The structure of the X-ray bright corona above active region McMath 12628 and derived implications for the description of equilibria in the solar atmosphere
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Pye, J. P.↗
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Liquid-solid equilibria involving spinel, ilmenite, and ferropseudobrookite in the system 'FeO'-Al2O3-TiO2 in contact with metallic iron
Phase relations in the liquidus temperature region of the system 'FeO'-Al2O3-TiO2 in contact with metallic iron, at a total pressure below 1 atm, have been determined by the quenching technique. Four invariant points have been located, with phase assemblages and temperatures as follows; wuestite, ulvoespinel, nercynite and liquid, 1306 C; ulvoespinel, ilmenite, ferropseudobrookite and liquid, 1340 C; ulvoespinel, hercynite, ferropseudobrookite and liquid, 1367 C; hercynite, ferropseudobrookite, corundum and liquid, 1465 C. The data obtained confirm the presence of a miscibility gap between titanate and aluminate spinels, and provide quantitative data for the effect of Al2O3 on mutual stability relations among spinel, ilmenite, and ferropseudobrookite phases in the presence of liquid at high temperatures and strongly reducing conditions. It is shown that Al2O3 has a strong stabilizing effect on the phase assemblage ferropseudobrookite and spinel relative to ilmenite.
Schreifels, W. A.↗
Abyssal tholeiites from the Oceanographer Fracture Zone. II - Phase equilibria and mixing
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Walker, D.↗
Predicting major element mineral/melt equilibria - A statistical approach
Empirical equations have been developed for calculating the mole fractions of NaO0.5, MgO, AlO1.5, SiO2, KO0.5, CaO, TiO2, and FeO in a solid phase of initially unknown identity given only the composition of the coexisting silicate melt. The approach involves a linear multivariate regression analysis in which solid composition is expressed as a Taylor series expansion of the liquid compositions. An internally consistent precision of approximately 0.94 is obtained, that is, the nature of the liquidus phase in the input data set can be correctly predicted for approximately 94% of the entries. The composition of the liquidus phase may be calculated to better than 5 mol % absolute. An important feature of this 'generalized solid' model is its reversibility; that is, the dependent and independent variables in the linear multivariate regression may be inverted to permit prediction of the composition of a silicate liquid produced by equilibrium partial melting of a polymineralic source assemblage.
Hostetler, C. J.↗
Sulfur-dioxide/water equilibria between 0 and 50 C - An examination of data at low concentrations
In order to resolve the discrepancy noted in values currently used for the first dissociation constant of SO2 in water, the pertinent literature was critically examined and a value of 0.0132 M at 25 C was recommended. An expression correlating this value as a function of temperature for zero-50 C has been developed. Attention is also given to the literature for the Henry's law constant, and a value of 1.242 M/atm at 25 C is recommended. Ionic activity corrections and speciation in more concentrated solutions are discussed, and recommendations are made for estimating the activity coefficients of the various ionic species in solutions of moderate ionic strength.
Maahs, H. G.↗
Forced stationary solutions in a barotropic channel: Multiple equilibria and theory of nonlinear resonance
A barotropic flow over sinusoidal topography in a beta channel in the presence of forcing and dissipation was studied. The work is divided into two parts: (1) computation of the stationary solutions of the model, by Newton's method together with a finite difference approximation, and comparison of solutions with the solutions of the linear theory; (2) development of a nonlinear theory that reproduce the numerical solutions.
Rambaldi, S.↗
A thermodynamic model for subsolidus equilibria in the system CaO-MgO-Al2O3-SiO2
It is shown that the high temperature enthalpy of solution data for pure phases and solid solutions in the CMAS system are, for 'gabbroic' and 'peridotitic' compositions, consistent with available phase equilibrium data for the MAS, CAS and CMAS systems. A refined set of values of thermodynamic properties for these phases and solid solutions is tabulated. The small differences between the new data set and that of Helgeson et al. (1978) arise from new data on heat capacity and enthalpy being incorporated. The important constraints applied and the major difficulties in fitting which arose are summarized.
Wood, B. J.↗
Multiple Equilibria of the Barotropic Vorticity Equation on a Sphere
Multiple states of the barotropic vorticity equation in which the balance is between the first and third terms on the r.h.s. of (1) are given. Solutions of this type were also considered by Charney and Devore (1979) in their discussion of thermally, rather than topographically, forced waves. Whereas in the case of topographic forcing the multiplicity arises from what they called form-drag instability in the wave-zonal flow interaction, in the thermal forcing case the associated instability appears to be the Rossby-wave instability discussed by Lorenz (1972), and the multiple states of the highly truncated model proved to be unstable when more degrees of freedom were added. The multiple statistically steady solutions described are thus novel in that they do not involve form-drag instability, they have stable statistics in calculations with a large number of degrees of freedoms, and they occur on the sphere, with no artificial confinement in a resonant cavity. Furthermore, the solutions are obtained with no external forcing of the zonal flow. The full non-linear equations for two-dimensional non-divergent motion between smooth, rigid boundaries on a sphere were used.
Suarez, M. J.↗
Force-free equilibria of magnetized jets
Force-free equilibrium configurations of magnetic-pressure-dominated magnetized supersonic jets confined by slowly varying external pressure are investigated analytically. For the case where internal dissipation mechanisms are active, the lowest-energy field configuration is found to be the superposition of an axisymmetric mode and a helical mode with a wavelength equal to 5 times the jet radius, and the pressure below which the nonaxisymmetric mode becomes energetically favorable is given as 2700 times the product of the 4th power of the magnetic helicity per unit length and the -6th power of the magnetic flux. A model of the total and polarized emission of such a configuration is developed and applied to the extended well-collimated astronomically resolved jet NGC 6251. The model is shown to reproduce significant features such as transverse oscillations of the ridge line, width oscillations and emission knots, the projected magnetic-field configuration, oscillations of the degree of polarization, and the distribution of the Faraday rotation measure.
