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.     

Radiative Shock Experiments At Luli

We present the set-up and the results of a supercritical radiative shock experiment performed with the LULI nanosecond laser facility. Using specific designed targets filled with xenon gaz at low pressure, the propagation of a strong shock with a radiative precursor is evidenced. The main measured quantities related to the shock (electronic density, propagation velocities, temperature, radial dimension) are presented and compared with various numerical simulations.     

Geochemistry of Mesozoic intracontinental basalts from Yunnan, southern China: Implications for geochemical evolution of the subcontinental lithosphere

Summary Southwestern Yunnan, comprising the Yangtze and Shan-Thai microcontinents and the Simao block, has successively undergone subduction of an oceanic plate, followed by a collision of the microcontinents and intracontinental rifting associated with basaltic volcanism during Late Paleozoic to Mesozoic.The Triassic Nanjian basalts, erupted on the Yangtze microcontinent, have more enriched isotopic ratios and higher LREE/HFSE and LREE/HREE ratios. This suggests the existence of an enriched subcontinental lithosphere under the Yangtze microcontinent which stabilized over long periods of the earth's history (> 2Ga).The Middle Jurassic Simao basalts have more depleted geochemical features and also have element enrichments characteristic of a subduction zone environment, although the basalts were erupted in an intracontinental graben. It may be inferred that the lithospheric mantle of the Simao block was modified by subduction processes during Latest Carboniferous to Late Triassic prior to the onset of the Middle Jurassic continental rifting. The lack of correlation between depletion of HFSE, Y and HREE, and relative enriched Nd isotopic ratios suggests that the source depletion of the Simao basalts is not an old feature and has been contemporaneous with the subduction-related enrichment through mantle metasomatism shortly before the basalts were produced.The Middle Jurassic Baoshan basalts which erupted during the continental rifting on the Shan-Thai microcontinent have an Sr-Nd isotopic composition similar to the bulk earth and higher concentrations of incompatible trace elements. These features suggest that the subcontinental lithosphere under the Shan-Thai microcontinent underwent mantle metasomatism just prior to eruption of the Baoshan basalt.

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Geochemie mesozoischer interkontinentaler Basalte aus Jünnan, Südchina: Hinweise auf die geochemische Entwicklung der subkontinentalen Lithosphäre

Zusammenfassung Südwestjünnan umfaßt den Jangtse und den Shan-Thai Mikrokontinent und den Simao Block. Das Gebiet wurde von aufeinander folgenden Subduktionsphasen einer ozeanischen Platte betroffen, auf die Kollision der Mikrokontinente und interkontinentales Rifting folgte. Dieses war mit basaltischem Vulkanismus während des späten Paläozoikums bis ins Mesozoikum assoziiert.Die triassischen Nanjian-Basalte, die auf dem Jangtse Mikrokontinent eruptierten, haben mehr angereicherte Isotopenverhältnisse und höhere LREE/HFSE und LREE/HREE Verhältnisse. Dieses weist auf eine angereicherte subkontinentale Lithosphäre unter dem Jangtse Mikrokontinent hin, die sich während langer Perioden der Erdgeschichte stabilisierte (>2Ga).Die mittel jurassischen Simao-Basalte haben eine mehr verarmte geochemische Signatur aber auch Elementanreicherungen, die für ein Subduktionszonen-Milieu charakteristisch sind, obwohl die Basalte in einem interkontinentalen Graben ausgetreten sind. Man kann daraus schließen, daß der lithosphärische Mantel des Simao-Blockes durch Subduktionsprozesse während des jüngsten Karbons bis in die späte Trias vor dem Beginn des mittel-jurassischen kontinentalen Riftings modifiziert worden war. Das Fehlen einer Korrelation zwischen der Anreicherung von HFSE, Y und HREE und relativ angereicherter Nd-Isotopenverhältnisse weist darauf hin, daß die Verarmung der Quelle der Simaobasalte nicht weit zurückreicht. Sie dürfte viel eher gleichaltrig mit der subduktions-bedingten Anreicherung durch Mantel-Metasomatose kurz vor der Entstehung der Basalte sein.Die mittel-jurassischen Baoshan-Basalte, die während des kontinentalen Riftings auf den Shan-Thai Mikrokontintent eruptierten, haben eine Sr-Nd-Isotopensignatur, die ähnlich der Gesamterde ist, jedoch höhere Konzentrationen inkompatibler Spurenelemente zeigt. All dies legt nahe, daß die subkontinentale Lithosphäre unter dem Shan-Thai-Mikrokontinent kurz vor der Eruption der Baoshan-Basalte von Mantel-Metasomatose betroffen worden ist.

