SEARCH · Search NASA

Results for “RATIONAL FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

All sources NASA NTRS DOE OSTI

NASA NTRS1999

Continuous Risk Management: An Overview

Software risk management is important because it helps avoid disasters, rework, and overkill, but more importantly because it stimulates win-win situations. The objectives of software risk management are to identify, address, and eliminate software risk items before they become threats to success or major sources of rework. In general, good project managers are also good managers of risk. It makes good business sense for all software development projects to incorporate risk management as part of project management. The Software Assurance Technology Center (SATC) at NASA GSFC has been tasked with the responsibility for developing and teaching a systems level course for risk management that provides information on how to implement risk management. The course was developed in conjunction with the Software Engineering Institute at Carnegie Mellon University, then tailored to the NASA systems community. This is an introductory tutorial to continuous risk management based on this course. The rational for continuous risk management and how it is incorporated into project management are discussed. The risk management structure of six functions is discussed in sufficient depth for managers to understand what is involved in risk management and how it is implemented. These functions include: (1) Identify the risks in a specific format; (2) Analyze the risk probability, impact/severity, and timeframe; (3) Plan the approach; (4) Track the risk through data compilation and analysis; (5) Control and monitor the risk; (6) Communicate and document the process and decisions.

Rosenberg, Linda↗

NASA NTRS1993

Structured adaptive grid generation using algebraic methods

The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration of points to the grid redistribution scheme. The evaluation of the weighting mesh is accomplished by utilizing the weight function representing the solution variation and the equidistribution law. The selection of the weight function plays a key role in grid adaptation. A new weight function utilizing a properly weighted boolean sum of various flowfield characteristics is defined. The redistribution scheme is developed utilizing Non-Uniform Rational B-Splines (NURBS) representation. The application of NURBS representation results in a well distributed smooth grid by maintaining the fidelity of the geometry associated with boundary curves. Several algebraic methods are applied to smooth and/or nearly orthogonalize the grid lines. An elliptic solver is utilized to smooth the grid lines if there are grid crossings. Various computational examples of practical interest are presented to demonstrate the success of these methods.

Yang, Jiann-Cherng↗

NASA NTRS1984

Relationship between Allan variances and Kalman Filter parameters

A relationship was constructed between the Allan variance parameters (H sub z, H sub 1, H sub 0, H sub -1 and H sub -2) and a Kalman Filter model that would be used to estimate and predict clock phase, frequency and frequency drift. To start with the meaning of those Allan Variance parameters and how they are arrived at for a given frequency source is reviewed. Although a subset of these parameters is arrived at by measuring phase as a function of time rather than as a spectral density, they all represent phase noise spectral density coefficients, though not necessarily that of a rational spectral density. The phase noise spectral density is then transformed into a time domain covariance model which can then be used to derive the Kalman Filter model parameters. Simulation results of that covariance model are presented and compared to clock uncertainties predicted by Allan variance parameters. A two state Kalman Filter model is then derived and the significance of each state is explained.

Vandierendonck, A. J.↗

NASA NTRS1987

A strategy for space biology and medical science for the 1980s and 1990s

A guideline is provided for developing NASA's long-term mission plans and a rational, coherent research program. Ten topical areas for research are addressed: developmental biology, gravitropism in plants, sensorimotor integration, bone and mineral metabolism, cardiovascular/pulmonary function, muscle remodeling, nutrition, human reproduction, space anemia, and human behavior. Scientific goals, objectives, and required measurements and facilities for each of the major areas of space biology and medicine are identified and described along with primary goals and objectives for each of these disciplines. Proposals are made concerning the use of scientific panels to oversee the implementation of the strategy, life sciences' need for continuous access to spaceflight opportunities, the advantages of a focused mission strategy, certain design features that will enhance spaceflight experimentation, and general facilities. Other topics that are considered include mission planning, crew selection and training, and interagency and international cooperation.

Source record↗

NASA NTRS1975

Analysis of multiloop, multirate sampled-data systems

Based upon new identities between z-transforms at a basis rate, z-transforms at faster rates, and modified z-transforms, the equivalence between the frequency decomposition method and the switch decomposition method is precisely presented so that results of one method are easily obtained from results of the other. Next, a method is developed for determining the closed loop transfer function of multiloop, multirate sampled-data systems with noninteger ratio sampling rates. Previously, this process involved solving a complex system of equations with rational polynomial coefficients. Herein, this is avoided by introducing a systematic decomposition of matrix operators which naturally arise from the switch decomposition method. The matrix operators are simplified by introducing the shifted transforms of signals sampled at one of the faster rates.

