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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

One-way nesting for a primitive equation ocean model

Prognostic numerical models for atmospheric and oceanic circulations require initial fields, boundary conditions, and forcing functions in addition to a consistent set of partial differential equations, including a state relation and equations expressing conservation of mass, momentum, and energy. Depending on the horizontal domain to be modeled, the horizontal boundary conditions are either physically obvious or extremely difficult to specify consistently. If the entire atmosphere is modeled, periodic horizontal boundary conditions are appropriate. On the other hand, the physical horizontal boundaries on the entire ocean are solid walls. Obviously, the normal velocity at a solid wall is zero while the specification of the tangential velocity depends on the mathematical treatment of the horizontal viscous terms. Limitations imposed by computer capacity and cost, as well as research interests, have led to the use of limited area models to study flows in the atmosphere and ocean. The limited area models do not have physical horizontal boundaries, merely numerical ones. Correctly determining these open boundary conditions for limited-area numerical models has both intrigued and frustrated numerical modelers for decades. One common approach is to use the closed or solid wall boundary conditions for a limited-area model. The argument given for this approach is that the boundary conditions affect flow near the walls but that none of these effects are propagated into the interior. Therefore, one chooses a big enough domain that the central region of interest is not corrupted by the boundary flow. Research in progress to model the North Atlantic circulation vividly illustrates the pitfalls of this approach. Two model runs are compared: (1) the southern boundary at 20S between latitudes 0 and 40W is artificially closed; and (2) the same boundary is specified as open with an inward transport of 15 Sv (determined from a global model with the same physics) uniformly spread across the boundary. A comparison of both runs is presented.

Blake, D. W.↗
NASA NTRS1996

SSME Condition Monitoring Using Neural Networks and Plume Spectral Signatures

For a variety of reasons, condition monitoring of the Space Shuttle Main Engine (SSME) has become an important concern for both ground tests and in-flight operation. The complexities of the SSME suggest that active, real-time condition monitoring should be performed to avoid large-scale or catastrophic failure of the engine. In 1986, the SSME became the subject of a plume emission spectroscopy project at NASA's Marshall Space Flight Center (MSFC). Since then, plume emission spectroscopy has recorded many nominal tests and the qualitative spectral features of the SSME plume are now well established. Significant discoveries made with both wide-band and narrow-band plume emission spectroscopy systems led MSFC to develop the Optical Plume Anomaly Detection (OPAD) system. The OPAD system is designed to provide condition monitoring of the SSME during ground-level testing. The operational health of the engine is achieved through the acquisition of spectrally resolved plume emissions and the subsequent identification of abnormal emission levels in the plume indicative of engine erosion or component failure. Eventually, OPAD, or a derivative of the technology, could find its way on to an actual space vehicle and provide in-flight engine condition monitoring. This technology step, however, will require miniaturized hardware capable of processing plume spectral data in real-time. An objective of OPAD condition monitoring is to determine how much of an element is present in the SSME plume. The basic premise is that by knowing the element and its concentration, this could be related back to the health of components within the engine. For example, an abnormal amount of silver in the plume might signify increased wear or deterioration of a particular bearing in the engine. Once an anomaly is identified, the engine could be shut down before catastrophic failure occurs. Currently, element concentrations in the plume are determined iteratively with the help of a non-linear computer code called SPECTRA, developed at the USAF Arnold Engineering Development Center. Ostensibly, the code produces intensity versus wavelength plots (i.e., spectra) when inputs such as element concentrations, reaction temperature, and reaction pressure are provided. However, in order to provide a higher-level analysis, element concentration is not specified explicitly as an input. Instead, two quantum variables, number density and broadening parameter, are used. Past experience with OPAD data analysis has revealed that the region of primary interest in any SSME plume spectrum lies in the wavelength band of 3300 A to 4330 A. Experience has also revealed that some elements, such as iron, cobalt and nickel, cause multiple peaks over the chosen wavelength range whereas other elements (magnesium, for example) have a few, relatively isolated peaks in the chosen wavelength range. Iteration with SPECTRA as a part of OPAD data analysis is an incredibly labor intensive task and not one to be performed by hand. What is really needed is the "inverse" of the computer code but the mathematical model for the inverse mapping is tenuous at best. However, building generalized models based upon known input/output mappings while ignoring details of the governing physical model is possible using neural networks. Thus the objective of the research project described herein was to quickly and accurately predict combustion temperature and element concentrations (i.e., number density and broadening parameter) from a given spectrum using a neural network. In other words, a neural network had to be developed that would provide a generalized "inverse" of the computer code SPECTRA.