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With 8 Figures

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Visiting Fellow, Geology Department, Australian National University, Australia     

Distribution of Overturn Induced by Internal Tides and Thorpe Scale in Uchiura Bay

The vertical mixing process induced by internal tides was investigated by repeated conductivity, temperature, and depth (CTD) measurements and bottom-mounted acoustic Doppler current profiler (ADCP) in Uchiura Bay from July 24 to 25, 2001. Internal tides were observed with a wave height of 40 m and a horizontal current of 0.3 ms⁻¹. Density inversions were found in the CTD data, and the method of Galbraith and Kelley (1996) was applied to the data to identify overturns and to calculate Thorpe scale. Most of the overturns distributed in the region of low Richardson number, so that they were considered to be caused by shear instability associated with the internal tides. Thorpe scale was calculated to be 0.48 m. From the Thorpe scale, the vertical eddy diffusivity due to internal tides in Uchiura Bay was estimated as K _ρ ∼ 10⁻⁴ m²s⁻¹. This revised version was published online in July 2006 with corrections to the Cover Date.     

Interactions of uranium with bacteria and kaolinite clay

We assessed the accumulation of uranium (VI) by a bacterium, Bacillus subtilis, suspended in a slurry of kaolinite clay, to elucidate the role of microbes on the mobility of U(VI). Various mixtures of bacteria and the koalinite were exposed to solutions of 8 × 10^− 6 M- and 4 × 10^− 4 M-U(VI) in 0.01 M NaCl at pH 4.7. After 48 h, the mixtures were separated from the solutions by centrifugation, and treated with a 1 M CH₃COOK for 24 h to determine the associations of U within the mixture. The mixture exposed to 4 × 10^− 4 M U was analyzed by transmission electron microscope (TEM) equipped with EDS. The accumulation of U by the mixture increased with an increase in the amount of B. subtilis cells present at both U concentrations. Treatment of kaolinite with CH₃COOK, removed approximately 80% of the associated uranium. However, in the presence of B. subtilis the amount of U removed was much less. TEM–EDS analysis confirmed that most of the U removed from solution was associated with B. subtilis. XANES analysis of the oxidation state of uranium associated with B. subtilis, kaolinite, and with the mixture containing both revealed that it was present as U(VI). These results suggest that the bacteria have a higher affinity for U than the kaolinite clay mineral under the experimental conditions tested, and that they can immobilize significant amount of uranium.     

Chemistry and Sulfur Isotopes of the Chert-Clastic Sequence Surrounding the Kajika Massive Sulfide Ores at the Ashio Copper Mine, Ashio Terrane, Central Japan

Abstract. Chemical and sulfur isotopic compositions were obtained for a series of rocks within the chert‐clastic sequence surrounding the Kajika massive sulfide ore horizon at Shibukawasawa in the Ashio copper‐mining district, Ashio Terrane, central Japan. The sequence is lithologically classified into three units: chert, siliceous shale with basic volcanics, and sandstone‐shale, in ascending stratigraphic order. The Kajika ore horizon corresponds to the lowermost part of the unit that contains siliceous shale with basic volcanics. The rocks around the Kajika ore horizon are enriched in P₂O₅ (max. 0.22 %), Ba (max. 2400 ppm), Cu (595 ppm), V (323 ppm), Pb (168 ppm), Zn (124 ppm), and Mo (24 ppm) in siliceous shale; and Ba (4220 ppm), Zr (974 ppm), Cr (718 ppm), Ni (492 ppm), V (362 ppm), Zn (232 ppm), Nb (231 ppm), and Co (71 ppm) in the basic volcanics. The siliceous shale is enriched in a number of redox‐sensitive elements such as Cu, V, Pb, Zn, and Mo, which are known to be enriched in black shale and anoxic and hydrothermal sediments. The δ³⁴S values of sulfides in the chert and sandstone‐shale lie in the range of 0±2 %, and those in the siliceous shale range from ‐5 to ‐14 %. The measured δ³⁴S values in the basic volcanics are ‐0.3, ‐2.7, and ‐31.5 %. These heavier δ³⁴S signatures (around 0 %) recorded throughout the sequence indicate that the rocks formed under anoxic bottom‐water conditions. Slightly lighter δ³⁴S values recorded in siliceous shale might reflect significant mixing of sulfides that formed by sulfate‐reducing bacteria in an overlying oxic environment. The long‐term duration of anoxic conditions indicated by the heavier δ³⁴S signature is considered to have played an important role in protecting the Kajika sulfide ores from oxidative decomposition and preserving the ores in sedimentary accumulations.     

