Search NASA⌕ Search

SEARCH · Search NASA

Results for “equilibrium”

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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Analytic solutions for single and multiple cylinders of gravitating polytropes in magnetostatic equilibrium

Exact analytic solutions for the static equilibrium of a gravitating plasma polytrope in the presence of magnetic fields are presented. The means of generating various equilibrium configurations to illustrate directly the complex physical relationships between pressure, magnetic fields, and gravity in self-gravitating systems is demonstrated. One of the solutions is used to model interstellar clouds suspended by magnetic fields against the galactic gravity such as may be formed by the Parker (1966) instability. It is concluded that the pinching effect of closed loops of magnetic fields in the clouds may be a dominant agent in further collapsing the clouds following their formation.

Lerche, I.↗
NASA NTRS1980

A dynamic analysis of the motion of a low-wing general aviation aircraft about its calculated equilibrium flat spin mode

The properties of the flat spin mode of a general aviation configuration have been studied through analysis of rotary balance data, numerical simulation, and analytical study of the equilibrium state. The equilibrium state is predicted well from rotary balance data. The variations of yawing moment and pitching moment as functions of sideslip have been shown to be of great importance in obtaining accurate modeling. These dependencies are not presently available with sufficient accuracy from previous tests or theories. The stability of the flat spin mode has been examined extensively using numerical linearization, classical perturbation methods, and reduced order modeling. The stability exhibited by the time histories and the eigenvalue analyses is shown to be strongly dependent on certain static cross derivatives and more so on the dynamic derivatives. Explicit stability criteria are obtained from the reduced order models.

Tischler, M. B.↗
NASA NTRS1978

Phase diagram of KHF2 and non-equilibrium effects

The equilibrium diagram for the KHF2-H2O system was constructed from cooling and heating curves for the compositions between 5 wt% and 40 wt% KHF2 and the results are shown. The phase diagrams shown is typical of that of a two component system with miscible liquid phases and whole solid phases consist of pure components. A eutectic point was found at approximately 15% KHF2 which remains completely liquid down to a temperature of -9.0 C. No hydrate formation was observed and no anomalous behavior such as the occurrence of solid transitions or metastable states was observed. The effect of rapid freezing on the equilibrium diagram did not appear, and cooling curves exhibited only one halt. Also, at rapid freezing rates, the supercooling of the solutions was smaller than those observed at the slow cooling rates. The existence of a eutectic composition and the slow rate of dissolution of the salt are used to interpret heat absorption behavior in practical applications of the KHF2-H2O system.

Hobson, M. C.↗
NASA NTRS1980

On the equilibrium of a cylindrical plasma supported horizontally by magnetic fields in uniform gravity

The mechanical equilibrium of a cylinder of plasma suspended horizontally by magnetic fields in uniform gravity is examined. A set of exact solutions describing the equilibrium is derived assuming the plasma distribution to be cylindrically symmetric to obtain an exact force balance between plasma pressure, the Lorentz pressure, and gravity in space. The set of solutions considers a case of uniform temperature and cases where the temperature rises from zero at the center of the plasma cylinder to reach a constant asymptotic value outside the cylinder.

Lerche, I.↗
NASA NTRS1980

Collapse, equilibrium, and fragmentation of rotating, adiabatic clouds

Numerical calculations of the collapse of adiabatic clouds from uniform density and rotation initial conditions show that when restricted to axisymmetry, the clouds form either near-equilibrium spheroids or rings. Rings form in the collapse of low thermal energy clouds and have a ratio of rotational kinetic energy to the absolute value of gravitational potential energy greater than approximately 0.43. When the axisymmetric constraint is removed and an initial m = 2 density variation is introduced, clouds either collapse to form near-equilibrium ellipsoids or else fragment into binary systems through a bar phase. Ellipsoids form in the collapse of high thermal energy clouds and have a rotational kinetic energy/absolute value of gravitational potential energy ratio less than approximately 0.27. The results are consistent with the critical values of the rotational kinetic energy/absolute value of gravitational potential energy ratio for instabilities in Maclaurin spheroids, and suggest that protostellar clouds may undergo a dynamic fragmentation in the nonisothermal collapse regime.

Boss, A. P.↗
NASA NTRS1981

On the equilibrium distribution of the elements in the gas in the Coma cluster

The equilibrium distribution of the elements for the case of an isothermal plasma in a gravitational potential well is given governing equations and a rapidly converging iterative procedure for their solution. Results are applied to the intracluster gas in clusters of galaxies, and implications are identified for the controversy as to whether iron nuclei settle out in the cluster core, and with respect to the interpretation of distribution size and shape for continuum X-ray emission from clusters. A model for the Coma cluster is considered in which the intracluster gas is in equilibrium and partially processed. It is found that this model can account for the angular dependence of the continuum X-ray emission from Coma, as determined by Einstein Observatory observations, at least as well as the uniform composition model.