Hopkins, Randall↗
NASA NTRS2004

To Boldly Go: America's Next Era in Space. Machine Consciousness and the Exploration of Space

Dr. France Cordova, NASA's Chief Scientist, chaired this meeting, another part of the NASA Administrator's Seminar Series. She introduced Administrator Daniel S. Goldin, who welcomed the attendees, and noted that the two speakers have a running feud regarding the possibility of creating robots that can 'think'. Dr. Cordova then introduced the first speaker, Dr. Roger Penrose of the Mathematical Institute at Oxford in the U.K. His primary interests are in mathematics, physics, information systems technology, and artificial intelligence. He thinks that robots cannot be made to 'think' and that consciousness is not computable. Dr. Hans Moravec, who spoke next, has opinions and activities that are related to, but substantially different from those of Dr. Penrose. Dr. Moravec believes that he can build a robot that can act based on the deductions that it will make. To mimic human thinking capabilities, he figures that a robot ultimately will need to be able to handle ten trillion computations per second. He predicts that his goal of building a 'thinking' robot will be met in the 2030-2040 time period. He pointed out that he already has built a car that successfully drove itself from Washington, DC to San Diego, CA. He commented that a human being, was ready to take over driving the car, if necessary, but there was no need. The robots envisioned by Dr. Moravec would not only be able to 'think', but also would have human-like emotions, and ultimately would be able to reproduce. The discussion that followed raised questions about the morality of sending human-like robots into outer space. Also a concern was expressed that human-like robots might perceive humans as a threat and become dangerous to people.

Source record↗
NASA NTRS2010

Modeling Flight: The Role of Dynamically Scaled Free-Flight Models in Support of NASA's Aerospace Programs

The state of the art in aeronautical engineering has been continually accelerated by the development of advanced analysis and design tools. Used in the early design stages for aircraft and spacecraft, these methods have provided a fundamental understanding of physical phenomena and enabled designers to predict and analyze critical characteristics of new vehicles, including the capability to control or modify unsatisfactory behavior. For example, the relatively recent emergence and routine use of extremely powerful digital computer hardware and software has had a major impact on design capabilities and procedures. Sophisticated new airflow measurement and visualization systems permit the analyst to conduct micro- and macro-studies of properties within flow fields on and off the surfaces of models in advanced wind tunnels. Trade studies of the most efficient geometrical shapes for aircraft can be conducted with blazing speed within a broad scope of integrated technical disciplines, and the use of sophisticated piloted simulators in the vehicle development process permits the most important segment of operations the human pilot to make early assessments of the acceptability of the vehicle for its intended mission. Knowledgeable applications of these tools of the trade dramatically reduce risk and redesign, and increase the marketability and safety of new aerospace vehicles. Arguably, one of the more viable and valuable design tools since the advent of flight has been testing of subscale models. As used herein, the term "model" refers to a physical article used in experimental analyses of a larger full-scale vehicle. The reader is probably aware that many other forms of mathematical and computer-based models are also used in aerospace design; however, such topics are beyond the intended scope of this document. Model aircraft have always been a source of fascination, inspiration, and recreation for humans since the earliest days of flight. Within the scientific community, Leonardo da Vinci, George Cayley, and the Wright brothers are examples of early aviation pioneers who frequently used models during their scientific efforts to understand and develop flying machines. Progress in the technology associated with model testing in worldwide applications has firmly established model aircraft as a key element in new aerospace research and development programs. Models are now routinely used in many applications and roles, including aerodynamic data gathering in wind tunnel investigations for the analysis of full-scale aircraft designs, proof-of-concept demonstrators for radical aeronautical concepts, and problem-solving exercises for vehicles already in production. The most critical contributions of aerospace models are to provide confidence and risk reduction for new designs and to enhance the safety and efficiency of existing configurations.

Chambers, Joseph↗
NASA NTRS1975

Preliminary evaluation of the contaminant induced environment for the space shuttle orbiter

A preliminary evaluation of the on-orbit induced environment from identified major sources of contamination for the STS shuttle orbiter is presented. A contamination computer mathematical model is discussed that was used to develop the description and predictions of the induced environment along with the extent and physical makeup of the molecular induced environment from these sources. The predicted induced molecular environment from each source is evaluated against current Space Shuttle Program on-orbit contamination control criteria. The flash evaporator vents and the VCS 25-lb thrust engines are shown to significantly exceed applicable contamination control criteria and were the subject of extensive evaluation. Preliminary conclusions concerning the contaminant potential of these sources along with recommendations for various measures of contamination control regarding the shuttle orbiter design and operational activities are made.

