Analytical expressions for three different modes in harmonic motion of sliding structures

The problem of response of sliding structures subjected to harmonic support motions is considered. The periodic motions, consisting of the three different modes, stick-stick, stick-slip and slip-slip, are a significant part of the responses to harmonic excitations. Assuming the periodicity of the motion, the condition of the initiation of the slip-slip motion is derived. Then analytical expressions for the occurrence of the periodic motions are obtained without integrating the equations of motion. The accuracy of the analytical expressions is confirmed by comparison with numerical results herein obtained. It is observed that the numerical results are sensitive to the starting and ending times of slip motions.     

Coercivity maxima at low temperatures

Recent measurements have shown that the magnetic coercive forces of some Apollo lunar samples show an un-expected decrease with decreasing temperature at cryogenic temperatures. This behavior can be explained quantitatively in terms of a model which considers additive contributions from a soft, reversible magnetic phase and from a harder, hysteretic magnetic phase.     

Anisotropic magnetic susceptibility of rocks under mechanical stresses

Summary The magnetic susceptibility of a rock under a uniaxial compression () decreases along the axis of compression and increases along the direction perpendicular to the axis, with an increase of . Thus, the magnetic susceptibility of a compressed rock becomes anisotropic.The decrease of longitudinal susceptibility,K (), and the increase of transverse susceptibility,K (), are theoretically derived from a model of rock which assumes the uniaxial anisotropy and the isotropic magnetostriction of magnetic minerals in rocks and a random orientation of the minerals. Results show thatK () decreases toward zero whereasK () increases and approaches a finite asymptotic value with an increase of , and –(/)K () is twice as large as /K () for small values of . These results are in good agreement with experimental data.

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Zusammenfassung Die magnetische Suszeptibilität eines Steines unter zunehmender uniachsigen Druckspannung () nimmt ab längs der Achse der Druckspannung und nimmt zu längs der Richtung senkrecht der Achse. Somit wird die magnetische Suszeptibilität des gedrückten Steines anisotrop.Die Abnahme der longitudinalen Suszeptibilität,K (), und die Zunahme der transversalen Suszeptibilität,K (), werden theoretisch von einem Modell eines Steines hergeleitet, das die uniachsige Anisotropie, die isotrope Magnetostriktion, und eine nichtbevorzugte Orientierung der magnetischen Minerals im Stein annimmt. Die Ergebnisse zeigen, dass mit einer Zunahme des ,K () gegen Null abnimmt, währendK () zunimmt und sich einem begrenzten asymtotitschen Wert nähert und, dass für kleine Werte des , –(/)K () zweimal so gross wie /K () ist. Diese Ergebnisse stimmen gut mit den Versuchangaben überein.

     

Piezo-remanent magnetization of lunar rocks

Summary Characteristics of the piezo-remanent magnetization (PRM) of lunar rocks are particularly interesting in comparison with the PRM of terrestrial rocks, because ferromagnetic constituents in lunar materials are metallic iron grains whose average magnetostriction coefficient is negative. Experimentally observed characteristics of the PRM of lunar rocks are substantially the same as those of the PRM of terrestrial rocks and magnetites, in which is positive. These experimental results indicate that the acquisition mechanism of PRM is due to a non-linear superposition of the magnetoelastic pressure upon the magnetostatic pressure on both sides of the 90° domain walls in ferromagnetic particles, as suggested by Nagata and Carleton.

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Zusammenfassung Die Eigenschaften der piezo-remanenten Magnetisierung (PRM) der Mondgesteine sind besonders interessant im Vergleich mit der PRM der Erdgesteine, weil die ferromagnetischen Bestandteile der Mondmaterien die metallischen Eisenkörnchen sind, derer durchschnittliche Magnetostriktion-Koeffizient negativ ist. Die experimentelle gemessenen Eigenschaften von PRM der Mondgesteine sind wesentlich dieselbe der Erdgesteine und Magnetite, derer positive ist. Solche experimentaren Ergebnisse zeigen an, dass die Erwerbung von PRM durch eine nonlineare Übereinanderwirkung des magnetoelastischen Druckes und des magnetostatischen Druckes gegen die beiden Seiten der 90° Gebietwände der ferromagnetischen Teilchen ist, wie Nagata und Carleton vorgeschlagen haben.

