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Results for “Mathematical analysis”

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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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

The transmission of sonic boom signals into rooms through open windows.

This paper is the second of two companion papers. In the first paper, expressions for the acoustic field generated inside a room with an open window due to incoming transient or periodic signals have been presented. In this paper, the technique has been applied to the specific example of an N-wave type signal. Detailed mathematical analysis is followed by its approximate version and numerical computation. Results of controlled experiments, using simulated sonic booms, have been compared with theoretical predictions.

Vaidya, P. G.↗
NASA NTRS1973

Launch window definition for sky target experiments.

This paper is a brief report on the computer program developed for the Extraterrestrial Physics Barium Ion Cloud (BIC) Project. The mathematical analysis developed for the program along with its programing characteristics are pointed out to show that this program is adaptable to similar sky target projects. Definite viewing constraints are specified so that the chosen ground tracking stations can photograph the behavior of the sky target after its release. Viewing factors include the illumination of the target by the sun, the relative elevation look angle to the target from each tracking station, the solar and lunar depression angles at each tracking station, and the total sky background brightness of the target relative to each tracking station. Numeric values are assigned to each factor through program input. The program output is flexible so that the results of the window calculations can be studied to the depth required.

Michaud, N. H.↗
NASA NTRS1972

Thermal expansion compatibility of ceramic chip capacitors mounted on alumina substrates.

The thermal expansion coefficients of a representative sample of BaTiO3 and TiO2 ceramic chip capacitors and alumina substrates have been examined. These data have revealed large potential mechanical stresses under thermal cycling. A mathematical analysis of a composite model of the capacitor to predict the thermal expansion and modulus of elasticity and an analysis of the capacitor-substrate system to predict the magnitude of thermally induced stresses have been conducted. In all cases studied, thermally induced stresses great enough to cause capacitor body rupture or termination failure was predicted.

Allen, R. V.↗
NASA NTRS1973

Mass-energy metabolic characteristics of algae

A mathematical analysis is given for the mass energy characteristics of photosynthesizing algae. An engineering-biological approach to this allows for a detailed analysis of the characteristics for a broad spectrum of environmental situations in which such algae are used as a component of a life support system. Models of such systems are constructed and are employed to demonstrate actual and hypothetical situations. Computers are employed for this purpose.

Smirnov, I. V.↗
NASA NTRS1973

RI 1170 advanced strapdown gyro

The major components of the RI 1170 gyroscope are described. A detailed functional description of the electronics including block diagrams and photographs of output waveshapes within the loop electronics are presented. An electronic data flow diagram is included. Those gyro subassemblies that were originally planned and subsequently changed or modified for one reason or another are discussed in detail. Variations to the original design included the capacitive pickoffs, torquer flexleads, magnetic suspension, gas bearings, electronic design, and packaging. The selection of components and changes from the original design and components selected are discussed. Device failures experienced throughout the program are reported and design corrections to eliminate the failure modes are noted. Major design deficiencies such as those of the MSE electronics are described in detail. Modifications made to the gas bearing parts and design improvements to the wheel are noted. Changes to the gas bearing prints are included as well as a mathematical analysis of the 1170 gas bearing wheel by computer analysis. The mean free-path effects on gas bearing performance is summarized.

Source record↗
NASA NTRS1973

A composite model for a class of electric-discharge shock tubes

A gasdynamic model is presented and analyzed for a class of shock tubes that utilize both Joule heating and electromagnetic forces to produce high-speed shock waves. The model consists of several stages of acceleration in which acceleration to sonic conditions is achieved principally through heating, and further acceleration of the supersonic flow is obtained principally through use of electromagnetic forces. The utility of the model results from the fact that it predicts a quasi-steady flow process, mathematical analysis is straightforward, and it is even possible to remove one or more component stages and still have the model related to a possible shock-tube flow. Initial experiments have been performed where the electrical discharge configuration and current level were such that Joule heating was the dominant form of energy addition present. These experiments indicate that the predictions of the model dealing with heat addition correspond quite closely to reality. The experimental data together with the theory show that heat addition to the flowing driver gas after diaphragm rupture (approach used in the model) is much more effective in producing high-speed shock waves than heating the gas in the driver before diaphragm rupture, as in the case of the arc-driven shock tube.

