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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 NTRS1976

Nonclassical acoustics

A statistical approach to sound propagation is considered in situations where, due to the presence of large gradients of properties of the medium, the classical (deterministic) treatment of wave motion is inadequate. Mathematical methods for wave motions not restricted to small wavelengths (analogous to known methods of quantum mechanics) are used to formulate a wave theory of sound in nonuniform flows. Nonlinear transport equations for field probabilities are derived for the limiting case of noninteracting sound waves and it is postulated that such transport equations, appropriately generalized, may be used to predict the statistical behavior of sound in arbitrary flows.

Kentzer, C. P.↗

NASA NTRS1991

Programs For Modeling Fault-Tolerant Computing Systems

Pade Approximation with Scaling, (PAWS) and Scaling Taylor Exponential Matrix (STEM) computer programs are software tools for design and validation. Provide flexible, user-friendly, language-based interface for input of Markov mathematical methods describing behaviors of fault-tolerant computer systems. Markov models include both recovery from faults via reconfiguration and behaviors of such systems when faults occur. PAWS and STEM produce exact solutions of probability of system failure and provide conservative estimate of number of significant digits in solution. Written in PASCAL and FORTRAN.

Butler, Ricky W.↗

NASA NTRS1994

Estimating Lives Of Space Shuttle Parts

SSPOC (Space Shuttle Probabilistic Optimization Code) computer program, implements probabilistic mathematical model, accepts defined distributions of parameters controlling life of Space Shuttle main engine. Used to perform tradeoff studies to optimize between service life and acceptable level of risk, with greater accuracy. Also includes probability of removal and failure of parts, along with number of surviving parts for each interval of inspections. Written in FORTRAN 77, and user interface written in PASCAL(R).

Watkins, Tommie, Jr.↗

NASA NTRS2006

Distributed Constrained Optimization with Semicoordinate Transformations

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of "semicoordinate" variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for &sat constraint satisfaction problems and for unconstrained minimization of NK functions.

Macready, William↗

NASA NTRS2018

Investigation of Transient Gas Phase Column Density Due to Droplet Evaporation

Analytical expressions are developed for estimating column density near a rapidly evaporating droplet along general paths. The influence for instantaneous evaporation is created first as a limiting case, where the peak value occurs at the time it takes a wave of vapor to reach the closest point along the optical path traveling at its most probable thermal speed. Next the case for finite-period evaporation is evaluated for constant conditions. Compared to the instantaneous case, peak column density occurs shortly after droplet extinction at a lower intensity. A new mathematical function is discovered that solves the integrals associated with this case. Finally, ways to account for droplet motion and changes in evaporation rate with size and temperature are discussed.

transient↗

NASA NTRS2018

Investigation of Transient Gas Phase Column Density Due to Droplet Evaporation

Column Density↗

DOE OSTI2024

Asymptotic consistency of the WSINDy algorithm in the limit of continuum data

In this work we study the asymptotic consistency of the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) in the identification of differential equations from noisy samples of solutions. We prove that the WSINDy estimator is unconditionally asymptotically consistent for a wide class of models that includes the Navier–Stokes, Kuramoto–Sivashinsky and Sine–Gordon equations. We thus provide a mathematically rigorous explanation for the observed robustness to noise of weak-form equation learning. Conversely, we also show that, in general, the WSINDy estimator is only conditionally asymptotically consistent, yielding discovery of spurious terms with probability one if the noise level exceeds a critical threshold σ c . We provide explicit bounds on σ c in the case of Gaussian white noise and we explicitly characterize the spurious terms that arise in the case of trigonometric and/or polynomial libraries. Furthermore, we show that, if the data is suitably denoised (a simple moving average filter is sufficient), then asymptotic consistency is recovered for models with locally-Lipschitz, polynomial-growth nonlinearities. Our results reveal important aspects of weak-form equation learning, which may be used to improve future algorithms. We demonstrate our findings numerically using the Lorenz system, the cubic oscillator, a viscous Burgers-growth model and a Kuramoto–Sivashinsky-type high-order PDE.

asymptotic consistency↗

NASA NTRS1987

Probabilistic risk analysis of flying the space shuttle with and without fuel turbine discharge temperature redline protection

An exact mathematical model is presented of the Space Shuttle Main Engine computer voting logic in the presence of High Pressure Fuel Turbine (HPFT) overtemperature events and fuel turbine temperature sensor failures. The model provides estimates of the probability of erroneous engine shutdown and the probability of not detecting a HPFT overtemperature event. Because it is believed that the likelihood of sensor failures and overtemperature events in the HPFT greatly overshadows those in the High Pressure Oxygen Turbine (HPOT), this modeling effort focused on the HPFT. However, because the redline protection logic is the same for both turbines, estimation of the model parameters using relevant HPOT data would provide estimates of the risk of erroneous engine shutdown and an undetected overtemperature event in the HPOT. Because of the complexity of the model, it was necessary to program the solution which thus makes it feasible to accommodate a changing data base. This is considered to be of great interest because of the subjective nature in determining the relevancy of certain failures and the fact that the data base is constantly changing as a result of the frequent engine tests.

