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At least 235 records · Page 13

Crater saturation and equilibrium - A Monte Carlo simulation

Conditions of crater saturation and equilibrium have been simulated with a Monte Carlo computer program which utilizes a generating function of the form N = b x D to the -a. The following conclusions have been deduced from the results of the model: (1) saturation and equilibrium for large craters occur at crater densities substantially greater than those observed on the moon, Mars, and Mercury, an indication that the observed populations are essentially production populations, (2) generating functions with a greater than 2 lead to final crater populations with a = 2, (3) generating functions with a between 2 and 1.5 lead to crater populations with the parameter a approaching 1.0, and (4) changes in the slope of crater populations occur gradually and over a wide interval of crater densities and diameters as saturation is approached.

Woronow, A.↗

Stability of the equilibrium for atomic H in solid H2

The previously reported phenomenological rate process theory for the storage of atomic hydrogen free radicals in a tritium-impregnated crystalline molecular hydrogen solid is used to determine the dynamical stability of the constant uniform equilibrium solution. The analysis indicates that the equilibrium is unstable (thus, unattainable experimentally) for storage temperatures in a certain range (specifically between 0.134 and 0.80 K for 0.03% tritium by weight, and between 0.165 and 0.80 K for 1.20% tritium by weight), while being absolutely stable with respect to arbitrary small-amplitude perturbations for all storage temperatures below and above this range. The theory also predicts the maximum size for a stable H/H2 sample with an appreciable concentration of trapped H and a net excess rate of volumetric heating due to the tritium decay.

Rosen, G.↗

Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouguet Detonations. Interim Revision, March 1976

A detailed description of the equations and computer program for computations involving chemical equilibria in complex systems is given. A free-energy minimization technique is used. The program permits calculations such as (1) chemical equilibrium for assigned thermodynamic states (T,P), (H,P), (S,P), (T,V), (U,V), or (S,V), (2) theoretical rocket performance for both equilibrium and frozen compositions during expansion, (3) incident and reflected shock properties, and (4) Chapman-Jouguet detonation properties. The program considers condensed species as well as gaseous species.

Sanford Gordon↗

Mathematical and computational studies of equilibrium capillary free surfaces

The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated.

Albright, N.↗

On the ortho-para equilibrium of H2 in the atmospheres of the Jovian planets

The ratio for the equivalent widths for the unsaturated H2 quadrupole transitions observed in the Jovian planets is calculated and compared with a large number of observations. The comparison indicates that equilibrium hydrogen may be present in Jupiter and Saturn, while Uranus and Neptune exhibit ratios not in accord with equilibrium hydrogen. Observations which can differentiate among the possible states of H2 are proposed.

Smith, W. H.↗

Equilibrium swelling of elastomers in solvents

Two proposed empirical equations, developed from Eilers-VanDijk equation to characterize relative modulus of filled elastomers as function of filler content, describe: (1) equilibrium swelling for cases where fillers are composed of permanent aggregates of primary particles; and (2) equilibrium swelling when filler material is composed of non-aggregated particles.

Fedors, R. F.↗

SPINEQ: A program for determining aircraft equilibrium spin characteristics including stability

A computer program, SPINEQ, is described which can algebraically solve the nonlinear equations of motion for equilibrium spin conditions. Linear characteristics of the airplane about the equilibrium points are also determined. The theoretical basis of the program is outlined, computational flow is shown, the functions of major subroutines are described, and key parameters directing the computations are identified. Program input and output are described and illustrated by means of a test case. The program is available from COSMIC.

Adams, W. M., Jr.↗

Synthesis of Silane and Silicon in a Non-equilibrium Plasma Jet

The original objective of this program was to determine the feasibility of high volume, low-cost production of high purity silane or solar cell grade silicon using a non equilibrium plasma jet. The emphasis was changed near the end of the program to determine the feasibility of preparing photovoltaic amorphous silicon films directly using this method. The non equilibrium plasma jet should be further evaluated as a technique for producing high efficiency photovoltaic amorphous silicon films.

Calcote, H. F.↗

X-ray evidence for electron-ion equilibrium and ionization nonequilibrium in young supernova remnants

The A-2 spectroscopy experiment on HEAO 1 detected X-ray emission up to 25 keV from the supernova remnants Cas A and Tycho. The spectra must include continuum components with effective temperature equivalent or 10 to the 8th power K which could arise from optically thin plasmas in the collisionless shock fronts. This is the first indication of electron-ion temperature equilibrium in the expanding shell of young remnants. Measurements of the equivalent widths of the K alpha and K beta iron line blends in Cas A, show that their ratio is not compatible with the measured X-ray temperature in the collisional ionization equilibrium model. The search for hard X-ray pulsars in both remnants was unsuccessful.

