Reduced Dynamics from the Unitary Group to Some Flag Manifolds : Interacting Matrix Riccati Equations

In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equation satisfies. Our result is a natural generalization of the paper {\bf Chaturvedi et al} (arXiv : 0706.0964 [quant-ph]).Comment: Latex ; 13 pages ; no figur

The Deep Earthquake of June 22, 1966 in Banda Sea : A Multiple Shock

The body waves of the deep earthquake which occurred in the Banda Sea region on June 22, 1966, were recorded by the long-period seismographs of the WWSSN, and they showed very peculiar aspects compared with the waveforms of normal deep earthquakes. In the record of the P wave at each station two successive P phases were clearly distinguished. The fault plane solutions of the first P phases, P_1 and the second, P_2, showed nearly the same pattern. Accordingly P_1 phase was not the stopping phase that is to be expected from the moving source. The relation between the positions of the two foci and the difference between their origin times were determined from the distribution of the difference between the arrival times of the two P waves. The results showed that the second focus was situated on one of the nodal planes of the first shock at a distance of 22 kilometers in the direction of N170°E along the horizontal plane. The difference between the origin times was found to be about 4.8 seconds. The superposition of the two impulsive waves synthesized from the impulse response of the crust-instrumental system and the amplitudes calculated by assuming the fault plane solutions, the relation of the focal positions and the ratio of the seismic moments of the two shocks, gave the theoretical waveform for each station. They showed very good coincidence with the observed records. The most appropriate ratio of the seismic moments was 4.0. Comparing the amplitudes calculated from the point source of shear dislocation with the observed ones, the seismic moments of the first and second shocks were found to be about 1.4×10^25 and 5.6×10^25 dyne-cm, respectively

On the Nature of the Occurrence of Intermediate and Deep Earthquakes. 3. Focal Mechanisms of Multiplets

The relations between the distribution of the foci of foreshocks and aftershocks and the focal mechanisms of main shocks in twenty-five multiplets have been investigated. Foreshocks and aftershocks always occur on one of the nodal planes of a main shock. This is explained by the characteristics of a shear fault plane which has a strong tendency to propagate itself. Considering these properties of multiplets, the slip planes of main shocks are determined from the analyses of the distribution of foci. It is concluded that the slip planes of intermediate and deep earthquakes are generally parallel to the strike of the seismic plane in the regions, and in intermediate earthquakes the cases in which a deeper side block slips down are predominant. Two doublets with remarkably short time intervals are analyzed in detail and upper limit of the propagating velocity of fractures in deep foci is determined at being 4.7 km/sec