Howell, Leonard↗

NASA NTRS2019

Investigation of Transient Gas Phase Column Density Due to Droplet Evaporation

A NASA robotic refueling mission experiment on board the International Space Station (ISS) was designed to repeatedly transfer simulated cryogenic propellant between two dewars. After each metered transfer, the cryogen was to be vented overboard via sublimation or evaporation. ISS payload providers must conduct analyses to demonstrate that any planned gaseous venting generate no more than a certain level of material that may interfere with optical measurements from other payloads that may be located nearby. This requirement is expressed in terms of a maximum column number density (CND). For the experiment under consideration, fluid droplets likely would accompany any such vapor. Earlier related studies led to development of analytical expressions for column density along general paths for a number of practical cases under steady conditions, including droplet evaporation. These expressions are not appropriate for rapid evaporation of small droplets however, since the droplets cannot sustain mass flow rates consistent with steady conditions. In this work, analytical expressions are developed for estimating column density near a rapidly evaporating droplet along general paths. The influence for instantaneous evaporation is created first as a limiting case, where it is found the peak value occurs at the time it takes a wave of vapor to reach the closest point along the optical path traveling at its most probable thermal speed. Next, the case for finite-period evaporation is evaluated for constant conditions. Compared to the instantaneous case, peak column density occurs shortly after droplet extinction, but at a lower intensity. A new mathematical function is discovered that solves the integrals associated with this case. Finally, ways to account for droplet motion and changes in evaporation rate with size and temperature are discussed in this framework.

Woronowicz, M. S.↗

NASA NTRS1982

A model of human decision making in multiple process monitoring situations

Human decision making in multiple process monitoring situations is considered. It is proposed that human decision making in many multiple process monitoring situations can be modeled in terms of the human's detection of process related events and his allocation of attention among processes once he feels event have occurred. A mathematical model of human event detection and attention allocation performance in multiple process monitoring situations is developed. An assumption made in developing the model is that, in attempting to detect events, the human generates estimates of the probabilities that events have occurred. An elementary pattern recognition technique, discriminant analysis, is used to model the human's generation of these probability estimates. The performance of the model is compared to that of four subjects in a multiple process monitoring situation requiring allocation of attention among processes.

Greenstein, J. S.↗

NASA NTRS1993

Analyzing Impacts Of Meteoroids And Debris On Spacecraft

BUMPERII is modular computer program implementing numerical solution technique to calculate probability of no penetration (PNP) of spacecraft by orbiting artificial debris or impacts of meteoroids. Equation used to calculate PNP based on Poisson-distribution model applicable to similar analysis of smaller craft, but reflects more rigorous mathematical modeling of size, shape, orientation, and other characteristics of spacecraft that affect impacts, and necessary for PNP analysis of such larger structures as components of space station. Written in FORTRAN 77.

Bjorkman, Mike↗

NASA NTRS2002

Detection of Rotational Sequences for Global Oscillation Modes inside the Sun

A very simple mathematical sequence is detected in a half century of thermal radio flux from the Sun. Since the only known physical cause of the sequence is global oscillations trapped in the nonconvecting solar interior, g-modes and probably r-modes are active. If so, their rotation frequencies are detected and some previously reported difference frequencies are confirmed with high confidence. All angular harmonics for 2 less than or = l less than or = 7 are detected as well as some others up to the limit l less than or = 14 resolvable by the observations (a Fourier spectrum of the 10.7 cm flux time series). The mean sidereal rotation of the nonconvecting interior is 428.2 nHz as averaged by g-modes and 429.8 nHz by the r-modes, indicating that g-mode energy is a bit more centrally concentrated. Helioseismology measures such rotation rates near 0.36R (R = solar radius), so the global modes would have about half their kinetic energy above and below that level. This, and the known log(r) energy dependence of most modes implies that these oscillations are significantly reflected near 0.18R, the same level at which sound speed measurements display a maximum departure from theoretical models.

Wolff, Charles L.↗

NASA NTRS1960

Solution of Nonlinear Systems

The problem of solving systems of nonlinear equations has been relatively neglected in the mathematical literature, especially in the textbooks, in comparison to the corresponding linear problem. Moreover, treatments that have an appearance of generality fail to discuss the nature of the solutions and the possible pitfalls of the methods suggested. Probably it is unrealistic to expect that a unified and comprehensive treatment of the subject will evolve, owing to the great variety of situations possible, especially in the applied field where some requirement of human or mechanical efficiency is always present. Therefore we attempt here simply to pose the problem and to describe and partially appraise the methods of solution currently in favor.

