The linear stability of the post-Newtonian triangular equilibrium in the three-body problem

Continuing a work initiated in an earlier publication (Yamada et al. in Phys Rev D 91:124016, 2015), we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the standard linear algebraic analysis. In this paper, we start with the Einstein–Infeld–Hoffmann form of equations of motion for N-body systems in the uniformly rotating frame. As an extension of the previous work, we consider general perturbations to the equilibrium, i.e., we take account of perturbations orthogonal to the orbital plane, as well as perturbations lying on it. It is found that the orthogonal perturbations depend on each other by the first post-Newtonian (1PN) three-body interactions, though these are independent of the lying ones likewise the Newtonian case. We also show that the orthogonal perturbations do not affect the condition of stability. This is because these do not grow with time, but always precess with two frequency modes, namely, the same with the orbital frequency and the slightly different one due to the 1PN effect. The condition of stability, which is identical to that obtained by the previous work (Yamada et al. 2015) and is valid for the general perturbations, is obtained from the lying perturbations.     

Ab initio investigation into the elasticity of ultrahigh-pressure phases of SiO2

In this study, we report the elastic properties of three ultrahigh-pressure phases of SiO₂: pyrite, cotunnite and Fe₂P types between 300 and 1,500 GPa calculated by means of the density functional ab initio method. It is generally thought that materials tend to be more compact and isotropic with increasing pressure. These three ultrahigh-pressure phases of silica are mechanically stable in the investigated pressure range according to the Born criteria, while the cotunnite and Fe₂P types are unstable at lower pressure. The elastic azimuthal anisotropy of these ultrahigh-pressure phases of silica shows that all the structures counterintuitively have considerable anisotropies even at multimegabar pressures. Among the three investigated structures, the cotunnite type of SiO₂ is the most elastically anisotropic phase due to a soft compression along the b axis combined with a large distortion of the polyhedrons that make the structure. This might also be related to its thermodynamic unfavorability compared to the Fe₂P type under extreme pressure condition. The bond property analyses clearly show that the Si–O bond remains an ionic-covalent mixed bond even at multimegabar pressures with an invariable ionicity with pressure. This argument can explain the monotonously pressure dependence of the elastic anisotropy in the case of pyrite, while the changes in the velocity distribution patterns out of the thermodynamic instability range largely contribute to those of the cotunnite and Fe₂P types.     

X-ray CT based numerical analysis of fracture flow for core samples under various confining pressures

The X-ray CT based numerical analysis of fracture flow for core samples, recently developed by the authors, was applied to two granite core samples having either a mated artificial or a mated natural fracture at confining pressures of 5 to 50 MPa. A third-generation medical X-ray CT scanner was used to image the samples within a core holder consisting of an aluminum liner and a carbon fiber overwrap. Fracture models (i.e., aperture distributions) were obtained by the CT images, the resolution of which was coarser than the apertures, and a single-phase flow simulation was performed using a local cubic law-based fracture flow model. Numerical results were evaluated by a fracture porosity measurement and a solution displacement experiment using NaCl and NaI aqueous solutions. These numerical results coincided only qualitatively with the experimental results, primarily due to image noise from the aluminum liner of the core holder. Nevertheless, the numerical results revealed flow paths within the fractures and their changes with confining pressure, whereas the experimental results did not provide such results. Different stress-dependencies in the flow paths were observed between the two samples despite the similar stress-dependency in fracture porosity and permeability. The changes in total area of the flow paths with confining pressure coincided qualitatively with changes in breakthrough points in the solution displacement experiment. Although the data is limited, the results of the present study suggest the importance of analyzing fluid flows within naturally fractured core samples under in situ conditions in order to better understand the fracture flow characteristics in a specific field. As demonstrated herein, X-ray CT-based numerical analysis is effective for addressing this concern. Using a multi-phase flow model, as well as a core holder constructed of an engineered plastic, should provide a useful, non-destructive, and non-contaminative X-ray CT-based fracture flow analysis for core samples under in situ conditions in future studies.     

The slowly varying component of the solar radio emission around 1 cm wavelength

The slowly varying component of the solar radio emission (S-component) has been investigated from data obtained in the United States and Japan at 35, 17, 9.4 and 4 GHz. A good correlation occurs between the 35 GHz flux of the S-component and the corresponding plage area. This is interpreted by the assumption that the 35 GHz radiation is due to pure free-free emission, and the electron density in the coronal condensation is estimated to be about 2 × 10⁹/cm³, assuming the electron temperature to be 2 × 10⁶ K and the scale height of the coronal condensation to be 3 × 10⁴ km.The S-component radiation at 17 GHz has, in turn, two components, one is due to pure free-free emission and the other is due to thermal-gyro emission. It is concluded that in the active regions a magnetic field of more than 2000 gauss extends horizontally over about 10⁴ km.     

Detection and accuracy of landslide movement by InSAR analysis using PALSAR-2 data

Interferometric synthetic aperture radar (InSAR) analysis is a radar technique for generating large-area maps of ground deformation using differences in the phase of microwaves returning to a satellite. In recent years, high-resolution SAR sensors have been developed that enable small-scale slope deformation to be detected, such as the partial block movement of a landslide. The L-band SAR (PALSAR-2) is mounted on Advanced Land Observing Satellite-2 (ALOS-2), which was launched on 24 Mar. 2014. Its main improvements compared with ALOS are enhanced resolution of as high as 3 m with a high-frequency recurrence period (14 days). Owing to its high resolution and the use of the L-band, PALSAR-2 can obtain reflective data passing through a tree canopy surface, unlike the other synthetic aperture radars. Therefore, the coherence of InSAR in mountainous forest areas is less likely to decrease, making it advantageous for the extraction of slope movement. In this study, to verify the accuracy of InSAR analysis using PALSAR-2 data, we compared the results of InSAR analysis and the measurement of the displacement in a landslide by global navigation satellite system (GNSS) observation. It was found that the average difference between the displacements obtained by InSAR analysis and the field measurements by GNSS was only 15.1 mm in the slant range direction, indicating the high accuracy of InSAR analysis. Many of the areas detected by InSAR analysis corresponded to the locations of surface changes due to landslide activity. Additionally, in the areas detected by InSAR analysis using multiple datasets, the ground changes due to landslide movement were confirmed by site investigation.     

