Search NASA⌕ Search

SEARCH · Search NASA

Results for “Number theory”

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.

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

At least 55 records · Page 3

A model for generation of bow-shock-associated upstream waves

A model is proposed for the generation of upstream hydromagnetic waves by proton beams reflected at the earth's bow shock. It is assumed that the reflection process can produce some gyrophase bunching of the protons, thus creating a gyrophase disturbance that propagates with the beam as it streams back along interplanetary field lines. This leads to the production of driven hydromagnetic waves in the left-hand mode. The resulting theory predicts a wave amplitude, frequency, and polarization in the solar wind rest frame. The amplitude depends on the fraction of protons assumed to be phase coherent in their gyromotion and on the plasma beta, beam velocity, temperatures, and the Alfven Mach number. The theory also predicts the Doppler-shifted frequencies and the apparent sense of polarization that would be observed in satellite measurement frames.

Fredricks, R. W.↗

Analysis of Mossbauer Fe-57 absorption in an F.C.C. Fe-Co-V alloy

Mossbauer Fe-57 absorption spectra of superparamagnetic F.C.C. Fe sub .34 Co sub .52 V sub 14 (Vicalloy II) have been analyzed using a cluster model and magnetic resonance relaxation theory. The number and magnetic moment of the clusters were determined from magnetization data. A least squares fit to the spectrum at 4.2 K gives sub Hhyp = 175. kG, substantially greater than the value 55 kG inferred just from the observed broadening of the single line spectrum. From this broadening an estimate of 40 kG is obtained for the width of the distribution in Hhyp at 4.2 K arising from compositional fluctuations sub and small cluster effects.

Bambakidis, G.↗

Hydrogen interactions with metals

Review of the literature on the nature and extent of hydrogen interactions with metals and the role of hydrogen in metal failure. The classification of hydrogen-containing systems is discussed, including such categories as covalent hydrides, volatile hydrides, polymeric hydrides, and transition metal hydride complexes. The use of electronegativity as a correlating parameter in determining hydride type is evaluated. A detailed study is made of the thermodynamics of metal-hydrogen systems, touching upon such aspects as hydrogen solubility, the positions occupied by hydrogen atoms within the solvent metal lattice, the derivation of thermodynamic functions of solid solutions from solubility data, and the construction of statistical models for hydrogen-metal solutions. A number of theories of hydrogen-metal bonding are reviewed, including the rigid-band model, the screened-proton model, and an approach employing the augmented plane wave method to solve the one-electron energy band problem. Finally, the mechanism of hydrogen embrittlement is investigated on the basis of literature data concerning stress effects and the kinetics of hydrogen transport to critical sites.

Mclellan, R. B.↗

Thermal energy storage

The principles involved in thermal energy storage by sensible heat, chemical potential energy, and latent heat of fusion are examined for the purpose of evolving selection criteria for material candidates in the low ( 0 C) and high ( 100 C) temperature ranges. The examination identifies some unresolved theoretical considerations and permits a preliminary formulation of an energy storage theory. A number of candidates in the low and high temperature ranges are presented along with a rating of candidates or potential candidates. A few interesting candidates in the 0 to 100 C region are also included. It is concluded that storage by means of reactions whose reversibility can be controlled either by product removal or by catalytic means appear to offer appreciable advantages over storage with reactions whose reversability cannot be controlled. Among such advantages are listed higher heat storage capacities and more favorable options regarding temperatures of collection, storage, and delivery. Among the disadvantages are lower storage efficiencies.

Grodzka, P. G.↗

Spectra of turbulent static pressure fluctuations in jet mixing layers

Spectral similarity laws are derived for the power spectra of turbulent static pressure fluctuations by application of dimensional analysis in the limit of large turbulent Reynolds number. The theory predicts that pressure spectra are generated by three distinct types of interaction in the velocity fields: a fourth order interaction between fluctuating velocities, an interaction between the first order mean shear and the third order velocity fluctuations, and an interaction between the second order mean shear rate and the second order fluctuating velocity. Measurements of one-dimensional power spectra of the turbulent static pressure fluctuations in the driven mixing layer of a subsonic, circular jet are presented, and the spectra are examined for evidence of spectral similarity. Spectral similarity is found for the low wavenumber range when the large scale flow on the centerline of the mixing layer is self-preserving. The data are also consistent with the existence of universal inertial subranges for the spectra of each interaction mode.