Pravdo, S. H.↗

Derivation of the chemical-equilibrium rate coefficient using scattering theory

Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.

Mickens, R. E.↗

Dielectronic recombination rates, ionization equilibrium, and radiative energy-loss rates for neon, magnesium, and sulfur ions in low-density plasmas

Results of detailed and systematic calculations are presented for the total dielectronic recombination rate coefficients for the ions of Ne, Mg, and S in a low-density predominantly hydrogen plasma. The new recombination rates are used to calculate solar corona ionization-equilibrium distributions of the ions. The most important effect of dielectronic recombination for ions in corona equilibrium is found to be a shift in the maximum-abundance temperatures toward higher temperatures, which are in some cases reduced from those predicted on the basis of the simple Burgess formula.

Jacobs, V. L.↗

Statistical equilibrium in cometary C2. II - Swan/Phillips band ratios

Statistical equilibrium calculations have been made for both the triplet and ground state singlets for C2 in comets, using the exchange rate as a free parameter. The predictions of the results are consistent with optical observations and may be tested definitively by accurate observations of the Phillips and Swan band ratios. Comparison with the one reported observation indicates compatibility with a low exchange rate and resonance fluorescence statistical equilibrium.

Swamy, K. S. K.↗

Torque equilibrium attitude control for Skylab reentry

All the available torque equilibrium attitudes (most were useless from the standpoint of lack of electrical power) and the equilibrium seeking method are presented, as well as the actual successful application during the 3 weeks prior to Skylab reentry.

Glaese, J. R.↗

Effects of various assumptions on the calculated liquid fraction in isentropic saturated equilibrium expansions

The saturated equilibrium expansion approximation for two phase flow often involves ideal-gas and latent-heat assumptions to simplify the solution procedure. This approach is well documented by Wegener and Mack and works best at low pressures where deviations from ideal-gas behavior are small. A thermodynamic expression for liquid mass fraction that is decoupled from the equations of fluid mechanics is used to compare the effects of the various assumptions on nitrogen-gas saturated equilibrium expansion flow starting at 8.81 atm, 2.99 atm, and 0.45 atm, which are conditions representative of transonic cryogenic wind tunnels. For the highest pressure case, the entire set of ideal-gas and latent-heat assumptions are shown to be in error by 62 percent for the values of heat capacity and latent heat. An approximation of the exact, real-gas expression is also developed using a constant, two phase isentropic expansion coefficient which results in an error of only 2 percent for the high pressure case.

Bursik, J. W.↗

X-ray evidence for electron-ion equilibrium and ionization nonequilibrium in Young supernova remnants

X-ray emission up to 25 keV from the supernova remnants Cas A and Tycho has been detected with the A-2 spectroscopy experiment on HEAO 1. The spectra must include continuum components with effective temperature of about 10 to the 8th K which could arise from optically thin plasmas in the collisionless shock fronts. This is the first indication of electron-ion temperature equilibrium in the expanding shell of young remnants. The equivalent widths of the K-alpha and K-beta iron line blends in Cas A have also been measured and it is found that their ratio is not compatible with the measured X-ray temperature in the collisional ionization equilibrium model. Finally, an unsuccessful search has been conducted for hard X-ray pulsars in both remnants.

Pravdo, S. H.↗

Stellar atmosphere in statistical equilibrium

A static atmosphere with only Lyman continuum radiation in radiative equilibrium is studied for the effects of radiative and collisional ionization on deviations from local thermodynamic equilibrium (LTE). Large increases and decreases of the kinetic temperature (range in T of about factor 2) and, correspondingly, very large over- and underpopulation of the bound state (range in b of about factor 1,000,000) are found, depending on the frequency dependence of the photoionization cross section. Despite these large deviations from LTE, which strongly modify the emergent spectrum, there is almost no effect on the particle densities, the degree of ionization, and the basic structure of the atmosphere.

Kalkofen, W.↗

On the equilibrium structures of self-gravitating masses of gas containing axisymmetric magnetic fields

The general equations describing the equilibrium shapes of self-gravitating gas clouds containing axisymmetric magnetic fields are presented. The general equations admit of a large class of solutions. It is shown that if one additional (ad hoc) asumption is made that the mass be spherically symmetrically distributed, then the gas pressure and the boundary conditions are sufficiently constraining that the general topological structure of the solution is effectively determined. The further assumption of isothermal conditions for this case demands that all solutions possess force-free axisymmetric magnetic fields. It is also shown how the construction of aspherical (but axisymmetric) configurations can be achieved in some special cases, and it is demonstrated that the detailed form of the possible equilibrium shapes depends upon the arbitrary choice of the functional form of the variation of the gas pressure along the field lines.

Lerche, I.↗