Bareiss, L. E.↗
NASA NTRS1999

A Spherical Earth Solution for TOA Lightning Location Retrieval

With the advent of high-speed digital computers, the method of chi square minimization is a highly practical means for analyzing a wide variety of (otherwise intractable) nonlinear inversion problems in applied mathematical physics. Little thought or effort is required to apply the chi square method to obtain quick and reasonable estimates of a solution, and the method offers a means to assess retrieval errors. Because the method is simple and practical it is sometimes hastily applied to problems that can be solved by formal analytic or quasi-analytic means. Presently, Global Atmospherics Inc. (GAI) finds the minimum of a chi square function to analyze time-of-arrival (TOA) and magnetic bearing data derived from the National Lightning Detection Network (NLDN); ellipsoidal Earth geometry is assumed. An analytic solution to this problem has not yet been attained, but the consideration and solving of less general problem statements might eventually lead to a final solution. In the present study, the problem of retrieving lightning ground-strike location on a spherical Earth surface using a network of 4 or more time-of-arrival (TOA) sensors is considered. It is shown that this problem has an analytic solution and therefore does not require the use of nonlinear estimation theory (such as the chi square method mentioned above). The mathematical robustness of the analytic solution is tested using computer-generated lightning sources and simulated TOA measurement errors. A quasi-analytic extension of the spherical Earth solution for an oblate spheroidal Earth geometry is considered in a related study. The incorporation of magnetic bearing information into these analytic solutions would lead to a general and elegant analytic retrieval scheme that would most likely replace the chi square estimation theory currently employed by Global Atmospherics Inc. (GAI).

Koshak, William J,↗
NASA NTRS2004

Unfolding of Proteins: Thermal and Mechanical Unfolding

We have employed a Hamiltonian model based on a self-consistent Gaussian appoximation to examine the unfolding process of proteins in external - both mechanical and thermal - force elds. The motivation was to investigate the unfolding pathways of proteins by including only the essence of the important interactions of the native-state topology. Furthermore, if such a model can indeed correctly predict the physics of protein unfolding, it can complement more computationally expensive simulations and theoretical work. The self-consistent Gaussian approximation by Micheletti et al. has been incorporated in our model to make the model mathematically tractable by signi cantly reducing the computational cost. All thermodynamic properties and pair contact probabilities are calculated by simply evaluating the values of a series of Incomplete Gamma functions in an iterative manner. We have compared our results to previous molecular dynamics simulation and experimental data for the mechanical unfolding of the giant muscle protein Titin (1TIT). Our model, especially in light of its simplicity and excellent agreement with experiment and simulation, demonstrates the basic physical elements necessary to capture the mechanism of protein unfolding in an external force field.

Hur, Joe S.↗
NASA NTRS1994

Turbulent Flow In A Circular-To-Rectangular Transition Duct

NASA technical memorandum describes experiments and analysis of experimental data pertaining to subsonic, turbulent flow of air in duct that includes gradual transition from circular cross section at inlet to rectangular cross section at outlet. Study intended to support further research on physics of flow, by providing comprehensive set of data for calibration and verification of computer codes for simulation of transition-duct flows and mathematical models of turbulence in flows in which effects of curvature of streamlines important.

Davis, David O.↗
NASA NTRS1966

Computer program determines chemical composition of physical system at equilibrium

FORTRAN 4 digital computer program calculates equilibrium composition of complex, multiphase chemical systems. This is a free energy minimization method with solution of the problem reduced to mathematical operations, without concern for the chemistry involved. Also certain thermodynamic properties are determined as byproducts of the main calculations.

Kwong, S. S.↗
NASA NTRS1992

Mathematical Model For Engineering Analysis And Optimization

Computational support for engineering design process reveals behavior of designed system in response to external stimuli; and finds out how behavior modified by changing physical attributes of system. System-sensitivity analysis combined with extrapolation forms model of design complementary to model of behavior, capable of direct simulation of effects of changes in design variables. Algorithms developed for this method applicable to design of large engineering systems, especially those consisting of several subsystems involving many disciplines.

Sobieski, Jaroslaw↗
NASA NTRS1995

The Topographic Torque on a Bounding Surface of a Rotating Gravitating Fluid and the Excitation by Core Motions of Decadal Fluctuations in the Earth's Rotation

General expressions (with potential applications in several areas of geophysical fluid dynamics) are derived for all three components of the contribution made by the geostrophic part of the pressure field associated with flow in a rotating gravitating fluid to the topographic torque exerted by the fluid on a rigid impermeable bounding surface of any shape. When applied to the Earth's liquid metallic core, which is bounded by nearly spherical surfaces and can be divided into two main regions, the "torosphere" and "polosphere," the expressions reduce to formulae given previously by the author, thereby providing further support for his work and that of others on the role of topographic coupling at the core-mantle boundary in the excitation by core motions of Earth rotation fluctuations on decadal time scales. They also show that recent criticisms of that work are vitiated by mathematical and physical errors. Contrary to these criticisms, the author's scheme for exploiting Earth rotation and other geophysical data (either real or simulated in computer models) in quantitative studies of the topography of the core-mantle boundary (CMB) by intercomparing various models of (a) motions in the core based on geomagnetic secular variation data and (b) CMB topography based on seismological and gravity data has a sound theoretical basis. The practical scope of the scheme is of course limited by the accuracy of real data, but this is a matter for investigation, not a priori assessment.

