Necessary condition for the existence of algebraic first integrals

Existence of algebraic first integrals for a class of dynamical systems is discussed in connection with the nature of the singularities of solutions. It is shown that under some conditions, the existence of algebraic first integrals controls a quantity characterising a singularity (Kowalevski's exponent) which can be calculated in a finite procedure. Two simple examples are given, which illustrate how main theorems work.     

The behavior of a two-dimensional dual forced plume

The behavior of two plumes ejected into a thin water tank is investigated experimentally. As the time elapses, the plume axes deflect towards each other. Time evolution of this two-dimensional, dual forced plume is found to be similar to that of a two-dimensional, single plume ejected near a vertical wall. The symmetric plane of the two plumes in the former case plays the role of the vertical wall. The time required for the dual plume to attain a quasi-steady state is shorter than that for the single plume. The deflection angles of the plume axes are smaller for the dual plume, and the plume water remains near the free water surface in a quasi-steady state. Water circulation in a triangular region surrounded by the free water surface, the side of the plume and the symmetric plane (or the vertical wall for the single plume case) may account for this difference; the circulation is much more pronounced in the single plume case.     

Giant Megamullion in the Parece Vela Backarc Basin

We present results of high-resolution bathymetric studies of the extinct intermediate-spreading Parece Vela Basin in the northwestern Pacific, where we have identified an extremely large mullion structure, here termed a giant megamullion. We find that the giant megamullion is nearly an order of magnitude larger than the similar structures in the slow-spreading Mid-Atlantic Ridge (`megamullions'). The giant megamullion has slightly elevated mantle Bouguer anomaly, and yields serpentinized peridotites and gabbros, suggesting that they are exposing oceanic crust and upper mantle. An off-axis rugged `chaotic terrain' was also identified in the Parece Vela Basin. The terrain consists of isolated and elevated blocks capped by corrugated axis-normal lineations, and associated deeps. We thus interpret it as analogues to the Mid-Atlantic Ridge megamullions. We propose that amagmatic tectonics producing the giant megamullion and the chaotic terrain occupied a significant part in crustal construction in the Parece Vela Basin evolution.     

Recent Occurrences of Dinophysis fortii (Dinophyceae) in the Okkirai Bay, Sanriku, Northern Japan, and Related Environmental Factors

Occurrence of Dinophysis fortii, a causative organism of diarrhetic shellfish poisoning, in the Okkirai Bay, Sanriku was surveyed in 1995, 1996, 1998 and 1999. In each year, its major occurrence was detected from the late May or early June and continued until the late June or early July. Seawater temperature, salinity and nutrients measurements suggested that inflows of offshore water into the bay played key role on the first major occurrence of D. fortii. With an analysis of continuous temperature data in the Otsuchi Bay which locates north of the Okkirai Bay, this influent was considered to be intermittent inflow of the offshore water by internal tidal waves which propagated from north to south. First occurrence peak of D. fortii was synchronous with phycobilin containing microalgae, synechococcoid cyanobacteria and cryptomonad, in all years. In vivo fluorescence measurement of D. fortii cells in 1995 and 96 showed that the cells in these microalgal-rich water contained more phycobilin pigment than those in the microalgal-poor water. The result may support a hypothesis that D. fortii acquires phycobilin by an uptake of these microalgae. After the first major occurrence in the bay, D. fortii sometimes occurred in rather inshore waters where showed elevated ammonium level possibly due to increased heterotrophic activity. Together with another finding that D. fortii is mixotrophic, it could be assumed that the environment being suited to heterotrophic nutrition also stimulates D. fortii growth in the bay.     

