SEARCH · Search NASA

Results for “Equation discovery”

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 19 records

All sources NASA NTRS DOE OSTI

NASA NTRS1980

Structure and meteorology of the middle atmosphere of Venus Infrared remote sensing from the Pioneer orbiter

The results of the Pioneer Venus orbiter radiometric temperature-sounding experiment are presented with examples of each of the primary data products. The measured temperature field is used to model the dynamics of the middle atmosphere from 60 to 140 km, and the thermal and solar fluxes are used to calculate the planetary radiation budget. The data for the diurnal variation of temperature at a given height show fairly small amplitudes up to an altitude of about 95 km, above which the day to night contrast increases rapidly with height. At the equator the dependence of temperature in the stratosphere on solar longitude is dominated by a wave number 2 solar tide with an amplitude of about 10 K. The equator to pole gradients are larger than expected, and the stratosphere is typically 15 to 20 K warmer at the pole than at the equator. The most significant discovery concerning the cloud morphology is a dipole structure consisting of two clearings in the cloud at locations straddling the pole and rotating around it every 2.7 days.

Taylor, F. W.↗

NASA NTRS1975

Prolongation structures of nonlinear evolution equations

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Wahlquist, H. D.↗

NASA NTRS1975

Point-connected rigid bodies in a topological tree

The purpose of the present paper is to explore the applicability of several methods of analytical mechanics to the modern problem of formulating generic equations of motion of a point-connected set of rigid bodies in a topological tree, in order to compare the results of the previously published Hooker-Margulies/Hooker equations. The unexpected result of the inquiry is the discovery that with the substitution of a key kinematical identity from the Hooker and Margulies vector-dyadic equations for the multiple-rigid-body tree, identical equations emerge from each of four quite different derivation procedures.

Likins, P. W.↗

NASA NTRS1989

Universal features of the equation of state of solids

A study of the energetics of solids leads to the conclusion that the equation of state for all classes of solids in compression can be expressed in terms of a universal function. The form of this universal function is determined by scaling experimental compression data for measured isotherms of a wide variety of solids. The equation of state is thus known (in the absence of phase transitions), if zero-pressure volume and isothermal compression and its pressure derivative are known. The discovery described in this paper has two immediate consequences: first, despite the well known differences in the microscopic energetics of the various classes of solids, there is a single equation of state for all classes in compression; and second, a new method is provided for analyzing measured isotherms and extrapolating high-pressure data from low-pressure (e.g. acoustic) data.

Vinet, Pascal↗

NASA NTRS1973

Which electromagnetic equations apply in rotating coordinates

It was discovered some years ago by Schiff that two equations for fields in vacuum do not carry over without change from an inertial frame to a frame with rotating axes of space coordinates, even for a region with all velocities much lower than the speed of light. However, the belief that all four of the field equations are invariant under such conditions is still prevalent and causes misconceptions in physical applications, including astrophysical and geophysical ones. The purpose of the present paper is therefore to call attention to Schiff's discovery, discussing its basis and its extension to fields in material media, and to interpret the additional terms that must be added to the equations in order to obtain valid transformations to rotating axes of coordinates.

Webster, D. L.↗

NASA NTRS1978

New trends in cosmology

A review of big-bang cosmology is presented, emphasizing the big-bang model, hypotheses on the origin of galaxies, observational tests of the big-bang model that may be possible with the Large Space Telescope, and the scale-covariant theory of gravitation. Detailed attention is given to the equations of general relativity, the redshift-distance relation for extragalactic objects, expansion of the universe, the initial singularity, the discovery of the 3-K blackbody radiation, and measurements of the amount of deuterium in the universe. The curvature of the expanding universe is examined along with the magnitude-redshift relation for quasars and galaxies. Several models for the origin of galaxies are evaluated, and it is suggested that a model of galaxy formation via the formation of black holes is consistent with the model of an expanding universe. Scale covariance is discussed, a scale-covariant theory is developed which contains invariance under scale transformation, and it is shown that Dirac's (1937) large-numbers hypothesis finds a natural role in this theory by relating the atomic and Einstein units.

