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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 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.↗
NASA NTRS1976

Stability of flow of a thermoviscoelastic fluid between rotating coaxial circular cylinders

The stability problem of thermoviscoelastic fluid flow between rotating coaxial cylinders is investigated using nonlinear thermoviscoelastic constitutive equations due to Eringen and Koh. The velocity field is found to be identical with that of the classical viscous case and the case of the viscoelastic fluid, but the temperature and pressure fields are found to be different. By imposing some physically reasonable mechanical and geometrical restrictions on the flow, and by a suitable mathematical analysis, the problem is reduced to a characteristic value problem. The resulting problem is solved and stability criteria are obtained in terms of critical Taylor numbers. In general, it is found that thermoviscoelastic fluids are more stable than classical viscous fluids and viscoinelastic fluids under similar conditions.

Ghandour, N. N.↗
NASA NTRS1977

Evaluation of quasi-square wave inverter as a power source for induction motors

The relative merits of quasi-square wave inverter-motor technology versus a sine wave inverter-motor system were investigated. The empirical results of several tests on various sizes of wye-wound induction motors are presented with mathematical analysis to support the conclusions of the study. It was concluded that, within the limitations presented, the quasi-square wave inverter-motor system is superior to the more complex sine wave system for most induction motor applications in space.

Guynes, B. V.↗
NASA NTRS1976

The optical constants of several atmospheric aerosol species - Ammonium sulfate, aluminum oxide, and sodium chloride

An investigation is conducted of problems which are related to a use of measured optical constants in the simulation of the optical constants of real atmospheric aerosols. The techniques of measuring optical constants are discussed, taking into account transmission measurements through homogeneous and inhomogeneous materials, the immersion of a material in a liquid of a known refractive index, the consideration of the minimum deviation angle of prism measurement, the interference of multiply reflected light, reflectivity measurements, and aspects of mathematical analysis. Graphs show the real and the imaginary part of the refractive index as a function of wavelength for aluminum oxide, NaCl, and ammonium sulfate. Tables are provided for the dispersion parameters and the optical constants.

Toon, O. B.↗
NASA NTRS1975

Cardiovascular imaging and image processing: Theory and practice - 1975; Proceedings of the Conference, Stanford University, Stanford, Calif., July 10-12, 1975

The present collection of papers outlines advances in ultrasonography, scintigraphy, and commercialization of medical technology as applied to cardiovascular diagnosis in research and clinical practice. Particular attention is given to instrumentation, image processing and display. As necessary concomitants to mathematical analysis, recently improved magnetic recording methods using tape or disks and high-speed computers of large capacity are coming into use. Major topics include Doppler ultrasonic techniques, high-speed cineradiography, three-dimensional imaging of the myocardium with isotopes, sector-scanning echocardiography, and commercialization of the echocardioscope. Individual items are announced in this issue.

Harrison, D. C.↗
NASA NTRS1977

A method of determining spectral dye densities in color films

A mathematical analysis technique called characteristic vector analysis, reported by Simonds (1963), is used to determine spectral dye densities in multiemulsion film such as color or color-IR imagery. The technique involves examining a number of sets of multivariate data and determining linear transformations of these data to a smaller number of parameters which contain essentially all of the information contained in the original set of data. The steps involved in the actual procedure are outlined. It is shown that integral spectral density measurements of a large number of different color samples can be accurately reconstructed from the calculated spectral dye densities.

Friederichs, G. A.↗
NASA NTRS1977

Orbit-orbit resonances among natural satellites

A qualitative physical description of the orbital resonance mechanism based on a previously published (Greenberg et al. 1972; Greenberg, 1973) mathematical analysis is presented. The fundamental principles of the resonance mechanism are illustrated by an examination of the Titan-Hyperion case. More complex resonances, including Enceladus-Dione, Mimas-Tethys are considered. Resonance phenomena involving the rings of Saturn, the inner three satellites of Uranus, and the inner three Galilean satellites of Jupiter are also discussed. The role of analyses of resonance phenomena in developing theories of satellite formation and evolution is examined.

Greenberg, R.↗
NASA NTRS1977

Viking and STP P78-2 electrostatic charging designs and testing

The design provisions of the Viking and the P78-2 (SCATHA) vehicles and a mathematical analysis of the effect of arcing on typical interface circuits are given. Results of verification testing of the analysis are presented as well as vehicle testing for tolerance to arcing.

Lewis, R. O., Jr.↗
NASA NTRS1977

Research on battery-operated electric road vehicles

Mathematical analysis of battery-operated electric vehicles is presented. Attention is focused on assessing the influence of the battery on the mechanical and dynamical characteristics of dc electric motors with series and parallel excitation, as well as on evaluating the influence of the excitation mode and speed control system on the performance of the battery. The superiority of series excitation over parallel excitation with respect to vehicle performance is demonstrated. It is also shown that pulsed control of the electric motor, as compared to potentiometric control, provides a more effective use of the battery and decreases the cost of recharging.

Varpetian, V. S.↗
NASA NTRS1978

Helicopter external noise prediction and correlation with flight test

Mathematical analysis procedures for predicting the main and tail rotor rotational and broadband noise are presented. The aerodynamic and acoustical data from Operational Loads Survey (OLS) flight program are used for validating the analysis and noise prediction methodology. For the long method of rotational noise prediction, the spanwise, chordwise, and azimuthwise airloading is used. In the short method, the airloads are assumed to be concentrated at a single spanwise station and for higher harmonics an airloading harmonic exponent of 2.0 is assumed. For the same flight condition, the predictions from long and short methods of rotational noise prediction are compared with the flight test results. The short method correlates as well or better than the long method.

Gupta, B. P.↗
NASA NTRS1978

Width of a planetary ring system and the C-ring of Saturn

The growth of particles in a planetary ring system is considered with reference to the C-ring of Saturn. Small particles arising from various sources collide with and temporarily adhere to larger particles, and the paper presents a mathematical analysis of the conditions under which the small particles will stay long enough on the surface of the larger ones so that a permanent bond will develop. It is initially assumed that the only force acting between the particles is gravitational attraction, and upper and lower limits for the width of a planetary ring are determined. The effects of van der Waals forces are then considered.

Smoluchowski, R.↗