded. Conclusion: High-LET DNA damage affects the frequencies of chromosomal aberrations. The ratio of rings to dicentrics is correct for the genomic size cut-offs corresponding to available experimental data. The present work predicts a relative abundance of small rings following irradiation by heavy ions.

Ponomarev, Artem L.↗

NASA NTRS1990

Stochastic estimation of tropospheric path delays in global positioning system geodetic measurements

Water vapor radiometric and surface meteorological measurements taken during three GPS geodetic experiments are used to calculate process noise levels for random walk and first-order Gauss-Markov temporal models of tropospheric path delays. Entire wet and combined wet and dry zenith delays at each network site are estimated simultaneously with the geodetic parameters without prior calibration. The path delays and corresponding baseline estimates are compared to those obtained with calibrated data and stochastic residual delays. In this manner, the marginal utility of a priori tropospheric calibration is assessed given the ability to estimate the path delays directly using only the GPS data. Estimation of total zenith path delays with appropriate random walk or Gauss-Markov models yields baseline repeatabilities of a few parts in 100 million. Results suggest that GPS data alone have sufficient strength to resolve centimeter-level zenith path delay fluctuations over periods of a few minutes.

Tralli, David M.↗

NASA NTRS1990

A chaotic attractor in timing noise from the Vela pulsar?

Fourteen years of timing residual data from the Vela pulsar have been analyzed in order to determine if a chaotic dynamical process is the origin of timing noise. Using the correlation sum technique, a dimension of about 1.5 is obtained. This low dimension indicates underlying structure in the phase residuals which may be evidence for a chaotic attractor. It is therefore possible that nonlinear dynamics intrinsic to the spin-down may be the cause of the timing noise in the Vela pulsar. However, it has been found that the stimulated random walks in frequency and frequency derivative often used to model pulsar timing noise also have low fractal dimension, using the same analysis technique. Recent work suggesting that random processes with steep power spectra can mimic strange attractors seems to be confirmed in the case of these random walks. It appears that the correlation sum estimator for dimension is unable to distinguish between chaotic and random processes.

Harding, Alice K.↗

DOE OSTI2024

A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE↗

NASA NTRS1999

Dynamical Signatures of Living Systems

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Zak, M.↗

NASA NTRS1992

Monitoring global geodynamical parameter variations with GPS and low earth satellites

A low earth satellite enhances global geodynamical parameters determination with GPS in two ways. First, it improves the GPS orbits, which in turn improve the estimates of other parameters. Secondly, a low earth satellite completes an orbit cycle in far shorter time (90 to 120 minutes) than do GPS satellites (12 hours); it observes more GPS satellites than a ground receiver does in shorter time and increases the correlation between GPS orbit errors. This reduces the error in the determination of nonrotational coordinate parameters, i.e., geocentric offset of ground tracking sites. Covariance results with the global geodynamical parameters modeled as constants, and as random-walk parameters to closer reflect the actual variations, are compared. The effects of using different GPS data quality and different ground tracking network are studied. The case of using two earth satellites in orthogonal orbital planes is also investigated.

Wu, S. C.↗

NASA NTRS1993

Generalized Levy-walk model for DNA nucleotide sequences

We propose a generalized Levy walk to model fractal landscapes observed in noncoding DNA sequences. We find that this model provides a very close approximation to the empirical data and explains a number of statistical properties of genomic DNA sequences such as the distribution of strand-biased regions (those with an excess of one type of nucleotide) as well as local changes in the slope of the correlation exponent alpha. The generalized Levy-walk model simultaneously accounts for the long-range correlations in noncoding DNA sequences and for the apparently paradoxical finding of long subregions of biased random walks (length lj) within these correlated sequences. In the generalized Levy-walk model, the lj are chosen from a power-law distribution P(lj) varies as lj(-mu). The correlation exponent alpha is related to mu through alpha = 2-mu/2 if 2 < mu < 3. The model is consistent with the finding of "repetitive elements" of variable length interspersed within noncoding DNA.

NASA Discipline Number 14-10↗

NASA NTRS1985

Structure of ducted particle-laden turbulent jets

New and existing measurements have been used to develop and evaluate models of particle-laden jets and sprays, yielding encouraging results for a stochastic separated flow (SSF) model which treats effects of interphase slip and turbulence on the basis of random walk computations of particle or drop motion. An evaluation of the SSF model using the measurements of Modarress et al. (1982, 1983) yielded results comparable to earlier work, suggesting that data from coflowing jets in ducts should be accompanied by static pressure measurements, since even small pressure gradients appreciably influence jet properties.

Zhang, Q.-F.↗