Abramopoulos, F.↗
NASA NTRS1980

Spinel cataclasites in 15445 and 72435 - Petrology and criteria for equilibrium

The problem of establishing the existence of equilibrium among the coexisting phases in the rock is addressed by presenting petrographic and mineral chemistry data on a new spinel cataclasite from 15445 (clast H) and data more extensive than those previously available on two clasts in 72435. Criteria useful in reconstructing the original petrology of these and other spinel cataclasites are analyzed by considering equilibrium among the different phases, that is, the mono- or polymict nature of these cataclasized samples. Finally, the role of impact processes in disturbing the equilibria is discussed.

Baker, M. B.↗
NASA NTRS1982

A numerical experiment on the equilibrium and stability of a rotating galactic bar

A self-consistent, three-dimensional numerical experiment is performed on an N-body system whose initial state is a realization of a certain theoretical model of a rotating triaxial galaxy. The model is a stellar-dynamical counterpart of a uniformly rotating polytrope of index equal to 0.5. The aim of the experiment is to study the equilibrium of the system and, in particular, to test its stability. The experimental system behaves in the mean like a realization of the theoretical model for at least seven crossing times. The principal departure of the system from equilibrium is an oscillation which is identified as a radial pulsation. There is no indication in its behavior that the system is unstable with respect to anu mode with an e-folding time shorter than or of the order of two crossing times. Certain changes that occur in the state of the system are interpreted, with the aid of the theoretical model, as secular changes which result from a slight failure of our numerical methods to conserve the mass, energy, and angular momentum of the system; these effects are small enough that they do not vitiate the experiment on a dynamical time scale.

Miller, R. H.↗
NASA NTRS1982

A search for equilibrium states

An efficient search algorithm is described for the location of equilibrium states in a search set of states which differ from one another only by the choice of pure phases. The algorithm has three important characteristics: (1) it ignores states which have little prospect for being an improved approximation to the true equilibrium state; (2) it avoids states which lead to singular iteration equations; (3) it furnishes a search history which can provide clues to alternative search paths.

Zeleznik, F. J.↗
NASA NTRS1982

X-ray emission from young supernova remnants - Nonionization equilibrium abundances and emissivities

X-ray line emission from hot, low-density plasma in young supernova remnants is strongly enhanced by departures from ionization equilibrium. The X-ray emission from a Sedov blast wave has been calculated using a nonequilibrium evolutionary treatment of the ionization structure, and the resulting spectrum has been fitted to HEAO 2 SSS data for Tycho's remnant. These models yield dramatically different elemental abundances for heavy elements (Ne, Mg, Si, S, Ar, Ca, and Fe), compared with two-temperature component equilibrium models of Becker et al. (1979, 1980). Nonequilibrium broad-band X-ray emissivities result in lower mass determinations for the supernova ejecta. Areas of further improvement of remnant X-ray modeling are suggested.

Shull, J. M.↗
NASA NTRS1984

The possibility of steady state nonionization equilibrium conditions in soft X-ray flare plasmas

The possibility of the existence in soft X-ray flare plasmas of conditions that result in a steady state departure of ion abundances from ionization equilibrium values is considered. The observed flare plasma is assumed to be a result of many small 'elementary bursts' that occur on time scales comparable to the ionization and recombination times of highly ionized atoms of iron and calcium. Specific models are adopted, the time-dependent equations for ion abundances are solved numerically, and X-ray line intensities and line ratios are computed and averaged over the effective time of a single burst. The computed results are compared to observed variations for a number of different line ratios. Although the behavior of certain line ratios can be explained in the context of the burst models considered in this paper, the behavior of the set of all the available line ratios cannot be explained in this manner. The observed departures of line ratios from equilibrium values that can be explained in terms of a burst scenario can also be accounted for by uncertainties in the atomic physics.

Doschek, G. A.↗
NASA NTRS1984

Spectra from pair-equilibrium plasmas

A numerical model of relativistic nonmagnetized plasma with uniform temperature and electron density distributions is considered, and spectra from plasma in pair equilibrium are studied. A range of dimensionless temperature (T) greater than about 0.2 is considered. The spectra from low pair density plasmas in pair equilibrium vary from un-Comptonized bremsstrahlung spectra at Thomson cross section tau(N) much less than one to Comptonized bremsstrahlung spectra with tau(N) over one. For high pair density plasmas the spectra are flat for T greater than about one, and have broad intensity peaks at energy roughly equal to 3T for T less than one. In the latter region the total luminosity is approximately twice the annihilation luminosity. All spectra are flat in the X-ray region, in contradiction to observed AGN spectra. For dimensionless luminosity greater than about 100, the cooling time becomes shorter than the Thomson time.