Boykin, W. H.↗

NASA NTRS1989

Determination of the thermal stability of perfluoroalkylethers by tensimetry: Instrumentation and Procedure

A computerized tensimeter and experimental procedure for determination of the thermal decomposition temperature (T sub d) of perfluoro alkylethers were developed and tested. Both the apparatus and the procedure are described in detail. Results of testing with bis(2-ethylhexyl) phthalate and trimethylolpropane triheptanoate demonstrate that the reciprocal of the decomposition temperature is a linear function of the logarithm of the gas volume/heated liquid volume ratio. The T sub d obtained for each compound at a gas volume/heated liquid volume ration of one was similar to the value previously reported using an isoteniscope technique. Results of testing with a polymer of hexafluoropropylene oxide demonstrate that this instrument and procedure can be used to determine the T sub d of perfluoroalkylethers.

Helmick, Larry S.↗

NASA NTRS1990

Determination of the thermal stability of fluids by tensimetry - Instrumentation and procedure

Helmick, Larry S.↗

NASA NTRS1965

Investigation to define the propagation characteristics of a finite amplitude acoustic pressure wave, phase 1 final report, 29 jun. 1964 - 29 jul. 1965

The contribution of high entropy production regions to the generation and propagation characteristics of a finite amplitude pressure is considered. Preliminary analysis indicates that, for nozzles where pressure rations are above critical, the predominant contribution may come from the shock layer formation in the exhaust region. Temperature effects indicate high dependence of the forcing function upon the initial temperature of the media.

WAVE PROPAGATION↗

NASA NTRS1998

Prebiotic Polymer Synthesis and the Origin of Glycolytic Metabolism

Our research resulted in several discoveries which contributed to understanding the origin and operation of life. (1) Most importantly, we discovered a new pathway of prebiotic amino acid synthesis in which formaldehyde and glycolaldehyde (formose reaction substrates) react with ammonia to give alanine and homoserine in the presence of thiol catalysts. The thiol-dependent synthesis of amino acids undoubtedly occurs via amino acid thioester intermediates capable of forming peptides. This 'one-pot' reaction system operates under mild aqueous conditions, and like modern amino acid biosynthesis, uses sugar intermediates which are converted to amino acids by energy-yielding redox disproportionation. Preliminary evidence suggests that this type of process can be "evolved" by a serial transfer methods that lead to enrichment of autocatalytic molecules. (2) We established that prebiotic peptide polymers can be made by condensation of amino acid thioesters (homocysteine thiolactone and S-(N-beta-orotidyl- diaminopropionic acid) ethanethiol), and that prebiotic polydisulfide polymers can be generated by oxidation of dithiols with iron(III) in minerals. (3) In our analysis of metabolism we discovered the primary energy source of biosynthesis -- chemical energy made available by the redox disproportionation of substrate carbon groups. We concluded that the energy and reactivity of sugars make them the optimal substrate for the origin and operation of terrestrial (or extraterrestrial) life. (4) Since it is likely that the use of optimal sugar substrates in biosynthesis sets the average oxidation number of functional biocarbon throughout the Universe near 0.0 (the reduction level of formaldehyde), we proposed that a line(s) in the microwave spectrum of formaldehyde could be rationally selected as a frequency for interstellar communication that symbolizes life. (5) Finally, in preparation for the analysis of Martian meteorite samples, we upgraded our HPLC system to one femtomole sensitivity, and developed a new electrophoretic method of sample preparation for HPLC analysis of the meteoritic amino acids. In a sample of the KT boundary layer from Sussex Wyoming, we found about 300 picomoles per gram of meteoritic alpha-aminoisobutyric acid per gram of KT layer.

Weber, Arthur L.↗

NASA NTRS2001

Distribution functions of probabilistic automata

Each probabilistic automaton M over an alphabet A defines a probability measure Prob sub(M) on the set of all finite and infinite words over A. We can identify a k letter alphabet A with the set {0, 1,..., k-1}, and, hence, we can consider every finite or infinite word w over A as a radix k expansion of a real number X(w) in the interval [0, 1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x) := Prob sub(M) { w: X(w) < x }. Utilizing the fixed-point semantics (denotational semantics), extended to probabilistic computations, we investigate the distribution functions of probabilistic automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0, 1] can be generated by a prob abilistic automaton iff all the roots of F'(x) = 0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.

