Basic phase relations of polybaric batch, percolative and critical melting

Summary ?Partial melting of the mantle is polybaric which implies that the phase relations change during partial melting. In addition to the pressure the composition of the melt depends on the melting mode. Various melting models have been suggested. Here the basic phase relations of polybaric batch, percolative, and critical melting are considered, using a simple ternary system. The percolative melts are in equilibrium with their residua, but differ somewhat in composition from those of batch melting. Critical melting is a fractional type of melting where the residuum contain interstitial melt. The critical melts differ in composition from batch melts. The linear trends of peridotites from ophiolites show that the extracted melts had nearly constant compositions, and therefore were extracted within a small pressure interval. A comparison between the trends of mantle peridotite and experimental batch melts suggests strongly that the melt extracted from the peridotites are in equilibrium with their residua. This could suggest that either batch or percolative melting are relevant melting modes for the mantle. However, isotopic disequilibria favor instead a critical mode of melting. This inconsistency can be avoided if the ascending melts are accumulated within a source region and equilibrate with the residuum before the melt is extracted from the source region. The evidence for equilibrium suggests that multisaturation of tholeiitic compositions in PT-diagrams is relevant for estimating pressure and temperature of generation of primary tholeiitic magmas. Received September 2, 2001; revised version accepted March 20, 2002     

Evidence for a small,high-Z,iron-like solar core

Radial and nonradial oscillation equations without and with the gravitation perturbation (with and without the Cowling approximation, CA) are solved numerically using the profile from a more accurate high-Z core (HZC) solar model. This more accurate HZC model was generated with the CRAY X-MP/48 supercomputer at the San Diego Supercomputer Center. Frequencies of oscillation in the five-min band (5MB) and frequencies with period near 160 min are presented in tables and plotted in echelle diagrams. The model was generated by integrating the stellar structure equations from the center to he surface, as done in Rouse (1964), using a maximum space step, ;x _m = 5 × 10^–4, decreasing to 10^–6 in the hydrogenionization zone just below the photosphere. Two subsets of space mesh points are used to calculate the oscillation frequencies, viz., one with a maximum space step of 5 × 10^–3, decreasing to 10^–6 with a total of 621 points (mesh 5I) and the other with a maximum space step of 2 × 10^–3, with a total of 867 points (mesh 5J).With the surface boundary condition applied at x = 1.0, the l – 1 degree nonradial frequencies with CA and the l-degree frequencies without CA are in very good agreement with the frequency spacings for observed frequencies of oscillation labeled l = 1 to 5, but with the l – 1 frequencies with CA about 10 Hz or so less than the observations and the l frequencies without CA about 10 Hz or so greater than the observations. And for the Duvall and Harvey (1983) observations labeled l = 10 and l = 20, the l = 9 and l = 19 nonradial solutions with CA agree to about 5 Hz or less with the observations. Considering from the two preceeding papers in this series that increasing the density in the outer envelope and photosphere will increase the 5MB frequencies and applying the outer boundary condition at x > 1.0 will decrease the 5MB frequencies, the net affects of such changes could move one or the other set of frequencies closer to the observations — or require a slightly different model structure to obtain accurate agreements with the values of the observed frequencies throughout the 5MB.In either case, it is concluded that the first-order, radially-symmetric structure of the model outside the HZC is close to the structure of the real Sun. This is of fundamental importance because a real gas adiabatic temperature gradient (Rouse, 1964, 1971) is used in the outer convective region without free parameters.Other aspects of agreements and differences between radial and nonradial solutions, with CA and without CA are discussed. In particular, the l = 4, 6, 8, and 9 g-mode solutions with CA indicate that the observed 160.01 min period may be a common l-mode period of oscillation. More research is proposed.     

The buckling of a corrugated carbon fibre cylinder under external hydrostatic pressure

A theoretical and an experimental investigation was carried out, where a carbon fibre corrugated circular cylinder was tested to destuction under external hydrostatic pressure. The theoretical investigation was via the finite element method, where the structure was modelled with several orthotropic axisymmetric thin-walled shell elements. The experimental observations were aided with strategically placed strain gauges. Comparison between theory and experiment showed that the experimentally observed buckling pressure was a little lower than the theoretical prediction. This may have been due to the fact that the model had slight initial geometrical imperfections in the circumferenential direction.     