Canuto, V. M.↗

NASA NTRS1984

Scaling relations in the equation of state, thermal expansion, and melting of metals

A simple and yet quite accurate prediction of volume as a function of pressure for metals and alloys is presented. Thermal expansion coefficients and melting temperatures are predicted by simple, analytic expressions and results compare favorably with experiment for a broad range of metals. All of these predictions are made possible by the discovery of universality in binding energy relations for metals.

Guinea, F.↗

NASA NTRS1982

Interaction of heat production, strain rate and stress power in a plastically deforming body under tensile test

At high strain rates the heat produced by plastic deformation can give rise to a rate dependent response even if the material has rate independent constitutive equations. This effect has to be evaluated when interpreting a material test, or else it could erroneously be ascribed to viscosity. A general thermodynamic theory of tensile testing of elastic-plastic materials is given in this paper; it is valid for large strain at finite strain rates. It enables discovery of the parameters governing the thermodynamic strain rate effect, provides a method for proper interpretation of the results of the tests of dynamic plasticity, and suggests a way of planning experiments in order to detect the real contribution of viscosity.

Paglietti, A.↗

NASA NTRS1979

Dynamics of liquid films and thin jets

The theory of liquid films and thin jets as one- and two-dimensional continuums is examined. The equations of motion have led to solutions for the characteristic speeds of wave propagation for the parameters characterizing the shape. The formal analogy with a compressible fluid indicates the possibility of shock wave generation in films and jets and the formal analogy to the theory of threads and membranes leads to the discovery of some new dynamic effects. The theory is illustrated by examples.

Zak, M.↗

NASA NTRS1985

The electrostatics of a dusty plasma

Voyager 1 and 2 observations of the Saturnian ring system have led to the discovery of several interesting phenomena associated with its fine dust component. The dust grains are immersed in a plasma. The present paper is concerned with the electrostatics of a dusty plasma, giving particular attention to the capacitance and charge of an individual grain in the presence of neighboring grains and the surrounding plasma. The Poisson equation and gauge considerations are discussed along with a solution of the Poisson equation for several models, taking into account impermeable grains, permeable grains, and a spherical capacitor model. A comparison of potential shapes for three models is conducted, and the effect of neighbors on charging currents is explored.

Whipple, E. C.↗

NASA NTRS1978

Cosmic-ray streaming perpendicular to the mean magnetic field. II - The gyrophase distribution function

The distribution function of cosmic rays streaming perpendicular to the mean magnetic field in a turbulent medium is reexamined. Urch's (1977) discovery that in quasi-linear theory, the flux is due to particles at 90 deg pitch angle is discussed and shown to be consistent with previous formulations of the theory. It is pointed out that this flux of particles at 90 deg cannot be arbitrarily set equal to zero, and hence the alternative theory which proceeds from this premise is dismissed. A further, basic inconsistency in Urch's transport equation is demonstrated, and the connection between quasi-linear theory and compound diffusion is discussed.

Forman, M. A.↗

NASA NTRS1980

A global biogeocenotical biosphere simulation

This model of the D. Forrester type, constructed in differential equations, predicts the food and mineral supply for the factors biosphere population, depending on two socio-economic factors, until about the year 2500. If contemporary rates of natural resources utilization are maintained and there is no management of the environment, food resources will begin to limit human population growth after 2200, and mineral resources will after 2300. A decrease in the biosphere pollution, increase in effective agricultural production, and discovery of new energy sources may forestall or completely avert the onset of a crisis situation. Conservation measures, according to the model, are to a considerable extent realizable only if carried out simultaneously in both areas.

Moiseyev, N. N.↗

NASA NTRS1988

Chemseal 3808-A2 penetration into small leak path

A possible fix to a leak in the oxidizer system of the Space Shuttle Discovery's attitude control system was proposed by MSFC. This fix involved the passing of a shuttlecock past the leaking Dynaflow fitting and sealing the vent tube containing the fitting with Chemseal 3808-A2. The question of whether the Chemseal 3808-A2 can flow into the leak path and provide a better seal was addressed analytically and by experiment to verify the analytical formula used. The results show that the equations are applicable and that the Chemseal will flow into the expected leak path and seal.

