Exponential instability of collision orbit in the anisotropic Kepler problem

The straight-line collision solution in the anisotropic Kepler problem is extended to a periodic solution by means of Sundman's analytic continuation. It is shown that this collision periodic solution is always exponentially unstable.     

A note on Kowalevski exponents and the non-existence of an additional analytic integral

In Hamiltonian systems with a homogeneous rational potential and two degrees of freedom, the presence of imaginary Kowalevski exponents implies the non-existence of an additional analytic integral, i.e., non-integrability of the system.     

Non-uniform across-shelf variations in thickness, grain size, and frequency of turbidites in a transgressive outer-shelf, the Middle Pleistocene Kakinokidai Formation, Boso Peninsula, Japan

Across-shelf variations in thickness, grain size, and frequency of sandstone beds in a transgressive outer-shelf succession were investigated from the Middle Pleistocene (ca. 0.7 Ma) Kakinokidai Formation on the Boso Peninsula, Japan. The transgressive deposits are generally muddy and contain slumps and slump scars. The intercalated sandstone beds are interpreted to have been formed from turbidity currents as a response to erosion and resuspension of sandridge-complex deposits in the southwestern upslope area during storm events. Mapping of volcanic ash beds and a transgressive surface in the base of the formation permits detailed bed-by-bed correlation of the outer-shelf sandstone beds. Although, overall, thickness, grain size, and frequency of sandstone beds decrease in the downslope direction, some sandstone beds locally thin out and coarsen in association with slump scars in the surrounding muddy deposits. These sandstone beds subsequently thicken and fine, and finally thin out in the farther downslope area. In addition to the local thinning of sandstone beds, the frequency of sandstone beds first decreases and then increases in the farther offshore direction. From this evidence, we concluded that these non-uniform patterns of across-outer-shelf variations in thickness, grain size, and frequency of sandstone beds were caused by the local increases in flow speeds and subsequent expansion and reduced speeds of turbidity currents, along with a local increase in the seafloor gradient that was induced by the development of slump scars in the transgressive outer-shelf floor. These physiographic features in the outer shelf are interpreted not to have permitted monotonous downslope thinning and fining of sandstone beds, compared with the bed-shape models of depletive turbidity currents and with the proximality trend of shelf sandstones from modern and ancient highstand-stage shelf systems.     

Scoria cone formation through a violent Strombolian eruption: Irao Volcano, SW Japan

Scoria cones are common volcanic features and are thought to most commonly develop through the deposition of ballistics produced by gentle Strombolian eruptions and the outward sliding of talus. However, some historic scoria cones have been observed to form with phases of more energetic violent Strombolian eruptions (e.g., the 1943–1952 eruption of Parícutin, central Mexico; the 1975 eruption of Tolbachik, Kamchatka), maintaining volcanic plumes several kilometers in height, sometimes simultaneous with active effusive lava flows. Geologic evidence shows that violent Strombolian eruptions during cone formation may be more common than is generally perceived, and therefore it is important to obtain additional insights about such eruptions to better assess volcanic hazards. We studied Irao Volcano, the largest basaltic monogenetic volcano in the Abu Monogenetic Volcano Group, SW Japan. The geologic features of this volcano are consistent with a violent Strombolian eruption, including voluminous ash and fine lapilli beds (on order of 10^?1 km³ DRE) with simultaneous scoria cone formation and lava effusion from the base of the cone. The characteristics of the volcanic products suggest that the rate of magma ascent decreased gradually throughout the eruption and that less explosive Strombolian eruptions increased in frequency during the later stages of activity. During the eruption sequence, the chemical composition of the magma became more differentiated. A new K–Ar age determination for phlogopite crystallized within basalt dates the formation of Irao Volcano at 0.4?±?0.05 Ma.     