Characterization of water quality variation in the Mekong River at Vientiane by frequent observations

To better understand the variation of water quality in the Mekong River, sampling and measurement were scheduled twice a week for about 3 years at Vientiane, followed by basic statistical analysis of the observed data. The frequent measurement revealed detailed characteristics of the water quality variation, which had not been detected by monthly observation in the previous studies. The variation in total ionic content was considered to be governed by dilution of the amount of water. Increases in turbidity could be attributed to physical effects including surface soil erosion and bed material resuspension at the time of discharge increase. Nitrogen concentrations were stably low during the low flow period and abruptly increased in May. After the annual maximum in late May, the nitrate concentration steadily decreased regardless of the remarkable rise in the discharge from mid‐July, whereas the ammonium concentration remained at a similar level until October. It was considered that the first small discernable runoff after the long dry season flushed the accumulated nitrogen in the surface soil and mobilized the nitrogen in the riverbed. The variation in phosphorus concentrations was different from that in nitrogen concentrations. During the high flow period, continual dilutions at discharge peaks and occasional large additions of phosphorus by surface runoff were suggested. Copyright © 2011 John Wiley & Sons, Ltd.     

The continuous limit of the multiple lens effect and the optical scalar equation

We study the continuous limit of the multiple gravitational lensing theory based on the thin lens approximation. We define a new, light-path dependent angular diameter distance     and show that it satisfies the optical scalar equation. The distance provides relations between quantities used in gravitational lensing theory (the convergence, the shear and the twist terms) and those used in scalar optics theory (the rates of expansion, shear and rotation).     

Air-Sea Interactions under the Existence of Opposing Swell

Data of a comprehensive laboratory study on the coexistent system of wind waves and opposing swell (Mitsuyasu and Yoshida, 1989) have been reanalyzed to clarify the air-sea interaction phenomena under the coexistence of wind waves and swell. It is shown that the magnitude of the decay rate of swell due to an opposing wind is almost the same as that of the growth rate of swell caused by a following wind, as measured by Mitsuyasu and Honda (1982). The decay rate is much smaller than that obtained recently by Peirson et al. (2003), but the reason for the disagreement is not clear at present. The effect of an opposing swell on wind waves is very different from that of a following swell; wind waves are intensified by an opposing swell while they are attenuated by a following one. The phenomenon contradicts the model of Phillips and Banner (1974), but the reason for this is not clear at this time. The high-frequency spectrum of wind waves shows a small increase of the spectral density. Wind shear stress increases a little due to the effect of opposing swell. The intensification of wind waves by opposing swell and the small increase of the spectral density in a high-frequency region can be attributed to the increase of wind shear stress. Such organized phenomena lead to the conclusion that the hypothesis of local equilibrium for pure wind waves (Toba, 1972) can also be satisfied for wind waves that coexist with opposing swell. The recent finding of Hanson and Phillips (1999) can be explained by this mechanism.     

Effects of deposit feeder Stichopus japonicus on algal bloom and organic matter contents of bottom sediments of the enclosed sea

Algae growing in an enclosed sea may inhibit eutrophication because they absorb nutrients in the water. However, dead algae often cause anaerobic conditions in the water just above and on sediment after they are deposited on the bottom. We found that Stichopus japonicus inhibited the anaerobic processes coupling water sulfite production in sediment. The present study investigates whether S. japonicus inhibits algal flourish and influences sediment properties such as organic matter contents. Aquarium experiments were carried out at Komatsushima port in Tokushima Prefecture, western Japan. The aquaria used in the experiments were supplied with water directly from the adjacent sea (6 L/min), laid with sand of 10 cm depths, and lighted at 12 h intervals. Six aquaria each containing a sea cucumber from Komatsushima port and six aquaria without any were used in the experiments. Water temperature ranged between 9 and 15 degrees C during December 2000 and April 2001. Salinity ranged between 32 per thousand and 34 per thousand. Algae began to cover the bottom of the aquaria without S. japonicus after 2 weeks, whereas no growth was evident in the aquaria containing sea cucumbers. Chlorophyll a concentration in the surface sediment of the aquaria with S. japonicus (6.1+/-3.6 microg/g, mean S.D.+/-standard deviation) was significantly lower than that without it (60+/-17 microg/g, U-test, p<0.05). Phaeophytin concentration in the surface sediment of the aquaria with S. japonicus (0.9+/-0.09 microg/g) was also significantly lower than that without it (4.5+/-1.0 microg/g, U-test, p<0.05). TOC concentration in the surface sediment of the aquaria with S. japonicus (2.6+/-1.3 microg/g) was slightly lower than that without it (4.0+/-1.2 microg/g). These results showed that algal biomass and organic matter concentration of the bottom were decreased in the presence of S. japonicus. Therefore, S. japonicus inhibits algal bloom and decrease the contents of organic matter deposited on the bottom of enclosed sea areas.