Turner, L. R.↗

NASA NTRS1991

Interaction between photons and leaf canopies

The physics of neutral particle interaction for photons traveling in media consisting of finite-dimensional scattering centers that cross-shade mutually is investigated. A leaf canopy is a typical example of such media. The leaf canopy is idealized as a binary medium consisting of randomly distributed gaps (voids) and regions with phytoelements (turbid phytomedium). In this approach, the leaf canopy is represented by a combination of all possible open oriented spheres. The mathematical approach for characterizing the structure of the host medium is considered. The extinction coefficient at any phase-space location in a leaf canopy is the product of the extinction coefficient in the turbid phytomedium and the probability of absence gaps at that location. Using a similar approach, an expression for the differential scattering coefficient is derived.

Knyazikhin, Yuri V.↗

NASA NTRS2004

Complexity of life via collective mind

e mind is introduced as a set of simple intelligent units (say, neurons, or interacting agents), which can communicate by exchange of information without explicit global control. Incomplete information is compensated by a sequence of random guesses symmetrically distributed around expectations with prescribed variances. Both the expectations and variances are the invariants characterizing the whole class of agents. These invariants are stored as parameters of the collective mind, while they contribute into dynamical formalism of the agents' evolution, and in particular, into the reflective chains of their nested abstract images of the selves and non-selves. The proposed model consists of the system of stochastic differential equations in the Langevin form representing the motor dynamics, and the corresponding Fokker-Planck equation representing the mental dynamics (Motor dynamics describes the motion in physical space, while mental dynamics simulates the evolution of initial errors in terms of the probability density). The main departure of this model from Newtonian and statistical physics is due to a feedback from the mental to the motor dynamics which makes the Fokker-Planck equation nonlinear. Interpretation of this model from mathematical and physical viewpoints, as well as possible interpretation from biological, psychological, and social viewpoints are discussed. The model is illustrated by the dynamics of a dialog.

collective intelligence↗

NASA NTRS1991

Hidden-Markov-Model Analysis Of Telemanipulator Data

Mathematical model and procedure based on hidden-Markov-model concept undergoing development for use in analysis and prediction of outputs of force and torque sensors of telerobotic manipulators. In model, overall task broken down into subgoals, and transition probabilities encode ease with which operator completes each subgoal. Process portion of model encodes task-sequence/subgoal structure, and probability-density functions for forces and torques associated with each state of manipulation encode sensor signals that one expects to observe at subgoal. Parameters of model constructed from engineering knowledge of task.

Hannaford, Blake↗

NASA NTRS1991

Large scale lunar horizon glow and a high altitude lunar dust exosphere

All three Apollo 17 astronauts sketched a `lunar horizon glow', seen from orbit above the moon. It is shown that the shape of the glow is compatible with scattering of sunlight off of gas or dust at high altitudes above the moon. The present mathematical modeling best simulates the glow with submicron dust grains whose spatial density varies with altitude above the moon as exp(-H/H(s)), where H(s) is in the range of 5 to 20 km. These dust grains are probably electrically charged and ejected above the lunar surface by local electric fields.

Zook, Herbert A.↗

NASA NTRS1998

MAPS of Cancer

Our goal was to produce an interactive visualization from a mathematical model that successfully predicts metastases from head and neck cancer. We met this goal early in the project. The visualization is available for the public to view. Our work appears to fill a need for more information about this deadly disease. The idea of this project was to make an easily interpretable visualization based on what we call "functional maps" of disease. A functional map is a graphic summary of medical data, where distances between parts of the body are determined by the probability of disease, not by anatomical distances. Functional maps often beat little resemblance to anatomical maps, but they can be used to predict the spread of disease. The idea of modeling the spread of disease in an abstract multidimensional space is difficult for many people. Our goal was to make the important predictions easy to see. NASA must face this problem frequently: how to help laypersons and professionals see important trends in abstract, complex data. We took advantage of concepts perfected in NASA's graphics libraries. As an analogy, consider a functional map of early America. Suppose we choose travel times, rather than miles, as our measures of inter-city distances. For Abraham Lincoln, travel times would have been the more meaningful measure of separation between cities. In such a map New Orleans would be close to Memphis because of the Mississippi River. St. Louis would be close to Portland because of the Oregon Trail. Oklahoma City would be far from Little Rock because of the Cheyenne. Such a map would look puzzling to those of us who have always seen physical maps, but the functional map would be more useful in predicting the probabilities of inter-site transit. Continuing the analogy, we could predict the spread of social diseases such as gambling along the rivers and cattle rustling along the trails. We could simply print the functional map of America, but it would be more interesting to show meaningful patterns of dispersal. We had previously published the functional map of the head and neck, but it was difficult to explain to either patients or surgeons because that view of our body did not resemble anatomy. This discrepancy between functional and physical maps is just a mathematical restatement of the well-known fact that some diseases, such as head and neck cancer, spread in complex patterns, not always to the next nearest site. We had discovered that a computer could re-arrange anatomy so that this particular disease spreads to the next nearest site. The functional map explains over 95% of the metastases in 1400 patients. In a sense, we had graphed what our body "looks like" to a tumor. The tumor readily travels between adjacent areas in the functional map. The functional map is a succinct visual display of trends that are not easily appreciated in tables of probabilities.

Gray, Lincoln↗