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At least 901 records · Page 50

The rate of the reaction between C2H and C2H2 at interstellar temperatures

The reaction between the radical C2H and the stable hydrocarbon C2H2 is one of the simplest neutral-neutral hydrocarbon reactions in chemical models of dense interstellar clouds and carbon-rich circumstellar shells. Although known to be rapid at temperatures > or = 300 K, the reaction has yet to be studied at lower temperatures. We present here ab initio calculations of the potential surface for this reaction and dynamical calculations to determine its rate at low temperature. Despite a small potential barrier in the exit channel, the calculated rate is large, showing that this reaction and, most probably, more complex analogs contribute to the formation of complex organic molecules in low-temperature sources.

Non-NASA Center↗

Theory of hydrophobicity: transient cavities in molecular liquids

Observation of the size distribution of transient cavities in computer simulations of water, n-hexane, and n-dodecane under benchtop conditions shows that the sizes of cavities are more sharply defined in liquid water but the most-probable-size cavities are about the same size in each of these liquids. The calculated solvent atomic density in contact with these cavities shows that water applies more force per unit area of cavity surface than do the hydrocarbon liquids. This contact density, or "squeezing" force, reaches a maximum near cavity diameters of 2.4 angstroms. The results for liquid water are compared to the predictions of simple theories and, in addition, to results for a reference simple liquid. The numerical data for water at a range of temperatures are analyzed to extract a surface free energy contribution to the work of formation of atomic-size cavities. Comparison with the liquid-vapor interfacial tensions of the model liquids studied here indicates that the surface free energies extracted for atomic-size cavities cannot be accurately identified with the macroscopic surface tensions of the systems.

NASA Center ARC↗

Non-Lipschitz Dynamics Approach to Discrete Event Systems

This paper presents and discusses a mathematical formalism for simulation of discrete event dynamics (DED) - a special type of 'man- made' system designed to aid specific areas of information processing. A main objective is to demonstrate that the mathematical formalism for DED can be based upon the terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.

Mathematics Newtonian Dynamics Scientific Computin↗

The X-43A Flight Research Program: Lessons Learned on the Road to Mach 10

During an aerospace engineer's undergraduate studies, he or she will attend classes in aerodynamics, thermodynamics, structures, stability and control, dynamics, design, propulsion, and computer science, along with the related courses in mathematics, physics, statistics, and chemistry required to understand the material. Upon graduation, the new engineer will have acquired a basic knowledge of how to build an aerospace vehicle. What only comes through experience, however, is the understanding of the inevitable imperfect process through which an aerospace vehicle is built. This is the adventure of turning a basic concept into functional hardware. Engineers working on a project must often deal with ambiguous situations. They are routinely asked by management to provide risk assessments of a project, yet even after careful analysis uncertainties remain. The project must be accomplished within finite limits of time and money. The question an engineer answers is whether the solution to potential problem is worth the cost and schedule delay, or if the solution might actually be worse than the problem it is meant to solve. Review protocols are established to ensure that an unknown has not been overlooked. But these cannot protect against an unknown unknown. Examples of these situations can be found in the history of the X-43A Hyper-X (Hypersonic Experiment) program. In this NASA project, a supersonic combustion ramjet (scramjet) engine was flight tested on a subscale vehicle. The X-43A Hyper-X Research Vehicle (HXRV) was launched from a B-52B mothership, then boosted to the test speed by a modified Pegasus rocket first stage, called the Hyper-X Launch Vehicle (HXLV). Once at the proper speed and altitude, the X-43A separated from the booster, stabilized itself, and then the engine test began. Although wind-tunnel scramjet engine tests had begun in the late 1950s, before the Hyper-X program there had never been an actual in-flight test of such an engine integrated with an appropriate airframe. Thus, while the scramjet had successfully operated in the artificial airflow of wind tunnels, the concept had yet to be proven in real air. These conditions meant changes in density and temperature, as well as changes in angle of attack and sideslip of a free-flying vehicle. A wind tunnel is limited in its ability to simulate these subtle factures, which have a major impact on almost any vehicle, but especially that of a scramjet's performance. The Hyper-X project was to provide a real-world benchmark of the ground test data. The full scale X-43A engine would be operated in the wind tunnel, and then flown, and the data from its operation would then be compared with projections. If these matched, the wind tunnel data would be considered a reliable design tool for future scramjet. If there were significant differences, the reasons for these would have to be identified. Until such information was available, scramjets would lack the technological maturity to be considered for future space launch or high-speed atmospheric flight vehicles.