Koenigl, A.↗
Determination of solid-liquid phase equilibria in hydrocarbon systems
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Neveu, M. C.↗
Hydrocarbon phase equilibria
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Neveu, M.↗
A coordinate free description of magnetohydrostatic equilibria
The question what geometrical restrictions are imposed on static magnetic fields by the magnetohydrostatic (MHS) equation is addressed. The general mathematical problem is therefore to determine the solutions of the MHS equations in the corona subject to an arbitrary normal component of the magnetic field at the boundary and arbitrary connectivity. What constraints the MHS equations impose on the geometry of the solutions, expressed in metric tensors, will be determined.
Martens, P. C. H.↗
Interfacial tension and vapor-liquid equilibria in the critical region of mixtures
In the critical region, the concept of two-scale-factor universality can be used to accurately predict the surface tension between near-critical vapor and liquid phases from the singularity in the thermodynamic properties of the bulk fluid. In the present work, this idea is generalized to binary mixtures and is illustrated using the data of Hsu et al. (1985) for CO2 + n-butane. The pressure-temperature-composition-density data for coexisting, near-critical phases of the mixtures are fitted with a thermodynamic potential comprised of a sum of a singular term and nonsingular terms. The nonuniversal amplitudes characterizing the singular term for the mixtures are obtained from the amplitudes for the pure components by interpolation in a space of thermodynamic 'field' variables. The interfacial tensions predicted for the mixtures from the singular term are within 10 percent of the data on three isotherms in the pressure range (Pc - P)/Pc of less than 0.5. This difference is comparable to the combined experimental and model errors.
Moldover, Michael R.↗
Three-dimensional equilibria for the extended magnetotail and the generation of field-aligned current sheets
Using the magnetotail equilibrium theory and a solution method outlined by Birn (1987), self-consistent three-dimensional models were constructed for the quiet average magnetotail beyond about 20 RE distance but earthward of a potential distant neutral line, which take into account the decrease of the tail flaring with distance. It is found that this effect is coupled with the presence of magnetic shear and thus with field-aligned electric currents. These currents have the signature of region 1 currents, toward the earth on the dawnside and away on the duskside, and contribute about 500,000 A to the total Birkeland current.
Birn, J.↗
Equilibria, stability and bifurcations of rotating columns of fluid subjected to planar disturbances
Long gyrostatically rotating drops bonded by surface tension are amenable to conventional bifurcation analysis and newer, computer-aided analytical methods, and therefore are useful prototypes of three-dimensional drops. A study is conducted by setting aside instability to Rayleigh's axisymmetric mode and investigating the effects of translationally symmetric (planar) disturbances. The disadvantage of employing single-coordinate representation of drop shapes close to break-up is brought out. It is shown that a family of symmetric two-lobed shapes bifurcates from the main family of perfectly cylindrical shapes when the rotation rate reaches a critical value, in accord with the linearized hydrodynamic analysis of Hocking.
Benner, R. E., Jr.↗
Collisionless reconnection in two-dimensional magnetotail equilibria
A two-dimensional particle simulation model based on the Darwin approximation to Maxwell's equations for studying collisionless reconnection in the magnetotail has been developed. Simulations of the pure ion tearing mode in a thin current sheet with normal B(z) field component demonstrate that in this limit this mode grows more slowly than expected based on previous analytic estimates. The saturation level of the tearing instability greatly surpasses estimates based on a simple trapping argument. The effect of the normal field component on the evolution of the tearing instability is considered. It is found that a normal field of even a few percent on axis strongly inhibits the growth of the instability.
Pritchett, P. L.↗
The equilibria and evolutions of magnetized, rotating, isothermal clouds. V - The effect of the toroidal field
The structures of magnetized clouds are studied from a standpoint of magnetohydrostatic equilibrium between the self-gravity and magnetic and thermal pressure forces. Toroidal as well as poloidal magnetic field is taken into account. Poloidal current flowing along the poloidal magnetic field forms a toroidal field which causes the cloud to be pinched toward the symmetric axis. In contrast to the poloidal field, which plays a role in supporting the cloud, the toroidal field has the effect of shrinking the cloud. A cloud that is pinched by the toroidal field but has a low central density often shows a prolate spheroidal shape. With increasing central density the cloud becomes a concaved oblate spheroid. The maximum mass of the cloud supported by magnetic field and thermal pressure decreases with increasing toroidal field strength. Assuming that a cloud encounters a torsional Alfven wave, and the magnetic field begins to be wound up, the cloud begins dynamical collapse if the cloud mass exceeds the marginally supported maximum mass. This indicates a new mode triggering star formation: toroidal field-induced collapse.
Tomisaka, Kohji↗
Phase equilibria and trace element partitioning in a magma ocean to 260 kilobars
A magma ocean can solidify in a way that is intermediate between perfect equilibrium and perfect fractional crystallization. In order to model quantitatively any fractional crystallization scenario, it is necessary to understand the geochemical characteristics of the phases that crystallize from a magma ocean, and how they vary with pressure. The crystallizing phase is called the liquidus phase, and their identities were determined by numerous experiments utilizing the multianvil apparatus. For chondritic compositions the liquidus phases are as follows: olivine at 1 atmosphere to 100 kilobars; garnet from 100 to about 260 kilobars; silicate perovskite from 260 kilobars to possibly the core-mantle boundary in the Earth.
Herzberg, Claude↗