Hide, Raymond↗
NASA NTRS1997

A correlated ab initio study of the A2 pi <-- X2 sigma+ transition in MgCCH

The A2 pi <-- X2 sigma+ transition in MgCCH was studied with correlation consistent basis sets and single- and multireference correlation methods. The A2 pi excited state was characterized in detail; the x2 sigma+ ground state has been described elsewhere recently. The estimated complete basis set (CBS) limits for valence correlation, including zero-point energy corrections, are 22668, 23191, and 22795 for the RCCSD(T), MRCI, and MRCI + Q methods, respectively. A core-valence correction of +162 cm-1 shifts the RCCSD(T) value to 22830 cm-1, in good agreement with the experimental result of 22807 cm-1.

Non-NASA Center↗
NASA NTRS2014

A Walsh Function Module Users' Manual

The solution of partial differential equations (PDEs) with Walsh functions offers new opportunities to simulate many challenging problems in mathematical physics. The approach was developed to better simulate hypersonic flows with shocks on unstructured grids. It is unique in that integrals and derivatives are computed using simple matrix multiplication of series representations of functions without the need for divided differences. The product of any two Walsh functions is another Walsh function - a feature that radically changes an algorithm for solving PDEs. A FORTRAN module for supporting Walsh function simulations is documented. A FORTRAN code is also documented with options for solving time-dependent problems: an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the usage of the Walsh function module including such features as operator overloading, Fast Walsh Transforms in multi-dimensions, and a Fast Walsh reciprocal.

Gnoffo, Peter A.↗
NASA NTRS2011

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

Jain, Abhinandan↗
NASA NTRS1987

A generalized procedure for constructing an upwind-based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some nonlinear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to a scalar nonlinear equation and constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance to numerical experiments. Then the formulation is formally extended to the nonlinear system of equations. It is demonstrated that use of the present procedure allows easy conversion of existing central or upwind, and second- or higher-order differencing schemes so as to preserve monotonicity and to yield physically admissible solutions. The formulation is simple mathematically as well as numerically; neither matrix-vector multiplication nor Riemann solver is required. Roughly twice as much computational effort is needed as compared to conventional scheme. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made. Numerical examples including various ranges of problems show both time- and spatial-accuracy in comparison with exact solutions.

Liou, Meng-Sing↗
NASA NTRS1992

Computational fluid dynamics combustion analysis evaluation

This study involves the development of numerical modelling in spray combustion. These modelling efforts are mainly motivated to improve the computational efficiency in the stochastic particle tracking method as well as to incorporate the physical submodels of turbulence, combustion, vaporization, and dense spray effects. The present mathematical formulation and numerical methodologies can be casted in any time-marching pressure correction methodologies (PCM) such as FDNS code and MAST code. A sequence of validation cases involving steady burning sprays and transient evaporating sprays will be included.

Kim, Y. M.↗
NASA NTRS2006

Using Satellite Data in Weather Forecasting: I

The GOES Product Generation System (GPGS) is a set of computer codes and scripts that enable the assimilation of real-time Geostationary Operational Environmental Satellite (GOES) data into regional-weather-forecasting mathematical models. The GPGS can be used to derive such geophysical parameters as land surface temperature, the amount of precipitable water, the degree of cloud cover, the surface albedo, and the amount of insolation from satellite measurements of radiant energy emitted by the Earth and its atmosphere. GPGS incorporates a priori information (initial guesses of thermodynamic parameters of the atmosphere) and radiometric measurements from the geostationary operational environmental satellites along with mathematical models of physical principles that govern the transfer of energy in the atmosphere. GPGS solves the radiative-transfer equation and provides the resulting data products in formats suitable for use by weather-forecasting computer programs. The data-assimilation capability afforded by GPGS offers the potential to improve local weather forecasts ranging from 3 hours to 2 days - especially with respect to temperature, humidity, cloud cover, and the probability of precipitation. The improvements afforded by GPGS could be of interest to news media, utility companies, and other organizations that utilize regional weather forecasts.

Jedlovec, Gary J.↗
NASA NTRS2011

Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b , where A is an m by x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as 4x(sub 1) + 6x(sub 2) + 5x (sub 3) = 10, where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or a minimum norm solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning.

Sen, Syamal K.↗