Dynamics of the long-period tides

The long-period tides are a tool for understanding oceanic motions at low frequencies and large scales. Here we review observations and theory of the fortnightly, monthly and pole tide constitutents. Observations have been plagued by low signal-to-noise ratios and theory by the complex lateral geometry and great sensitivity to bottom slopes. A new spectral element model is used to compute the oceanic response to tidal forcing at 2-week and monthly periods. The general response is that of a heavily damped (Q ≈ 5) system with both the energy input from the moon and the dissipation strongly localized in space. The high dissipation result is probably generally applicable to all low frequency barotropic oceanic motions. Over much of the ocean, the response has both the character of a large-scale and a superposed Rossby wave-like character, thus vindicating two apparently conflicting earlier interpretations. To the extent that free waves are excited they are consistent with their being dominated by Rossby and topographic Rossby wave components, although gravity modes are also necessarily excited to some degree. In general, a modal representation is not very helpful. The most active regions are the Southern Ocean and the western and northern North Atlantic. These results are stable to changes in geometry, topography, and tide period. On a global average basis, the dynamical response of Mm is closer to equilibrium than is Mf.     

A conceptual design of an underwater vehicle

The paper presents a conceptual design of an underwater star wars’ system, which will be more difficult to detect by the enemy than a recently proposed ‘surface’ star wars’ system.The paper suggests that for the proposed structures needed for the underwater star wars’ system, the material of construction should be a composite and not a metal, as use of the latter for large deep diving underwater vessels will result in such structures sinking to the bottom of the ocean like stones, due to the fact that they will have no reserve buoyancy. The paper also shows that composites have better sound absorption characteristics, thereby making the underwater structures difficult to detect through sonar equipment. It is proposed that these underwater structures should operate up to a depth of 7.16 miles (11.52 km), as at this depth, all of the oceans’ bottoms can be reached.The author shows that current technology can be used to construct and operate such vessels, but more progress needs to be made with metal matrix and ceramic composites, so that the hulls of underwater missiles and torpedoes can be constructed in these materials.     

Weak-contrast approximation of the elastic scattering matrix in anisotropic media

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.     

Solar noise storms coordinated observations: May 16–24, 1981

We present the main results obtained from the coordinated observations of solar radio noise storms organized by C.E.S.R.A. in May 1981. They concern the structure and polarization of radio sources, and the relation with the photospheric magnetic field. A model of coronal magnetic field, accounting for the observations, is briefly discussed.     

Distribution of lunar impacts by objects in parabolic low inclination orbits

This paper presents a computer investigation extending to the case of parabolic orbits, an earlier investigation conducted by Barricelli and Metcalfe (1969) on lunar impacts by external low eccentricity satellites as a means to interpret the asymmetric distribution of lunar maria. Parabolic orbits can be approximated by two kinds of objects:

1. High eccentricity external satellites may, near periapsis, approach the Moon with orbital velocity and other characteristics closely resembling those of a parabolic orbit.
2. Asteroids and meteoroids approaching the Earth-Moon system with a low velocity may have moved in a nearly parabolic orbit when they reached the lunar distance from the Earth at the time when the impacts which carved the lunar maria took place.

The investigation gives, therefore, not only additional information relevant to the interpretation of the distribution of lunar maria by the satellite impacts hypothesis (in this case high eccentricity ones), but also information about the alternative hypothesis (Wood, 1973) that asteroid impacts rather than satellite impacts were involved.     

Abrupt climate change: An alternative view

Hypotheses and inferences concerning the nature of abrupt climate change, exemplified by the Dansgaard-Oeschger (D-O) events, are reviewed. There is little concrete evidence that these events are more than a regional Greenland phenomenon. The partial coherence of ice core δ¹⁸O and CH₄ is a possible exception. Claims, however, of D-O presence in most remote locations cannot be distinguished from the hypothesis that many regions are just exhibiting temporal variability in climate proxies with approximately similar frequency content. Further suggestions that D-O events in Greenland are generated by shifts in the North Atlantic ocean circulation seem highly implausible, given the weak contribution of the high latitude ocean to the meridional flux of heat. A more likely scenario is that changes in the ocean circulation are a consequence of wind shifts. The disappearance of D-O events in the Holocene coincides with the disappearance also of the Laurentide and Fennoscandian ice sheets. It is thus suggested that D-O events are a consequence of interactions of the windfield with the continental ice sheets and that better understanding of the wind field in the glacial periods is the highest priority. Wind fields are capable of great volatility and very rapid global-scale teleconnections, and they are efficient generators of oceanic circulation changes and (more speculatively) of multiple states relative to great ice sheets. Connection of D-O events to the possibility of modern abrupt climate change rests on a very weak chain of assumptions.