Spectrum of slowly varying component of solar radio emission on millimeter wavelengths

The spectrum of the S-component of solar radio emission has been investigated at 4 GHz, 17 GHz, 35 GHz, 70 GHz, and 94 GHz. The spectrum for a spot group which appeared late in March 1966 (McMath plage No. 8223), seems to be flat at the frequencies above about 35 GHz. This implies that the emission is due to pure free-free emission at the frequencies above 35 GHz.     

Chemical reaction diversity of geofluids revealed by hydrothermal experiments under sub- and supercritical states

Abstract   Hydrothermal experiments of dissolution of granite and quartz with pure water up to 600°C and 60 MPa were carried out in order to evaluate chemical reaction under sub- and supercritical conditions. The supercritical region beyond the critical point for water has been inferred to be a homogeneous state, which does not correspond to either a true liquid phase, or a true vapor phase. Results of dissolution experiments of granite and quartz in a supercritical state (artificially defined as higher pressures and temperatures than the critical point), show this fluid can be subdivided into two apparent phases comprising a 'liquid-like' region and a 'vapor-like' region. Chemical phenomena with respect to dissolution reactions in the 'liquid-like' region are more similar to those of subcritical water, whilst those reactions in the 'vapor-like' region even in the supercritical state are considered to be weak. The critical point of various kinds of geofluids, composed of solutions in the H₂O-CO₂-NaCl system was experimentally determined using a visible type autoclave. Chemical reaction diversity, depending on location of the critical point for a given solution and apparent phase boundary in terms of chemical reaction within the supercritical state, was recognized by hydrothermal experiments.     

Sequential high-pressure transformations of FeGeO3 high-P clinopyroxene (C 2 /c) at temperatures up to 365 ¯C

 In order to elucidate high-pressure transformations of high-P clinopyroxene (C2/c) at kinetically low temperature where atoms are not thermally activated, the transformation processes of FeGeO₃ clinopyroxene (C2/c) have been investigated at pressures up to 20 GPa and 365 °C by powder X-ray diffraction using a synchrotron radiation source and TEM observation. With increasing pressure up to 20 GPa at room temperature, FeGeO₃ high-P clinopyroxene (C2/c) reversibly transforms into a new high-pressure phase, FeGeO₃(II). On increasing the temperature up to 365 °C, this phase rapidly transforms into FeGeO₃ ilmenite within about 2 h. Intensity analysis of the X-ray diffraction pattern reveals that the high-pressure phase of FeGeO₃(II) has an intermediate structure between clinopyroxene and ilmenite: the cation arrangement is similar to that of clinopyroxene and the oxygen arrangement is similar to that of ilmenite. The comparison of the crystal structures of these polymorphs suggests that clinopyroxene to FeGeO₃(II) and FeGeO₃(II) to ilmenite transformations are performed by the slight deformation of the oxygen packing and the short-range movement of cations, respectively. It is shown that this high-P clinopyroxene transforms into ilmenite through a low-activation energy path under the low-temperature condition. Received: 30 August 2000 / Accepted: 10 February 2001     

Survival and disruption of subsystems during a cold collapse

Cold collapse of a cluster composed of small identical clumps, each of which is in virial equilibrium, is considered. Since the clumps have no relative motion with respect to each other initially, the cluster collapses under its own gravity. At the first collapse of the cluster, most of the clumps are destroyed, but some survive. In order to find the condition for the clumps to survive, we made a systematic study in two-parameter space: the number of the clumps N _c and the size of the clump r _v . We obtained the condition N _c ≫ 1 and n _k  ≥ 1, where n _k is related to r _v and the initial radius of the cluster R _ini through the relation R _ini/ r _v  = 2 N ^{( n k +5)/6}_c. A simple analytical argument supports the numerical result. This n _k corresponds to the index of the power spectrum of the density fluctuation in the cosmological hierarchical clustering, and thus our result may suggest that in the systems smaller than 2/Ω h ²)Mpc, the first violent collapse is strong enough to sweep away all the substructures that exist before the collapse.     

Rb-Sr and Sm-Nd Mineral Isochron Ages of the Metamorphic Rocks in the Namaqualand Metamorphic Complex, South Africa

Rb-Sr and Sm-Nd isotopic studies were carried out for metamorphic rocks in the Namaqualand Metamorphic Complex, South Africa. The metamorphic rocks give the Rb-Sr mineral isochron ages (whole-rock - biotite - felsic fractions) of 844±85 Ma and 811.6±6.6 Ma for the lower granulite zone and of 776.5±5.4 Ma for the upper granulite zone. The rocks yield the Sm-Nd mineral isochron ages of 1071±18 Ma (whole-rock - garnet - felsic fractions) and 1067±158 Ma (whole-rock - hornblende - biotite rich fraction - felsic fractions) for the lower granulite zone and of 1052.0±3.6 Ma and 1002.5±1.4 Ma (whole-rock - garnet - felsic fractions) for the upper granulite zone. These age data suggest that the granulite facies metamorphism took place at 1060-1000 Ma, and that the rocks cooled down at 850-780 Ma. The Sr and Nd isotopic compositions of metamorphic rocks are different between the lower and upper granulite zones.