Elkins, R. T.↗
NASA NTRS1974

A stack algorithm for source coding with a fidelity criterion

Although coding of sources with respect to a fidelity criterion was first proposed by Shannon in 1959, only recently have effective schemes been developed. Another such algorithm based on a stack is described. Like the author's other algorithms (Jelinek and Anderson, 1971, 1973), this algorithm is conceived with tree codes in mind. It has various strengths and weaknesses relative to the earlier two, which are explored. By itself, the algorithm has an interesting mathematical analysis that yields insight into the faster-than-exponential behavior of tree variables and provides a new characterization of the rate-distortion function.

Anderson, J. B.↗
NASA NTRS1975

Thermal loading in the laser holography nondestructive testing of a composite structure

A laser holographic interferometry method that has variable sensitivity to surface deformation was applied to the investigation of composite test samples under thermal loading. A successful attempt was made to detect debonds in a fiberglass-epoxy-ceramic plate. Experimental results are presented along with the mathematical analysis of the physical model of the thermal loading and current conduction in the composite material.

Liu, H. K.↗
NASA NTRS1974

SUSSA ACTS: A computer program for steady and unsteady, subsonic and supersonic aerodynamics for aerospace complex transportation systems

The computer program SUSSA ACTS (Steady and Unsteady, Subsonic and Supersonic Aerodynamics for Complex Transportation Systems) are presented in the final version. The numerical formulation and the description of the program and numerical results are included. In particular, generalized forces for fully unsteady (complex frequency) aerodynamics for a wing-body configuration, in both subsonic and supersonic flows, are discussed. The mathematical analysis includes completely arbitrary motion. The numerical implementation was limited to steady and oscillatory flows. A more general aerodynamic formulation in the form of a fully transient response for time-domain analysis and the aerodynamic transfer function (Laplace transform of the fully unsteady operator) for frequency-domain analysis is outlined.

Tseng, K.↗
NASA NTRS1975

Monte Carlo variance reduction study

A mathematical analysis of the transport of nuclear radiation through matter is presented. A computer test bed that was developed is shown, along with flow charts.

Byrn, N. R.↗
NASA NTRS1975

The relationship between reliability and bonding techniques in hybrid microcircuits

Differential thermal expansion was shown to be responsible for many observed failures in ceramic chip capacitors mounted on alumina substrates. It is shown that the mounting techniques used in bonding the capacitors have a marked effect upon the thermally induced mechanical stress and thus the failure rate. A mathematical analysis was conducted of a composite model of the capacitor-substrate system to predict the magnitude of thermally induced stresses. It was experimentally observed that the stresses in more compliant bonding systems such as soft lead tin and indium solders are significantly lower than those in hard solder and epoxy systems. The marked dependence upon heating and cooling rate was proven to be a determining factor in the prediction of failure solder systems. It was found that the harder or higher melting solders are less susceptible to thermal cycling effects but that they are more likely to fail during initial processing operations. Strain gage techniques were used to determine thermally induced expansion stresses of the capacitors and the alumina substrates. The compliance of the different bonding mediums was determined. From the data obtained, several recommendations are made concerning the optimum bonding system for the achievement of maximum reliability.

Caruso, S. V.↗
NASA NTRS1974

U.S. National Congress of Applied Mechanics, 7th, University of Colorado, Boulder, Colo., June 3-7, 1974, Proceedings

A series of experimental, theoretical, and review papers dealing with various aspects of applied mechanics, including structural analysis, mathematical methods, and fluid dynamics. Some of the topics covered are: the direct formulation of two-dimensional mechanics problems, the mechanical aspects of athletics, Laplace's tidal equations, cochlear mechanics, dynamic constitutive equations, optical techniques for the determination of displacement and strain fields, chemical and biochemical problems involving nonlinear diffusion processes, thermal stresses, the rotating rod viscometer, finite-element methods in plasticity, ships of minimum resistance, and wide-band random vibration of structures. Individual items are announced in this issue.