Peebles, Curtis↗

NASA Tech Briefs, July/August 1986

Topic include: NASA TU Services; New Product Ideas; Electronic Components and Circuits; Electronic Systems; Materials; Computer Programs; Mechanics; Physical Sciences; Machinery; Fabrication Technology; Mathematics and Information Sciences; Life Sciences. 3

National Aeronautics and Space Administration↗

Dude Where's My Stars: A Novel Topologically Justified Approach to Star Tracking

In this paper, we consider two novel approaches to celestial navigation for spacecraft. Determining attitude without any prior knowledge using star tracking is known to be a difficult task, particularly given the computational complexity and the many potential sources of misinformation. We consider localization by optimizing matching parameters without explicit star identification in a computationally tractable manner. This is achieved using the mathematical tools of topological data analysis (TDA) and cellular sheaves to study the geometry and distribution of cataloged stars. A framework is gained that enhances the statistical approach to noise handling and false star detection, and heterogeneous sensor fusion. Finally, we discuss confidence bounds and minimum information requirements for successful operation.

Sheaf theory↗

Design of the UCLA general circulation model

An edited version is reported of notes distributed at the Summer Workshop on the UCLA General Circulation Model in June 1971. It presents the computational schemes of the UCLA model, along with the mathematical and physical principles on which these schemes are based. Included are the finite difference schemes for the governing fluid-dynamical equations, designed to maintain the important integral constraints and dispersion characteristics of the motion. Also given are the principles of parameterization of cumulus convection by an ensemble of identical clouds. A model of the ground hydrology, involving the liquid, ice and snow states of water, is included. A short summary is given of the scheme for computing solar and infrared radiation transfers through clear and cloudy air.

Arakawa, A.↗

A computer program for fitting smooth surfaces to an aircraft configuration and other three dimensional geometries

A computer program that uses a three-dimensional geometric technique for fitting a smooth surface to the component parts of an aircraft configuration is presented. The resulting surface equations are useful in performing various kinds of calculations in which a three-dimensional mathematical description is necessary. Programs options may be used to compute information for three-view and orthographic projections of the configuration as well as cross-section plots at any orientation through the configuration. The aircraft geometry input section of the program may be easily replaced with a surface point description in a different form so that the program could be of use for any three-dimensional surface equations.

Craidon, C. B.↗

Integration of viscous effects into inviscid computational methods

A variety of practical fluid dynamic problems related to the low-speed, high Reynolds number flow over aircraft and ground vehicles fall in a category where some simplified mathematical models become applicable. This provides the fluid dynamicists with a more economical computational tool, compared to the alternative solution of the Navier Stokes equations. The objective was to provide a brief survey of some of the viscous boundary layer solution methods and to propose a method for coupling between the inviscid outer flow and the viscous boundary layer solutions. Results of this survey and details of the viscous/inviscid flow coupling efforts are presented.

Katz, Joseph↗

A study of the dynamics of rotating space stations with elastically connected counterweight and attached flexible appendages. Volume 1: Theory

The formulation of a mathematical model for predicting the dynamic behavior of rotating flexible space station configurations was conducted. The overall objectives of the study were: (1) to develop the theoretical techniques for determining the behavior of a realistically modeled rotating space station, (2) to provide a versatile computer program for the numerical analysis, and (3) to present practical concepts for experimental verification of the analytical results. The mathematical model and its associated computer program are described.

Austin, F.↗

Identification of the stability parameters of an aeroelastic airplane

The problem of the parameter identification of large scale dynamic systems involving a system matrix characterized by approximately 200 elements is addressed. By using phase variable transformations, a mathematical model of an aeroelastic airplane is described in a form that is amenable to partial or piecemeal acceptance of parameters estimated from flight data. A mathematical model of the U.S. Air Force Total In-Flight Simulator was computed using the FLEXSTAB digital computer program. As data became available during the progress of the flight test program, this data was processed and substituted in the mathematical model for parameters analytically obtained from the FLEXSTAB program. The results tend to show a progressive and orderly transition from an analytically defined mathematical model to one obtained from the flight tests of the actual aircraft.

Rynaski, E. G.↗

Computer-controlled float zone crystal growth

A PC-based computer control system to automate a high-temperature float zone growth of titanium carbide is reported. The control strategy of the computer control system relies on the relations derived from a combination of empirical relations and results from detailed mathematical analysis of the physical transports of the entire float zone assembly. A system control computer program was written to establish real-time determination of the size of the molten zone from a thermal image, control parameters from established relationships, and collected processed data to achieve control objectives. We found that the developed computer control allows the growth process to be operated nearer the stability limit. Any slight variations in growth conditions can be corrected in time to avoid any instability growth, which otherwise cannot be adjusted via manual control.