Jones, B. G.↗

Electronic properties of PbMo6S8 and CuxMo6S8

Normal-state properties of sputtered, evaporated, and sintered PbMo6S8 and CuxMo6S8 (where x is between 1.6 and 2.5) samples are reported. These include the temperature dependence of resistivity, magnetoresistance, and Hall effect. When combined with superconducting properties (measured on the same samples) and theory, a number of Fermi-surface and superconducting parameters are derived. Fits to the temperature dependence of the resistivity are compared with similar fits for A-15 structure superconductors.

Woollam, J. A.↗

Baffle aperture design study of hollow cathode equipped ion thrusters

A simple theoretical model which can be used as an aid in the design of the baffle aperture region of a hollow cathode equipped ion thruster was developed. An analysis of the ion and electron currents in both the main and cathode discharge chambers is presented. From this analysis a model of current flow through the aperture, which is required as an input to the design model, was developed. This model was verified experimentally. The dominant force driving electrons through the aperture was the force due to the electrical potential gradient. The diffusion process was modeled according to the Bolm diffusion theory. A number of simplifications were made to limit the amount of detailed plasma information required as input to the model to facilitate the use of the model in thruster design. This simplified model gave remarkably consistant results with experimental results obtained with a given thruster geometry over substantial changes in operating conditions. The model was uncertain to about a factor of two for different thruster cathode region geometries. The design usefulness was limited by this factor of two uncertainty and by the accuracy to which the plasma parameters required as inputs to the model were specified.

Brophy, J. R., Jr.↗

Natural vibrations of laminated anisotropic plates

This paper contains a description of the three-dimensional elasticity equations and the associated finite element model for natural vibrations of laminated rectangular plates. The numerical results for natural frequencies are compared with those obtained by a shear deformable plate theory. A number of cross-ply and angle-ply rectangular plates are analyzed for natural frequencies. For relatively thick plates, the plate element predicts frequencies higher than those predicted by the 3-D element.

Reddy, J. N.↗

Some crucial corona and prominence observations

A number of theories and hypotheses are currently being developed to explain the often complex behavior of corona and prominence plasmas. In order to test the theories and hypotheses certain crucial observations are necessary. Some of these observations are examined and a few conclusions are drawn. Corona mass balance, corona and prominence classifications, prominence formation and stability, and coronal mass ejection are dicussed.

Tandberg-Hanssen, E. A.↗

Structural control by the use of piezoelectric active members

Large Space Structures (LSS) exhibit characteristics which make the LSS control problem different form other control problems. LSS will most likely exhibit low frequency, densely spaced and lightly damped modes. In theory, the number of these modes is infinite. Because these structures are flexible, Vibration Suppression (VS) is an important aspect of LSS operation. In terms of VS, the control actuators should be as low mass as possible, have infinite bandwidth, and be electrically powered. It is proposed that actuators be built into the structure as dual purpose structural elements. A piezoelectric active member is proposed for the control of LSS. Such a device would consist of a piezoelectric actuator and sensor for measuring strain, and screwjack actuator in series for use in quasi-static shape control. An experiment simulates an active member using piezoelectric ceramic thin sheet material on a thin, uniform cantilever beam. The feasibility of using the piezoelectric materials for VS on LSS was demonstrated. Positive positive feedback as a VS control strategy was implemented. Multi-mode VS was achieved with dramatic reduction in dynamic response.

Fanson, J. L.↗

Perspective on the local interstellar medium

Theoretical local-interstellar-medium (LISM) models designed to explain the observed soft-X-ray background (SXRB) are reviewed. Consideration is given to the LISM in the immediate solar vicinity (the Local Fluff, extending 3-10 pc), the local bubble (a large irregularly shaped cavity filled with very-low-density gas at 10 to the 6th K and surrounded by denser material), the three-dimensional structure of the SXRB emitting region, the thermal nature of the SXRB, and the implications of process time scales for LISM theories. A number of possible mechanisms are discussed in the context of a model in which the LISM hot gas is a remnant from the creation of the local bubble about 20 Myr ago and/or the product of supernova reheating as recently as 150 kyr ago.