Large-Eddy-Simulation Study of the Effects of Building-Height Variability on Turbulent Flows over an Actual Urban Area

Large-eddy simulation (LES) is used to investigate the effects of building-height variability on turbulent flows over an actual urban area, the city of Kyoto, which is reproduced using a 2-m resolution digital surface dataset. Comparison of the morphological characteristics of Kyoto with those of European, North American, and other Japanese cities indicates a similarity to European cities but with more variable building heights. The performance of the LES model is validated and found to be consistent with turbulence observations obtained from a meteorological tower and from Doppler lidar. We conducted the following two numerical experiments: a control experiment using Kyoto buildings, and a sensitivity experiment in which all the building heights are set to the average height over the computational region \(h_{all}\). The difference of Reynolds stress at height \(z=2.5h_{all}\) between the control and sensitivity experiments is found to increase with the increase in the plan-area index (\(\lambda _p\)) for \(\lambda _p > 0.32\). Thus, values of \(\lambda _p\approx 0.3\) can be regarded as a threshold for distinguishing the effects of building-height variability. The quadrant analysis reveals that sweeps contribute to the increase in the Reynolds stress in the control experiment at a height \(z= 2.5h_{all}\). The exuberance in the control experiment at height \(z=0.5h_{all}\) is found to decrease with increase in the building-height variability. Although the extreme momentum flux at height \(z=2.5h_{all}\) in the control experiment appears around buildings, it contributes little to the total Reynolds stress and is not associated with coherent motions.     

A simple two-way coupling method of BEM and VOF model for random wave calculations

A numerical method, which combines the boundary element method (BEM) and the volume of the fluid method (VOF method), has been presented to solve wave–structure interactions; the intense wave motion at the proximity of the structure is modeled by the VOF method and the rest of the fluid region is modeled by the BEM. The combined method can considerably reduce the time-consuming VOF domain, and thus practically makes it possible to apply the VOF method for random wave calculations, in which long time computations are usually required to obtain statistically meaningful results, and therefore the use of the single-VOF model often becomes prohibitive in terms of computational time and storage memories. A VOF model CADMAS-SURF, which is based on SMAC scheme and had been constructed by a number of VOF researchers in coastal engineering in Japan, is used in the combined BEM–VOF model. The two-way coupling treatment, which enables us to deal with bidirectional wave propagations, which was originally given for the SOLA-VOF model by Yan et al. (2003a) and later improved by Kim et al. (2007), was modified for the SMAC scheme. The coupling treatments are described in detail in the paper. The validity of the combined BEM–VOF model was investigated by comparing the numerical results with the theoretical results for the propagations of Stokes 5th order waves and random waves.     

Weathering rind formation in buried terrace cobbles during periods of up to 300ka

Weathering rinds formed in Mesozoic sandstone and basalt cobbles buried in terrace deposits for up to 300 ka have been investigated. The aim was to determine the formation process and elemental mass balances during rind development. The ages of terraces distributed in the western part of Fukui prefecture, central Japan have been determined as 50 ka, 120 ka and 300 ka based on a tephro-stratigraphic method. Detailed investigations across the weathering rinds, consisting of microscopic observations, porosity measurements, and mineralogical and geochemical analyses using X-ray diffractometry (XRD), X-ray fluorescence (XRF), secondary X-ray analytical microscopy (SXAM), scanning electron microanalyser (SEM) and electron probe microanalysis (EPMA) have been carried out. The results revealed that the Fe concentrations in the weathering rind of a basalt cobble slightly decreased from the cobble’s surface (rim) towards the unweathered core. In contrast, in a sandstone cobble formed under the same environmental conditions over the same period of time there is an Fe-rich layer at some distance below the cobble’s surface. Elemental mass balances across the rinds were determined by using open system mass balance (τ_i,j) calculations and show that the Fe was precipitated as Fe-oxyhydroxides in the basalt cobbles, although Fe was slightly removed from the rims. In sandstone cobbles, on the other hand, Fe migrated along a Fe concentration gradient by diffusion and precipitated as Fe-oxyhydroxide minerals to form the weathering rinds. Presumably, precipitation was due to the relatively higher pH conditions caused by mineral dissolution within the pores, principally involving calcite, but probably also silicates including feldspar. The detailed characterization of the weathering rinds revealed the influence of lithology on the accumulation and dissolution of Fe-oxyhydroxides, causing weathering rinds with different characteristics to develop in different kinds of buried cobbles under the same conditions. Relatively large climatic changes in the study area did not cause discernable variations in the mean formation rates of the studied rinds, which were in the order of 10^?8 m/a for both basalt and sandstone cobbles. These rates are 1–2 orders of magnitude slower than those reported for tropical areas elsewhere, most probably due to the lower rainfall in the studied area.