A type of second order linear ordinary differential equations with periodic coefficients for which the characteristic exponents have exact expressions

It is shown that the characteristic exponents can be exactly expressed for a type of second order linear ordinary differential equations with periodic coefficients (Hill's equation) which appear as the variational equations of certain periodic solutions of dynamical systems. Key points are the transformation of the equation to the Gauss' hypergeometric differential equation, and evaluation of the trace of monodormy matrix in the complex plane of the independent variable. Two simple examples are given for which the stability of periodic solutions is rigorously analyzed.     

High-resolution observations of solar radio bursts with multi-element compound interferometers at 3.75 and 9.4 GHz

High-resolution observations of solar radio bursts made simultaneously with multi-element compound interferometers at 3.75 and 9.4 GHz are presented.Preliminary results are: (1) The burst of December 16, 1967 showed a change in polarization distribution in the radio source, which suggests a magnetic field change in the source. (2) The existence of the multi-source burst is also confirmed at 3.75 GHz. (3) The source size of the impulsive burst is estimated to be 0.'5. (4) Among the GRF bursts there seem to be two kinds; one has a large angular size and the other has a small one.A brief discussion is given of the burst of December 16, 1967.     

Comparison of surface velocities determined from altimeter and drifting buoy data

Surface velocities determined from trajectory of a drifting buoy from March through November 1987 are compared with surface geostrophic velocities determined from sea surface dynamic topography (SSDT) obtained from altimetry data with the aid of long-term hydrographic observation data. In general, these velocities show similar temporal variations in both zonal and meridional components, except in a period when obvious error is found in the altimetric SSDT field. When the buoy was trapped by several mid-ocean meso-scale eddies, the comparison is especially good. Systematic discrepancy is found, however, when the buoy was in the Kuroshio region, because of using both temporally and spatially smoothed mean SSDT estimated from hydrographic data; instead, surface geostrophic velocities determined from the altimetric SSDT referred to the improved geoid model result in better comparison.     

Spin-up and spin-down processes of the large cold water mass of the Kuroshio south of Japan

Time variation of the cold water mass of the Kuroshio south of Japan, which was formed in August 1975 and disappeared in August 1980, is studied. Its lifecycle includes several repetitions of spin-down and spin-up processes. The spin-down (or the spin-up) process is accompanied by warming (cooling) of the cold water mass and descending (ascending) motion of the inner water. Expansion of the cold water area is also associated with the spin-up period while shrinking occurs in the spin-down period. The rate of spin-down of the cold water mass is approximately equal to that of the Gulf Stream rings. The spin-up process is not observed in the Gulf Stream rings and the longer lifetime of the cold water mass off Japan, in comparison with the Gulf Stream rings, is due to the existence of the spin-up periods. The spin-up process tends to occur in late spring to summer, and it seems to be related to the seasonal variation in intensity of the Kuroshio.     

Active strike–slip faulting and macroscopically nonrigid deformation of volcanic rocks in central Japan inferred from a paleomagnetic study

Detailed paleomagnetic investigation of a pyroclastic flow deposit has clarified the deformation mode around an active fault. In central Japan, the early Quaternary Nyukawa Pyroclastic Flow Deposit is cut by the active dextral Enako fault. Activity level of the fault is evaluated on the basis of geological and geomorphological surveys. Then, paleomagnetic samples are collected from 22 sites at exposures located on a lineament that is adjoining and parallel to the Enako fault. Stable thermoremanent magnetization (TRM) of the pyroclastic deposit is isolated through progressive thermal and/or alternating field demagnetization tests. Untilted site-mean directions of the TRMs simultaneously acquired during initial cooling indicate significant clockwise vertical-axis rotation. The lineament was then activated with right-lateral motions through the early Quaternary. Together with the late Quaternary activities along the adjoining Enako fault evaluated by our study, the present result exemplifies a migration of active segments within a fault system during the Quaternary. Paleomagnetic directions on the strike–slip fault are not concordant with uniform deformation predicted by the model of rotation of rigid blocks aligned on a master fault, but suggestive of a periodic deformation as a result of intense fracturing and differential rotation of blocks bounded by nested parallel faults.     