     

Melting relations of peridotite and the density crossover in planetary mantles

Melting relations of primitive peridotite were studied up to 25 GPa. The change of the liquidus phase from olivine to majorite occurs at 16 GPa. We confirmed the density crossover of the FeO-rich peridotite melt and the equilibrium olivine (Fo₉₀) at 7 GPa. Sinking of equilibrium olivine (Fo₉₅) in the primitive peridotite melt was observed up to 10 GPa. The compression curves of FeO-rich peridotitic and komatiite melts reported in this and earlier work suggest that the density crossover in the Earth's mantle will be located at 11–12 GPa at 2000°C, consistent with an previous estimation by C.B. Agee and D. Walker.

The density crossover can play a key role in the Moon and the terrestrial planets, such as the Earth, Venus and Mars. Majorite and some fraction of melt could have separated from the ascending diapir and sunk downwards at the depths below the density crossover. This process could have produced a garnet-rich transition zone in the Earth's mantle. The density crossover may exist in the FeO-rich lunar mantle at around the center of the Moon. The density crossover which exists at the depth of 600 km in the Martian mantle plays a key role in producing a fractionated mantle, which is the source the parent magmas of the SNC meteorites.     

Sr–Nd isotopic and chemical characteristics of the silicic magma reservoir of the Aira pyroclastic eruption, southern Kyushu, Japan

Sr and Nd isotope and geochemical investigations were performed on a remarkably homogeneous, high-silica rhyolite magma reservoir of the Aira pyroclastic eruption (22,000 years ago), southern Kyushu, Japan. The Aira caldera was formed by this eruption with four flow units (Osumi pumice fall, Tsumaya pryoclastic flow, Kamewarizaka breccia and Ito pyroclastic flow). Quite narrow chemical compositions (e.g., 74.0–76.5 wt% of SiO₂) and Sr and Nd isotopic values (⁸⁷Sr/⁸⁶Sr=0.70584–0.70599 and _Nd=−5.62 to −4.10) were detected for silicic pumices from the four units, with the exception of minor amounts of dark pumices in the units. The high Sr isotope ratios (0.7065–0.7076) for the dark pumices clearly suggest a different origin from the silicic pumices. Andesite to basalt lavas in pre-caldera (0.37–0.93 Ma) and post-caldera (historical) eruptions show lower ⁸⁷Sr/⁸⁶Sr (0.70465–0.70540) and higher _Nd (−1.03 to +0.96) values than those of the Aira silicic and dark pumices. Both andesites of pre- and post-caldera stages are very similar in major- and trace-element characteristics and isotope ratios, suggesting that the both andesites had a same source and experienced the same process of magma generation (magma mixing between basaltic and dacitic magmas). Elemental and isotopic signatures deny direct genetic relationships between the Aira pumices and pre- and post-caldera lavas. Relatively upper levels of crust (middle–upper crust) are assumed to have been involved for magma generation for the Aira silicic and dark pumices. The Aira silicic magma was derived by partial melting of a separate crust which had homogeneous chemistry and limited isotope compositions, while the magma for the Aira dark pumice was generated by AFC mixing process between the basement sedimentary rocks and basaltic parental magma, or by partial melting of crustal materials which underlay the basement sediments. The silicic magma did not occupy an upper part of a large magma body with strong compositional zonation, but formed an independent magma body within the crust. The input and mixing of the magma for dark pumices to the base of the Aira silicic magma reservoir might trigger the eruptions in the upper part of the magma body and could produce a slight Sr isotope gradient in the reservoir. An extremely high thermal structure within the crust, which was caused by the uprise and accumulation of the basaltic magma, is presumed to have formed the large volume of silicic magma of the Aira stage.     

End wall effects in experiments on water intrusion along the interface between two homogeneous layers

End wall effect puts an inherent limitation on tank experiments, especially when the problems in a stratified fluid are dealt with. During experiments involving horizontal intrusion along the interface between two homogeneous layers, a curious phenomenon was found, i.e., the tip of the intruding water wedge continues to extend for a short time after supply is stopped, but then it begins to retreat in the cases of relatively high Reynolds numbers. The cause of this retreat of the wedge was investigated and was shown to be attributable to the initial disturbance generated near the mouth of the feeder at the start of water supply which propagates along the interface layer and reflects at the end of the tank as a bulge of the interface layer. The retreat of the intruding wedge would not occur in a sufficiently long tank, and so the cause of the retreat can be considered as one kind of end wall effect in a tank.