Chan, Y. T.↗

Industrial Productivity

NASTRAN is an offshoot of the computer-design technique used in construction of airplanes and spacecraft. [n this technique engineers create a mathematical model of the aeronautical or space vehicle and "fly" it on the ground by means of computer simulation. The technique enables them to study performance and structural behavior of a number of different designs before settling on the final configuration and proceeding with construction. From this base of aerospace experience, NASA-Goddard developed the NASTRAN general purpose computer program, which offers an exceptionally wide range of analytic capability with regard to structures. NASTRAN has been applied to autos, trucks, railroad cars, ships, nuclear power reactors, steam turbines, bridges, and office buildings. NASA-Langley provides program maintenance services regarded as vital by many NASTRAN users. NASTRAN is essentially a predictive tool. It takes an electronic look at a computerire$.dedgn and reports how the structure will react under a great many different conditions. It can, for example, note areas where high stress levels will occur-potential failure points that need strengthening. Conversely, it can identify over-designed areas where weight and material might be saved safely. NASTRAN can tell how pipes stand up under strong fluid flow, how metals are affected by high temperatures, how a building will fare in an earthquake or how powerful winds will cause a bridge to oscillate. NASTRAN analysis is quick and inexpensive. It minimizes trial-and-error in the design process and makes possible better, safe, lighter structures affording large-scale savings in development time and materials. Some examples of the broad utility NASTRAN is finding among industrial firms are shown on these pages.

Source record↗

On the Computational Capabilities of Physical Systems: The Impossibility of Infallible Computation - Part 1

In this first of two papers, strong limits on the accuracy of physical computation are established. First it is proven that there cannot be a physical computer C to which one can pose any and all computational tasks concerning the physical universe. Next it is proven that no physical computer C can correctly carry out any computational task in the subset of such tasks that can be posed to C. This result holds whether the computational tasks concern a system that is physically isolated from C, or instead concern a system that is coupled to C. As a particular example, this result means that there cannot be a physical computer that can, for any physical system external to that computer, take the specification of that external system's state as input and then correctly predict its future state before that future state actually occurs; one cannot build a physical computer that can be assured of correctly 'processing information faster than the universe does'. The results also mean that there cannot exist an infallible, general-purpose observation apparatus, and that there cannot be an infallible, general-purpose control apparatus. These results do not rely on systems that are infinite, and/or non-classical, and/or obey chaotic dynamics. They also hold even if one uses an infinitely fast, infinitely dense computer, with computational powers greater than that of a Turing Machine. This generality is a direct consequence of the fact that a novel definition of computation - a definition of 'physical computation' - is needed to address the issues considered in these papers. While this definition does not fit into the traditional Chomsky hierarchy, the mathematical structure and impossibility results associated with it have parallels in the mathematics of the Chomsky hierarchy. The second in this pair of papers presents a preliminary exploration of some of this mathematical structure, including in particular that of prediction complexity, which is a 'physical computation analogue' of algorithmic information complexity. It is proven in that second paper that either the Hamiltonian of our universe proscribes a certain type of computation, or prediction complexity is unique (unlike algorithmic information complexity), in that there is one and only version of it that can be applicable throughout our universe.

Wolpert, David H.↗

Systolic VLSI for Kalman filters

A novel two-dimensional parallel computing method for real-time Kalman filtering is presented. The mathematical formulation of a Kalman filter algorithm is rearranged to be the type of Faddeev algorithm for generalizing signal processing. The data flow mapping from the Faddeev algorithm to a two-dimensional concurrent computing structure is developed. The architecture of the resulting processor cells is regular, simple, expandable, and therefore naturally suitable for VLSI chip implementation. The computing methodology and the two-dimensional systolic arrays are useful for Kalman filter applications as well as other matrix/vector based algebraic computations.

Yeh, H.-G.↗

SURE reliability analysis: Program and mathematics

The SURE program is a new reliability analysis tool for ultrareliable computer system architectures. The computational methods on which the program is based provide an efficient means for computing accurate upper and lower bounds for the death state probabilities of a large class of semi-Markov models. Once a semi-Markov model is described using a simple input language, the SURE program automatically computes the upper and lower bounds on the probability of system failure. A parameter of the model can be specified as a variable over a range of values directing the SURE program to perform a sensitivity analysis automatically. This feature, along with the speed of the program, makes it especially useful as a design tool.

Butler, Ricky W.↗