Denotational semantics↗

NASA NTRS1997

Rocket Engine Numerical Simulator (RENS)

Work is being done at three universities to help today's NASA engineers use the knowledge and experience of their Apolloera predecessors in designing liquid rocket engines. Ground-breaking work is being done in important subject areas to create a prototype of the most important functions for the Rocket Engine Numerical Simulator (RENS). The goal of RENS is to develop an interactive, realtime application that engineers can utilize for comprehensive preliminary propulsion system design functions. RENS will employ computer science and artificial intelligence research in knowledge acquisition, computer code parallelization and objectification, expert system architecture design, and object-oriented programming. In 1995, a 3year grant from the NASA Lewis Research Center was awarded to Dr. Douglas Moreman and Dr. John Dyer of Southern University at Baton Rouge, Louisiana, to begin acquiring knowledge in liquid rocket propulsion systems. Resources of the University of West Florida in Pensacola were enlisted to begin the process of enlisting knowledge from senior NASA engineers who are recognized experts in liquid rocket engine propulsion systems. Dr. John Coffey of the University of West Florida is utilizing his expertise in interviewing and concept mapping techniques to encode, classify, and integrate information obtained through personal interviews. The expertise extracted from the NASA engineers has been put into concept maps with supporting textual, audio, graphic, and video material. A fundamental concept map was delivered by the end of the first year of work and the development of maps containing increasing amounts of information is continuing. Find out more information about this work at the Southern University/University of West Florida. In 1996, the Southern University/University of West Florida team conducted a 4day group interview with a panel of five experts to discuss failures of the RL10 rocket engine in conjunction with the Centaur launch vehicle. The discussion was recorded on video and audio tape. Transcriptions of the entire proceedings and an abbreviated video presentation of the discussion highlights are under development. Also in 1996, two additional 3year grants were awarded to conduct parallel efforts that would complement the work being done by Southern University and the University of West Florida. Dr. Prem Bhalla of Jackson State University in Jackson, Mississippi, is developing the architectural framework for RENS. By employing the Rose Rational language and Booch Object Oriented Programming (OOP) technology, Dr. Bhalla is developing the basic structure of RENS by identifying and encoding propulsion system components, their individual characteristics, and cross-functionality and dependencies. Dr. Ruknet Cezzar of Hampton University, located in Hampton, Virginia, began working on the parallelization and objectification of rocket engine analysis and design codes. Dr. Cezzar will use the Turbo C++ OOP language to translate important liquid rocket engine computer codes from FORTRAN and permit their inclusion into the RENS framework being developed at Jackson State University. The Southern University/University of West Florida grant was extended by 1 year to coordinate the conclusion of all three efforts in 1999.

Davidian, Kenneth O.↗

NASA NTRS2003

Applicability of Markets to Global Scheduling in Grids: Critical Examination of General Equilibrium Theory and Market Folklore

Markets are often considered superior to other global scheduling mechanisms for distributed computing systems. This claim is supported by: a casual observation from our every-day life that markets successfully equilibrate supply and demand, and the features of markets which originate in the general equilibrium theory, e.g., efficiency and the lack of necessity of 2 central controller. This paper describes why such beliefs in markets are not warranted. It does so by examining the general equilibrium theory, in terms of scope, abstraction, and interpretation. Not only does the general equilibrium theory fail to provide a satisfactory explanation of actual economies, including a computing-resource economy, it also falls short of supplying theoretical foundations for commonly held views of market desirability. This paper also points out that the argument for the desirability of markets involves circular reasoning and that the desirability can be established only vis-a-vis a scheduling goal. Finally, recasting the conclusion of Arrow's Impossibility Theorem as that for global scheduling, we conclude that there exists no market-based scheduler that is rational (in the sense defined in microeconomic theory), takes into account utility of more than one user, and yet yields a Pareto-optimal outcome for arbitrary user utility functions.