Structure refinement of a nonstoichiometric pyroxene synthesized under ambient pressure

Structure refinement was carried out on a nonstoichiometric clinopyroxene grown under the ambient pressure from a glass with composition of 23%(mol)Di+53%Es+24%An. The degree of nonstoichiometry in this crystal is significantly larger than those of clinopyroxenes reported previously, which were found in high pressure products. The refinement gave the empirical chemical formula (Ca_0.742Fe_0.087)(Mg_0.016Al_0.888Fe_0.075)(Al_0.500Si_1.500)O₆ for the crystal and showed that vacancies are located mainly at M2 sites. Despite replacement of Si by Al, the crystal has a smaller cell volume than diopside primarily owing to a significant amount of Mg at M1 being replaced by Al. Received: 25 June 1997 / Revised, accepted: 6 September 1997     

The crystal structure of CaFe3+SiAlO6 and the crystal chemistry of Fe3+—Al3+ substitution in calcium Tschermak's pyroxene

The crystal structure of a synthetic CaFe³⁺Al-SiO₆ pyroxene (20 kb, 1,375° C) with unit cell dimensions a=9.7797(16), b=8.7819(14), c=5.3685(5) Å, =105.78(1), space group C2/c has been refined by the method of least squares to an R-factor of 0.025 based on 812 reflections measured on an automatic single crystal diffractometer. The octahedral M1 site is occupied by 0.82 Fe³⁺ and 0.18 Al³⁺. Within the tetrahedral T site, Si⁴⁺ (0.50), Al³⁺ (0.41) and Fe³⁺ (0.09) ions are completely disordered, although submicroscopic domains with short-range order are very likely. The octahedral site preference energy of the Fe³⁺ ions with respect to Al³⁺ ions in CaFe³⁺AlSiO₆ is about 10 kcal/mole, which is much higher than that found in Y₃Al _x Fe_5–2O₁₂ garnets. Topologically the structure of CaFe³⁺AlSiO₆ is intermediate between that of diopside and calcium Tschermak's pyroxene, CaAlAlSiO₆. For CaM³⁺ AlSiO₆ clinopyroxenes an increase in the size of the M1 octahedron is accompanied by an increase in the average M2-0, bridging T-0 and 03-03 distances and kinking of the tetrahedral chain.     

57Fe mössbauer study of synthetic Fe3+-melilites

Synthetic Fe³⁺-melilites containing NaCaFe³⁺-Si₂O₇-, Ca₂Fe³⁺AlSiO₇- or Sr₂Fe³⁺AlSiO₇-components have been studied by ⁵⁷Fe Mössbauer spectroscopy. The spectrum of åkermanite containing an NaCaFe³⁺Si₂O₇-component consists of one doublet identified to belong to Fe³⁺ in T1 sites. The spectra of åkermanite and gehlenite containing Ca₂Fe³⁺ AlSiO₇- or Sr₂Fe³⁺ AlSiO₇-component consist of two doublets. The inner and outer doublets are identified to belong to Fe³⁺ in the less distorted T1 and that in the more distorted T2 sites, respectively. The area ratios of the spectra show that the site occupancy of Fe³⁺ (T1) in gehlenite is less than that in åkermanite in which the distribution of Fe³⁺ in T1 and T2 sites is apparently random. The different distributions can be explained in terms of competition between minimizing the deficiency in the electrostatic valence and the preference of Al for T1 sites which the isomer shift measurements show to be more ionic.     

A preliminary study of D/H ratios of chlorites

Chemistry dependence of D of chlorites is inferred from data for natural chlorites. D of water equilibrated with those chlorites is estimated to be –2–8.     

Non-linear models for simulating the dynamic damaging process of low-rise reinforced concrete buildings during severe earthquakes

This paper is a study of idealizing a planar reinforced concrete frame as a non-linear dynamic system for the purpose of simulating its inelastic behaviour during severe earthquakes. After having estimated the restoring force characteristics of all constituent members by experimental means (represented, for example, by a group of empirical equations), it is possible to estimate the non-linear characteristics of the complete structure and to trace the damaging process for each constituent member under a given ground motion disturbance. However, this technique, which is directly based on member-level properties, generally requires rather laborious computational procedures; for practical reasons it is necessary to develop a simplified model, reducing the required calculation without losing the substance of the mechanical phenomena. Thus the reliability of simplification by conventional shear modelling is examined in direct comparison with the response results from rigorous modelling. It is concluded that the shear modelling generally yields an inadequate and, in many cases, erroneous result. The primary cause leading to this discrepancy is identified and, based on this discussion, a more appropriate modelling as simple as conventional shear modelling is proposed.