Source record↗
NASA NTRS1975

Pulse modulation effect on velocity fringes

The degradation of a hologram caused by object motion can be utilized to measure the rate of change of the length of an object beam. A rectangular shaped laser pulse is ordinarily used to illuminate the object in such an investigation. The velocity fringes obtained are considered in the calculation. There are no velocity fringes for Gaussian shaped pulses or for the pulses produced by a Q-switched ruby laser. It is shown with the aid of a mathematical analysis that a pulse of oscillating intensity or a pulse train will yield velocity fringes regardless of the shape of an individual pulse.

Decker, A. J.↗
NASA NTRS1975

The relationship between reliability and bonding techniques in hybrid systems

Differential thermal expansion has been shown to be responsible for many observed failures in ceramic chip capacitors mounted on alumina substrates. The present work has shown that the mounting techniques used in bonding the capacitors have a marked effect upon the thermally induced mechanical stress and thus the failure rate. A mathematical analysis of a composite model of the capacitor-substrate system to predict the magnitude of thermally induced stresses have been conducted. It has been experimentally observed that the stresses in more compliant bonding systems such as soft lead/tin and indium solders are significantly lower than those in hard solder and epoxy systems. From the data obtained, several recommendations are made concerning the optimum bonding system for the achievement of maximum reliability.

Kinser, D. L.↗
NASA NTRS1975

Angular velocities, angular accelerations, and coriolis accelerations

Weightlessness, rotating environment, and mathematical analysis of Coriolis acceleration is described for man's biological effective force environments. Effects on the vestibular system are summarized, including the end organs, functional neurology, and input-output relations. Ground-based studies in preparation for space missions are examined, including functional tests, provocative tests, adaptive capacity tests, simulation studies, and antimotion sickness.

Ashton Graybiel↗
NASA NTRS1975

The neutrino charge form-factor

Mathematical analysis and dispersion relations are used to obtain the general functional form of the neutrino charge form-factor. It is shown that if the scale for weak interactions is given by G, where G is the Fermi coupling constant, then for a large range of momentum transfer values, the form-factor may be approximated by a function that is linear in the square of the momentum transfer.

Mickens, R. E.↗
NASA NTRS1975

The relationship between reliability and bonding techniques in hybrid systems

Differential thermal expansion has been shown to be responsible for many observed failures in ceramic chip capacitors mounted on alumina substrates. The present work has shown that the mounting techniques used in bonding the capacitors have a marked effect upon the thermally induced mechanical stress and thus the failure rate. A mathematical analysis of a composite model of the capacitor-substrate system to predict the magnitude of thermally induced stresses has been conducted. It has been observed that the stresses in more compliant bonding systems such as soft lead/tin and indium solders are significantly lower than those in hard solder and epoxy systems. The marked dependence upon heating and cooling rate has proven to be a determining factor in the prediction of failure in both the indium and tin/lead solder systems. This study has shown that the harder or higher melting solders are less susceptible to thermal cycling effects but that they are more likely to fail during initial processing operations. Recommendations are made concerning the optimum bonding system for the achievement of maximum reliability.

Kinser, D. L.↗
NASA NTRS1976

Non-dimensional groups in the description of finite-amplitude sound propagation through aerosols

Several parameters, which have fairly transparent physical interpretations, appear in the analytic description of finite-amplitude sound propagation through aerosols. Typically, each of these parameters characterizes, in some sense, either the sound or the aerosol. It also turns out that fairly obvious combinations of these parameters yield non-dimensional groups which, in turn, characterize the nature of the acoustic-aerosol interaction. This theme is developed in order to illustrate how a quick examination of such parameters and groups can yield information about the nature of the processes involved, without the necessity of extensive mathematical analysis. This concept is developed primarily from the viewpoint of sound propagation through aerosols, although complimentary acoustic-aerosol interaction phenomena are briefly noted.

Scott, D. S.↗