Carruth, M. R., Jr.↗

NASA NTRS1981

Discovery and observation of BY Draconis variables

The discovery of BY Draconis variables was efficiently accomplished by a spectroscopic survey of dK-M stars for weak H-alpha emissions, using 1-2 A resolution. The four BY Dra variables discovered are all spectroscopic binaries with P values lower than about 10 d, in light of which, it is noted that the onset of high surface activity and appearance of H-alpha emission occur sharply at v(equator) of approximately 5 km/sec. At v(equator) of about 3 km/sec, dK-M stars have low levels of surface activity. It is found that while there is a range of Ca II emission strength, and only the strongest emitters of this line are BY Dra and/or flare stars, the H-alpha feature changes abruptly to an emission feature signaling the onset of flaring and/or the BY Dra syndrome. An increase of the rotation rate above v(equator) 5 km/sec does not appear to increase the level of surface activity.

Bopp, B. W.↗

NASA NTRS1985

Energy partitioning in the Io plasma torus

The Io plasma torus, which emits substantial amounts of EUV radiation from multiply ionized oxygen and sulfur, represents one of the significant discoveries of the Voyager 1 mission. The present study is concerned with the effects of various physical processes on the density and energy partitioning of the Io plasma torus. For the ions the dominant effects, which have different relative importance in different parameter regimes, are electron impact ionization, charge exchange, electron-ion collisions, and confinement time loss. Attention is given to a physical model, the solution of the quasi-linear equations, the obtained results, and an interpretation of observations in relation to the model results.

Smith, R. A.↗

NASA NTRS1974

Discovery of a magnetic DA white dwarf

The spectrum of the white dwarf suspect, GD 90, is shown to contain broad Balmer lines with resolved Zeeman structure. All the observed features correspond to the calculated spectrum of hydrogen at 5 plus or minus 0.5 MG. A region of approximately 20% of the observed stellar disk must be subject to a reasonably uniform field of this strength. The sigma components of the Zeeman patterns in H beta and H gamma are found to be circularly polarized, indicating that the field has a component directed along the line of sight. There is evidence for an additional stronger and less homogeneous field, as would be expected if the dominant 5 -MG region were at the equator of a dipolar field.

Angel, J. R. P.↗

NASA NTRS1980

Saturn's magnetosphere, rings, and inner satellites

The discovery of the Saturn magnetosphere and its characterization by Pioneer 11 are reported, and findings on the planet's rings and satellites obtained by energetic charged particle measurements within the inner magnetosphere are presented. Bow shock crossings identified by the Pioneer plasma analyzer and magnetometer at distances of 24.1, 23.1 and 20.0 Saturn radii indicate the presence of a magnetosphere with physical dimensions and charged particle populations intermediate between those of the earth and Jupiter, with a scale more similar to that of the earth. Particle angular distributions on the inbound leg of the trajectory are consistent with a dipole magnetic field approximately perpendicular to the planet's equator, while on the outbound leg the distributions indicate the presence of an equatorial current sheet. Charged particle absorption features are detected at the orbits of Dione and Mimas, encompassing the orbits of Tethys and Enceladus, and at 2.534 and 2.343 Saturn radii indicating the presence of satellites of diameters greater than 170 km. Charged particle measurements also confirm the Pioneer division in the rings between 2.292 and 2.336 Saturn radii, a suspected satellite at 2.82 Saturn radii, the presence of the F ring between 2.336 and 2.371 Saturn radii and the outer radius of the A ring at 2.292 Saturn radii.

Van Allen, J. A.↗

NASA NTRS1985

Radiative Amplification of Acoustic Waves in Hot Stars

The discovery of broad P Cygni profiles in early type stars and the detection of X-rays emitted from the envelopes of these stars made it clear, that a considerable amount of mechanical energy has to be present in massive stars. An attack on the problem, which has proven successful when applied to late type stars is proposed. It is possible that acoustic waves form out of random fluctuations, amplify by absorbing momentum from stellar radiation field, steepen into shock waves and dissipate. A stellar atmosphere was constructed, and sinusoidal small amplitude perturbations of specified Mach number and period at the inner boundary was introduced. The partial differential equations of hydrodynamics and the equations of radiation transfer for grey matter were solved numerically. The equation of motion was augmented by a term which describes the absorption of momentum from the radiation field in the continuum and in lines, including the Doppler effect and allows for the treatment of a large number of lines in the radiative acceleration term.

Wolf, B. E.↗