Cox, D. P.↗

Advances in understanding the gravity wave spectrum during MAP

Prior to MAP, virtually nothing was known about gravity wave spectra in the atmosphere. The development of observational techniques has played a major role in these studies. Radar and lidar have been particularly important since they can measure atmospheric parameters continuously over large height ranges. Some advances made are: (1) The observed fluctuations and power spectra in the free atmosphere are mostly if not entirely due to a superposition of gravity waves, which can be modeled by the Garrett Munk (GM) model; (2) There is no evidence that 2-D turbulence makes a significant contribution to the observed fluctuations. In any case, the agreement between observations and the GM model shows that the 2DT contribution must be relatively small; (3) Spectra versus vertical wave number are saturated at large wave number, with theory and observations indicating that t approximately equals 3; and (4) Vertical velocity fluctuations and spectra measured near rough terrain are strongly contaminated by mountain waves. But over very flat terrain the spectra are dominated by gravity waves at periods shorter than about 6 hours and apparently by synoptic scale velocities at periods longer than 6 hours. Thus it may be possible to study synoptic scale vertical velocities using radars located in very flat terrain.

Vanzandt, T. E.↗

Experimental and theoretical investigation of boundary-layer instability mechanisms on a swept leading edge at Mach 3.5

A brief outline of the experimental and theoretical investigation of boundary layer instability mechanisms on a swept leading edge at Mach 3.5 is presented. Transition is affected by wind tunnel noise only when roughness is present. Local bar-R sub * Reynolds number and k/eta sub * are useful correlation parameters for a wide range of free stream Mach numbers. Stability theory is in good agreement with the experimental cross flow vortex wavelength. These conclusions are briefly discussed.

Creel, Theodore R., Jr.↗

Group evaporation

Liquid fuel combustion process is greatly affected by the rate of droplet evaporation. The heat and mass exchanges between gas and liquid couple the dynamics of both phases in all aspects: mass, momentum, and energy. Correct prediction of the evaporation rate is therefore a key issue in engineering design of liquid combustion devices. Current analytical tools for characterizing the behavior of these devices are based on results from a single isolated droplet. Numerous experimental studies have challenged the applicability of these results in a dense spray. To account for the droplets' interaction in a dense spray, a number of theories have been developed in the past decade. Herein, two tasks are examined. One was to study how to implement the existing theoretical results, and the other was to explore the possibility of experimental verifications. The current theoretical results of group evaporation are given for a monodispersed cluster subject to adiabatic conditions. The time evolution of the fluid mechanic and thermodynamic behavior in this cluster is derived. The results given are not in the form of a subscale model for CFD codes.

Shen, Hayley H.↗

A preliminary assessment of the Titan planetary boundary layer

Results of a preliminary assessment of the characteristic features of the Titan planetary boundary are addressed. These were derived from the combined application of a patched Ekman surface layer model and Rossby number similarity theory. Both these models together with Obukhov scaling, surface speed limits and saltation are discussed. A characteristic Akman depth of approximately 0.7 km is anticipated, with an eddy viscosity approximately equal to 1000 sq cm/s, an associated friction velocity approximately 0.01 m/s, and a surface wind typically smaller than 0.6 m/s. Actual values of these parameters probably vary by as much as a factor of two or three, in response to local temporal variations in surface roughness and stability. The saltation threshold for the windblown injection of approximately 50 micrometer particulates into the atmosphere is less than twice the nominal friction velocity, suggesting that dusty breezes might be an occassional feature of the Titan meteorology.

Allison, Michael↗

Generation of radiation in solar corona and interplanetary space by energetic electrons

Emissions of electromagnetic waves with frequencies close to the plasma frequency and/or its second harmonic have been frequently observed in the solar corona and interplanetary space. In the past, a number of theories have been put forward to esplain the generation mechanism of the observed radiation. In this paper, a new model is proposed. The essential point of the present theory is that the Langmuir waves amplified as a result of the usual beam instability can lead to two important effects: first, electrostatic waves with frequencies close to twice the plasma frequency can be excited; and second, a significant modification of the dispersion relation can occur, so that these electrostatic waves can naturally change into electomagnetic waves as they propagate in a plasma in which the plasma density decreases spatially. The latter effect is attributed to a mode couplng process. In addition to the second harmonic emission, emission at the fundamental is also briefly discussed. In this case, as in many other theories, the presence of a very low frequency electostatic wave such as the ion-acoustic wave is assumed. The emission process discussed in the present theory stresses the importance of mode coupling and conversion rather than kinetic processes such as a nonlinear wave-wave or wave-particle scattering.

Wu, C. S.↗