Zdziarski, A. A.↗
NASA NTRS1984

Radiative-convective equilibrium models of Jupiter and Saturn

Radiative-convective equilibrium models for Jupiter and Saturn have been produced in a study concentrating on the stratospheric energy balance and the possible role of aerosol heating. These models are compared directly with the thermal structure profiles obtained from Voyager radio occultation measurements. The method is based on a straightforward flux divergence formulation derived from earlier work. The balance between absorbed and emitted energies is computed iteratively at each level in the atmosphere, assuming local thermodynamic equilibrium and employing a standard treatment of opacities. Results for Jupiter indicate that a dust-free model furnishes a good mean thermal profile for the stratosphere when compared with the Voyager 1 radio occultation measurements. Observations of the equatorial region exhibit periodic vertical structure. The Saturn models are relatively simple and in good agreement with the Voyager 2 radio occultation temperature profiles at all levels. Aerosol heating played a minor role in Saturn's midlatitude stratospheric energy balance at the time of the Voyager 2 encounter.

Appleby, J. F.↗
NASA NTRS1984

Electron-positron pair equilibrium in strongly magnetized plasmas

Steady states of thermal electron-positron pair plasmas at mildly relativistic temperatures and in strong magnetic fields are investigated. The pair density in steady-state equilibrium, where pair production balances annihilation, is found as a function of temperature, magnetic field strength and source size, by a numerical calculation which includes pair production attenuation and Compton scattering of the photons. It is found that there is a maximum pair density for each value of temperature and field strength, and also a source size above which optically thin equilibrium states do not exist.

Harding, A. K.↗
NASA NTRS1985

Modelling Equilibrium and Fractional Crystallization in the System MgO-FeO-CaO-Al2O3-SiO2

A mathematical modelling technique for use in petrogenesis calculations in the system MgO-FeO-CaO-Al2O3-SiO2 is reported. Semiempirical phase boundary and elemental distribution information was combined with mass balance to compute approximate equilibrium crystallization paths for arbitrary system compositions. The calculation is applicable to a range of system compositions and fractionation calculations are possible. The goal of the calculation is the computation of the composition and quantity of each phase present as a function of the degree of solidification. The degree of solidification is parameterized by the heat released by the solidifying phases. The mathematical requirement for the solution of this problem is: (1) An equation constraining the composition of the magma for each solid phase in equilibrium with the liquidus phase, and (2) an equation for each solid phase and each component giving the distribution of that element between that phase and the magma.

Herbert, F.↗
NASA NTRS1985

The equilibrium structure of thin magnetic flux tubes. I

A model atmosphere within a thin magnetic flux tube that is embedded in an arbitrarily stratified medium is presently constructed by solving the radiative transfer equation in the two-stream approximation for gray opacity, under the assumption that the magnetic field is sufficiently strong to warrant the neglect of both thermal conduction and convective diffusion; energy inside the flux tube therefore being transported solely by radiation. The structure of the internal atmosphere is determined on the basis of the hydrostatic and radiative equilibrium conditions of the tube embedded in an external atmosphere. The gas temperature along the axis of the tube is computed, and the geometry of the flux tube is determined on the basis of magnetic flux conservation and total pressure equilibrium.

Ferrari, A.↗
NASA NTRS1986

Equilibrium of magnetic fields with arbitrary interweaving of the lines of force. I - Discontinuities in the torsion

Consideration is given to the static force-free equilibrium of a magnetic field in which all of the lines of force connect without knotting between parallel planes. The field is formed by continuous deformation from an initial uniform field, and is conventiently described in terms of the scalar function psi, which is the stream function for the incompressible wrapping and interweaving of the lines of force. Local compression and expansion of the lines of force is described in terms of the scalar function Phi. Equilibrium in the field requires satisfaction of two independent equations which cannot be accomplished without the full freedom of both psi and Phi. It is shown that discontinuities in the torsional characteristics of the lines occur when psi is predetermined by an arbitrary pattern. Discontinuities in the winding pattern of the lines can lead to discontinuities in the associated current sheets.

Parker, E. N.↗
NASA NTRS1986

A two-dimensional, TVD numerical scheme for inviscid, high Mach number flows in chemical equilibrium

A new algorithm has been developed for hypervelocity flows in chemical equilibrium. Solutions have been achieved for Mach numbers up to 15 with no adverse effect on convergence. Two methods of coupling an equilibrium chemistry package have been tested, with the simpler method proving to be more robust. Improvements in boundary conditions are still required for a production-quality code.

Eberhardt, S.↗