Fluid production and isograd reactions at contacts of carbonate-rich and carbonate-poor layers during progressive metamorphism

ABSTRACT With increasing temperature during prograde metamorphism reactions will occur first at the lithological contacts of mixed pelite and calcsilicate terranes. At these interfaces, a fluid of lower chemical potential of H₂O and CO₂ than that required to produce a fluid in either layer can be produced whether reaction is caused by fluid infiltration or is initially fluid absent. If the interface region does not allow fluid transport then as temperature increases, a fluid pressure greater than lithostatic can develop. At some degree of over-pressure relative to rock pressure, the fluid hydraulically fractures the rock and a gradient in fluid composition away from the contact can be produced. These phenomena occur at the compositional interfaces whenever univariant reactions in the differing layers cross on a temperature vs. mole fraction of CO₂ diagram with slopes of opposite sign. The first occurrence of these reaction products at lithological contacts delineates an isograd that defines temperature as well as the mole fraction of CO₂ at constant pressure in systems open to fluid transport. These isograds can be contrasted with fluid-producing isograds in closed systems. As an illustration of possible effects, the reactions quartz + clinozoisite + muscovite = anorthite + K-feldspar + H₂O and phlogopite + quartz + calcite = tremolite + K-feldspar + H₂O + CO₂ at 4 kbar are analysed and equations for fluid production and transport are developed.     

Finite-element analysis of time-dependent large-deformation problems

An updated Lagrangian finite-element formulation has been developed for time-dependent problems of soil consolidation involving finite deformations. Large plastic strains as well as rotations occur in such problems and nominal stress measures are introduced in the formulation to redefine stresses. This leads to corrective terms for equilibrium and yield violations in addition to geometric stiffening terms in the governing integral equations. The soil is considered to be either a linear elastic or an elastoplastic, critical-state material. Some simple numerical examples are studied to validate the formulation, followed by a detailed analysis of the problem of penetration of a pile into soil. The results of this problem are viewed with emphasis on the physical interpretation and practical significance.     

Relaxation of the Vela pulsar’s angular velocity following its jumps

The dynamics of the vortex lattice in the inner crust of a neutron star is considered. A general equation of motion is obtained and solved under the assumption that there are regions of pinned and of free vortices. By comparing these solutions with observational data for the Vela pulsar, the relative moments of inertia of regions of relaxation with the corresponding characteristic times are calculated for two model stars with different equations of state. It is shown that the theory can be reconciled with observations of the relaxation of pulsar angular velocity only for model stars with extremely stiff equations of state. Translated from Astrofizika, Vol. 40, No. 1, pp. 67–76, January–March, 1997.     

Magnetic field and differential rotation in the radiative zone of the Sun

The problem of the interaction between magnetic fields and differential rotation in the radiative zone of the Sun is investigated. It is demonstrated that effects of magnetic buoyancy can be neglected in the analysis of this interaction. It is shown that hydromagnetic torsional waves propagating from the solar core cannot be responsible for the 22-year solar cycle. A possible geometry of the magnetic field that conforms with stationary differential rotation is considered. A verifying method for hypotheses on the structure of the magnetic field and torsional oscillations in the radiative zone of the Sun is proposed based on helioseismic data.     

Formation of galactic subsystems in light of the magnesium abundance in field stars: The thin disk

Data from our compiled catalog of spectroscopically determined magnesium abundances in stars with accurate parallaxes are used to select thin-disk dwarfs and subgiants according to kinematic criteria. We analyze the relations between the relative magnesium abundances in stars, [Mg/Fe], and their metallicities, Galactic orbital elements, and ages. The [Mg/Fe] ratios in the thin disk at any metallicity in the range ?1.0 dex <[Fe/H] < ?0.4 dex are shown to be smaller than those in the thick disk, implying that the thin-disk stars are, on average, younger than the thick-disk stars. The relative magnesium abundances in such metal-poor thin-disk stars have been found to systematically decrease with increasing stellar orbital radii in such a way that magnesium overabundances ([Mg/Fe] > 0.2 dex) are essentially observed only in the stars whose orbits lie almost entirely within the solar circle. At the same time, the range of metallicities in magnesium-poor stars is displaced from ?0.5 dex < [Fe/H] < +0.3 dex to ?0.7 dex < [Fe/H] < +0.2 dex as their orbital radii increase. This behavior suggests that, first, the star formation rate decreases with increasing Galactocentric distance and, second, there was no star formation for some time outside the solar circle, while this process was continuous within the solar circle. The decrease in the star formation rate with increasing Galactocentric distance is responsible for the existence of a negative radial metallicity gradient (grad _R[Fe/H] = ?0.05 ± 0.01 kpc^?1) in the disk, which shows a tendency to increase with decreasing age. At the same time, the relative magnesium abundance exhibits no radial gradient. We have confirmed the existence of a steep negative vertical metallicity gradient (grad _Z[Fe/H] = ?0.29 ± 0.06 kpc^?1) and detected a significant positive vertical gradient in relative magnesium abundance (grad _Z[Mg/Fe] = 0.13 ± 0.02 kpc^?1); both gradients increase appreciably in absolute value with decreasing age. We have found that there is not only an age-metallicity relation, but also an age-magnesium abundance relation, in the thin disk. We surmise that the thin disk has a multicomponent structure, but the existence of a negative trend in the star formation rate along the Galactocentric radius does not allow the stars of its various components to be identified in the immediate solar neighborhood.