Influence of fine sediment on the fluidity of debris flows

Debris flows include a great diversity of grain sizes with inherent features such as inverse grading, particle size segregation, and liquefaction of fine sediment. The liquefaction of fine sediment affects the fluidity of debris flows, although the behavior and influence of fine sediment in debris flows have not been examined sufficiently. This study used flume tests to detect the effect of fine sediment on the fluidity of laboratory debris flows consisting of particles with various diameters. From the experiments, the greatest sediment concentration and flow depth were observed in the debris flows mixed with fine sediment indicating increased flow resistance. The experimental friction coefficient was then compared with the theoretical friction coefficient derived by substituting the experimental values into the constitutive equations for debris flow. The theoretical friction coefficient was obtained from two models with different fine-sediment treatments: assuming that all of the fine sediments were solid particles or that the particles consisted of a fluid phase involving pore water liquefaction. From the comparison of the friction coefficients, a fully liquefaction state was detected for the fine particle mixture. When the mixing ratio and particle size of the fine sediment were different, some other cases were considered to be in a partially liquefied transition state. These results imply that the liquefaction of fine sediment in debris flows was induced not only by the geometric conditions such as particle sizes, but also by the flow conditions.     

Use of DEM data to monitor height changes due to deforestation

Deforestation has been a major cause of climate change and other environmental problems. An accurate estimation of the volume of deforested area is needed for United Nations Reducing Emissions from Deforestation and Forest Degradation (UN-REDD+) policies implementation and global carbon accounting. Accurate information about three-dimensional (3-D) structure of forests is required to quantify forest carbon stock. This study demonstrates the use of different digital elevation models (DEMs) to monitor changes in height due to deforestation in Cambodia to support climate change mitigation policies of UN-REDD+. The Shuttle Radar Topographic Mission-DEM (SRTM-DEM), Advanced Spaceborne Thermal Emission and Reflection Radiometer Global DEM (ASTER-GDEM) and Panchromatic Remote sensing Instrument for Stereo Mapping-Digital Surface Model (PRISM-DSM) data were calibrated using Ice Cloud and land Elevation Satellite Geoscience Laser Altimeter System (ICESat–GLAS) data. The results obtained from this study clearly indicate the changes in the height of forests due to deforestation activity. The height of cutover forest generated from the PRISM-DSM and SRTM-DEM is more reliable than that from the PRISM-DSM and ASTER-GDEM data. Field data has also been used to validate the height of the cutover forests, which shows ±5 m uncertainties in the estimation.     

Prediction of ground motion in the Osaka sedimentary basin associated with the hypothetical Nankai earthquake

We studied the long-period ground motions in the Osaka sedimentary basin, Japan, which contains a 1- to 3-km thickness of sediments and is the site of many buildings or construction structures with long-natural period. We simulated the broadband ground motions likely to be produced by the hypothetical Nankai earthquake: the earthquake expected to give rise to the most severe long-period ground motion within the basin. For the simulation, we constructed multiscale heterogeneous source models based on the Central Disaster Management Council of Japan (CDMC) source model and adopted a hybrid computation method in which long-period motion and short-period motion are computed using a 3-D finite difference method and the stochastic Green’s function method, respectively. In computing long-period motions, we used a 3-D structure model of the crust and the Osaka sedimentary basin. The ground motions are estimated to have peak velocities of 50–90 cm/s, prolonged durations exceeding 300 s, and long predominant periods of 5–10 s in the area with great thickness of sediments. The predominant periods are in agreement with an approximate evaluation by 4 H/V _s where H and V _s are the thickness of the sediment and the average S wave velocity, respectively.     

Recent progress in the theory and application of symplectic integrators

In this paper various aspect of symplectic integrators are reviewed. Symplectic integrators are numerical integration methods for Hamiltonian systems which are designed to conserve the symplectic structure exactly as the original flow. There are explicit symplectic schemes for systems of the formH=T(p)+V(q), and implicit schemes for general Hamiltonian systems. As a general property, symplectic integrators conserve the energy quite well and therefore an artificial damping (excitation) caused by the accumulation of the local truncation error cannot occur. Symplectic integrators have been applied to the Kepler problem, the motion of minor bodies in the solar system and the long-term evolution of outer planets.     

On a class of variational equations transformable to the Gauss hypergeometric equation

A new class of linear ordinary differential equations with periodic coefficients is found which can be transformed to the Gauss hypergeometric equation, and therefore the monodromy matrices are computable explicitly. These equations appear as the variational equations around a straight-line solution in Hamiltonian systems of the form H = T(p) + V(q), where T(p) and V(q) are homogeneous functions of p and q, respectively.