Nakai, Junko↗

NASA NTRS2005

A Comparative Study of Probability Collectives Based Multi-agent Systems and Genetic Algorithms

We compare Genetic Algorithms (GA's) with Probability Collectives (PC), a new framework for distributed optimization and control. In contrast to GA's, PC-based methods do not update populations of solutions. Instead they update an explicitly parameterized probability distribution p over the space of solutions. That updating of p arises as the optimization of a functional of p. The functional is chosen so that any p that optimizes it should be p peaked about good solutions. The PC approach works in both continuous and discrete problems. It does not suffer from the resolution limitation of the finite bit length encoding of parameters into GA alleles. It also has deep connections with both game theory and statistical physics. We review the PC approach using its motivation as the information theoretic formulation of bounded rationality for multi-agent systems. It is then compared with GA's on a diverse set of problems. To handle high dimensional surfaces, in the PC method investigated here p is restricted to a product distribution. Each distribution in that product is controlled by a separate agent. The test functions were selected for their difficulty using either traditional gradient descent or genetic algorithms. On those functions the PC-based approach significantly outperforms traditional GA's in both rate of descent, trapping in false minima, and long term optimization.

Huang, Chien-Feng↗

NASA NTRS1986

Observation of molecular rotational bands with a single Fabry-Perot interferometer

A method is described for using a single Fabry-Perot interferometer to study the emissions from an entire molecular rotation band, not just a single line to determine atmospheric temperature. It is shown that if the effective line spacing of the band to free spectral range is nearly a rational number, the resulting signal is highly temperature sensitive, particularly at low temperatures. It is shown that the finesse of the instrument is not extremely important but that the instrument function must be known very precisely. The method is illustrated with the O2 atmospheric band and an interferometer flown on the Dynamics Explorer 2 satellite.

Skinner, Wilbert R.↗

NASA NTRS1992

NASA/LMSC instrument design and fabrication

The topics addressed are: (1) class-10 flight test program; (2) class system requirements; (3) Doppler wind velocity measurement; (4) systems specifications rational; (5) signal-to-noise equation for remote atmospheric sensing laser velocimeter; (6) variation of signal-to-noise ratios and true wind velocity with distance; (7) velocity error as a function of signal-to-noise ratio, with turbulence; and (8) final class optomechanical design on NASA B/737.

Targ, Russel↗

NASA NTRS1948

The Development and Application of High-Critical-Speed Nose Inlets

An analysis of the nose-inlet shapes developed in previous investigations to represent the optimum from the standpoint of critical speed has shown that marked similarity exists between the nondimensional profiles of inlets which have widely different proportions and critical speeds. With the nondimensional similarity of such profiles established, the large differences in the critical speeds of these nose inlets must be a function of their proportions. An investigation was undertaken in the Langley 8-foot high-speed tunnel to establish the effects of nose-inlet proportions on critical Mach number to develop a rational method for the design of high-critical-speed nose inlets to meet desired requirements. The test results data have been arranged in the form of design charts from NACA 1-series nose-inlet proportions and can be selected for given values of critical Mach number and airflow quantity. Examples of nose-inlet selections are presented for a typical jet-propulsion installation (critical Mach number of 0.83) and for two conventional radial-engine installations (critical Mach number of 0.76).

Baals, Donald D↗

NASA NTRS1987

Quantitative analysis of the reconstruction performance of interpolants

The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed.

Lansing, Donald L.↗

NASA NTRS1943

On a new method for calculating the potential flow past a body of revolution

A new method is presented for obtaining the velocity potential of the flow about a body of revolution moving uniformly in the direction of its axis of symmetry in a fluid otherwise at rest. This method is based essentially on the fact that the form of the differential equation for the velocity potential is invariant with regard to conformal transformation of the meridian plane. By means of the conformal transformation of the meridian profile into a circle a system of orthogonal curvilinear coordinates is obtained, the main feature of which is that one of the coordinate lines is the meridian profile itself. The use of this type of coordinate system yields a simple expression of the boundary condition at the surface of the solid and leads to a rational process of iteration for the solution of the differential equation for the velocity potential. It is shown that the velocity potential for an arbitrary body of revolution may be expressed in terms of universal functions which, although not normal, are obtainable by means of simple quadratures. The general results are applied to a body of revolution obtained by revolving a symmetrical Joukowski profile about its axis of symmetry. A numerical example further serves to illustrate the theory.

Kaplan, Carl↗