How the Method of Minimization of Action Avoids Singularities

The method of minimization of action is a powerful technique of proving the existence of particular and interesting solutions of the n-body problem, but it suffers from the possible interference of singularities. The minimization of action is an optimization and, after a short presentation of a few optimization theories, our analysis of interference of singularities will show that:(A) An n-body solution minimizing the action between given boundary conditions has no discontinuity: all n-bodies have a continuous and bounded motion and thus all eventual singularities are collisions;(B) A beautiful extension of Lambert's theorem shows that, for these minimizing solutions, no double collision can occur at an intermediate time;(C) The proof can be extended to triple and to multiple collisions. Thus, the method of minimization of action leads to pure n-body motions without singularity at any intermediate time, even if one or several collisions are imposed at initial and/or final times.This method is suitable for non-infinitesimal masses only. Fortunately, a similar method, with the same general property with respect to the singularities, can be extended to n-body problems including infinitesimal masses.     

Tracing exhumation record in high-pressure micaschists: A new tectonometamorphic model of the evolution of the eastern part of the Fore Sudetic Block,Kamieniec Metamorphic Belt,NE Bohemian Massif,SW Poland

The Kamieniec Metamorphic Belt comprises a volcano-sedimentary succession exposed within a collision zone between the Saxothuringian and Brunovistulian crustal domains of the European Variscides. The studied rocks recorded two metamorphic episodes. The first episode, M₁, occurred at conditions of c. 485 ± 25 °C and 18 ± 1.8 kbar related to burial within a subduction zone. The subsequent episode, M₂, was linked to the final phases of exhumation to mid-crustal level, associated with pressure and temperature (P–T) conditions ranging from c. 520 ± 26 °C and 6 ± 0.6 kbar through 555 ± 28 °C and 7 kbar ± 0.7 to ~590 ± 30 °C and 3–4 ± 0.4 kbar. The documented deformation record is ascribed to three events, D₁ to D₃, interpreted as related to the burial and subsequent exhumation of the Kamieniec Metamorphic Belt. The D₁ event must have witnessed the subduction of the Kamieniec Metamorphic Belt rock succession whereas the D₂ event was associated with the exhumation and folding of the Kamieniec Metamorphic Belt in an E-W-directed shortening regime. A subsequent folding related to the D₂ event was initiated at HP conditions, however, the planar fabric produced during a late stage of the D₂ event, defined by a low-pressure mineral assemblage M₂, indicates that the D₂ final stage was synchronous with the onset of the M₂ episode. Consequently, the entire D₂ event seems to have been associated with the exhumation of the Kamieniec Metamorphic Belt to mid crustal level. The third deformation event D₃, synchronous with the M₂ episode, marked the last stage of the exhumation, and was linked to emplacement of granitoid veins and lenses. The latter resulted in heating and rheological weakening of the entire rock succession and in the formation of non-coaxial shear zones.     

应力分散型预应力抗拔桩系列技术研究与应用

根据目前国内外预应力抗拔抗浮桩、部分粘结预应力抗拔抗浮桩的优缺点以及使用的局限性——长螺旋钻机对于桩径＞800 mm或桩长＞30 m的桩力不从心,研究了应力分散型预应力抗拔桩及钢筋钢绞线笼系列技术,用于一个直径1 m、桩长60 m的抗拔桩工程,采用旋挖成孔,可实现在工程桩上进行大吨位试桩,受力合理,节省资金和工期,实践证明该系列技术有很好的应用前景。     

http://www.sciencedirect.com/science/article/pii/S1674987114001601

Data from a migmatised metapelite raft enclosed within charnockite provide quantitative constraints on the pressure-temperature-time[P-T-t) evolution of the Nagercoil Block at the southernmost tip of peninsular India.An inferred peak metamorphic assemblage of garnet,K-feldspar.sillimanite,plagioclase,magnetite,ilmenite,spinel and melt is consistent with peak metamorphic pressures of 6-8 kbar and temperatures in excess of 900℃.Subsequent growth of cordierite and biotite record high-temperature retrograde decompression to around 5 kbar and 800 C.SHRIMP U-Pb dating of magmatic zircon cores suggests that the sedimentary protoliths were in part derived from felsic igneous rocks with Palaeoproterozoic crystallisation ages.New growth of metamorphic zircon on the rims of detrital grains constrains the onset of melt crystallisation,and the minimum age of the metamorphic peak,to around560 Ma.The data suggest two stages of monazite growth.The first generation of REE-enriched monazite grew during partial melting along the prograde path at around 570 Ma via the incongruent breakdown of apatite.Relatively REE-depleted rims,which have a pronounced negative europium anomaly,grew during melt crystallisation along the retrograde path at around 535 Ma.Our data show the rocks remained at suprasolidus temperatures for at least 35 million years and probably much longer,supporting a long-lived high-grade metamorphic history.The metamorphic conditions,timing and duration of the implied clockwise P-T-t path are similar to that previously established for other regions in peninsular India during the Ediacaran to Cambrian assembly of that part of the Gondwanan supercontinent.     

Simulating urban flow and dispersion in Beijing by coupling a CFD model with the WRF model

The airflow and dispersion of a pollutant in a complex urban area of Beijing, China, were numerically examined by coupling a Computational Fluid Dynamics （CFD） model with a mesoscale weather model. The models used were Open Source Field Operation and Manipulation （OpenFOAM） software package and Weather Research and Forecasting （WRF） model. OpenFOAM was firstly validated against wind-tunnel experiment data. Then, the WRF model was integrated for 42 h starting from 0800 LST 08 September 2009, and the coupled model was used to compute the flow fields at 1000 LST and 1400 LST 09 September 2009. During the WRF-simulated period, a high pressure system was dominant over the Beijing area. The WRF-simulated local circulations were characterized by mountain valley winds, which matched well with observations. Results from the coupled model simulation demonstrated that the airflows around actual buildings were quite different from the ambient wind on the boundary provided by the WRF model, and the pollutant dispersion pattern was complicated under the influence of buildings. A higher concentration level of the pollutant near the surface was found in both the step-down and step-up notches, but the reason for this higher level in each configurations was different： in the former, it was caused by weaker vertical flow, while in the latter it was caused by a downward-shifted vortex. Overall, the results of this study suggest that the coupled WRF-OpenFOAM model is an important tool that can be used for studying and predicting urban flow and dispersions in densely built-up areas.     

星系的恒星速度弥散度的归算方法

星系的恒星视向速度分布是星系动力学模型的重要观测约束,其特征参数包括速度弥散度、分布轮廓以及红移。这些参数对研究星系的动力学、结构和演化以及中央黑洞的质量等都具有重要的价值。该文全面总结了从星系光谱归算星系的恒星视向速度分布及其弥散度的各种方法,以及对观测和处理的一些要求。这些方法都假设星系谱线可看作是模板星光谱经多普勒位移并加宽后的线性叠加。提取尽可能多的星系内部恒星运动信息、减少模板星失配的影响、简化误差分析,是这些方法追求的目标。