We consider the planar problem of three bodies which attract mutually with the force proportional to a certain negative integer
power of the distance between the bodies. We show that such generalisation of the gravitational three-body problem is not
integrable in the Liouville sense. 相似文献
Water, suspended matter and sediment samples from a system heavily impacted by wastewater from numerous small tanneries (the upper Dunajec River, southern Poland) were collected to establish the annual cycle of Cr. To study possible oxidation processes the speciation of Cr and Mn concentrations were also investigated. This study showed that Cr(III and VI) temporal and spatial distributions are regulated by coupled anthropogenic (source location and emissions) and hydrologic factors (water flow and particle transport). Chromium(III) concentrations in all compartments varied seasonally as a function of the hydrological regime, production cycle in tanneries and distance from the discharge location. Cr(III) was largely associated with the particulate phase and rapidly deposited in river bed sediments. Contaminated river sediments were however flushed during flood periods to the reservoir located downstream from tanneries. During the tanning season (November to March), Chromium(III) concentrations in the water column and total Cr concentration in sediments exceeded relevant ecotoxicological guidelines only upstream from the reservoir, which trapped about 70% of the annual Cr(III) load transported by the Dunajec river. A correlation between Cr(VI)/Cr(III) ratios and Mn concentration in sediments downstream from the reservoir suggests the possibility of Cr(III) oxidation in natural conditions. 相似文献
The pure cross-anisotropy is understood as a special scaling of strain (or stress). The scaled tensor is used as an argument in the elastic stiffness (or compliance). Such anisotropy can be overlaid on the top of any elastic stiffness, in particular on one obtained from an elastic potential with its own stress-induced anisotropy. This superposition does not violate the Second Law. The method can be also applied to other functions like plastic potentials or yield surfaces, wherever some cross-anisotropy is desired. The pure cross-anisotropy is described by the sedimentation vector and at most two constants. Scaling with more than two purely anisotropic constants is shown impossible. The formulation was compared with experiments and alternative approaches. Static and dynamic calibration of the pure anisotropy is also discussed. Graphic representation of stiffness with the popular response envelopes requires some enhancement for anisotropy. Several examples are presented. All derivations and examples were accomplished using the algebra program Mathematica.
Investigating the characteristics of model-forecast errors using various statistical and object-oriented methods is necessary for providing useful guidance to end-users and model developers as well. To this end, the random and systematic errors (i.e., biases) of the 2-m temperature and 10-m wind predictions of the NCAR-AirDat weather research and forecasting (WRF)-based real-time four-dimensional data assimilation (RTFDDA) and forecasting system are analyzed. This system has been running operationally over a contiguous United States (CONUS) domain at a 4-km grid spacing with four forecast cycles daily from June 2009 to September 2010. In the result an exceptionally useful forecast dataset was generated and used for studying the error properties of the model forecasts, in terms of both a longer time period and a broader coverage of geographic regions than previously studied. Spatiotemporal characteristics of the errors are investigated based on the 24-h forecasts between June 2009 and April 2010, and the 72-h forecasts between May and September 2010. It was found that the biases of both wind and temperature forecasts vary greatly seasonally and diurnally, with dependency on the forecast length, station elevation, geographical location, and meteorological conditions. The temperature showed systematic cold biases during the daytime at all station elevations and warm biases during the nighttime above 1,000 m above sea level (ASL), while below 600 m ASL cold biases occurred during the nighttime. The forecasts of surface wind speed exhibited strong positive biases during the nighttime, while the negative biases were observed in the spring and summer afternoons. The surface wind speed was mostly over-predicted except for the stations located between 1,000 and 2,100 m ASL, for which negative biases were identified for most forecast cycles. The highest wind-speed errors were found over the high terrain and near sea-level stations. The wind-direction errors were relatively large at the high-terrain elevation in the Rocky and Appalachian mountain ranges and the western coastal areas and the error structure exhibited notable diurnal variability. 相似文献
We develop a formalism to calculate energy-dependent fractional variability (rms) in accretion flows. We consider rms spectra resulting from radial dependences of the level of local variability (as expected from the propagation of disturbances in accretion flows) assuming the constant shape of the spectrum emitted at a given radius. We consider the cases when the variability of the flow is either coherent or incoherent between different radial zones. As an example of local emission, we consider blackbody, Wien and thermal Comptonization spectra. In addition to numerical results, we present a number of analytical formulae for the resulting rms. We also find an analytical formula for the disc Wien spectrum, which we find to be a very good approximation to the disc blackbody. We compare our results to the rms spectrum observed in an ultrasoft state of GRS 1915+105. 相似文献
A simple model for compaction of a sand, that may be useful in various geotechnical applications is presented. The model has been formulated in terms of the cyclic stress and strain amplitudes. The compaction properties of a dry sand are characterized by a common compaction curve described by two coefficients. The second aim of this paper is to show some applications of the theory proposed. The attention has been restricted to the two extreme cases of practical importance, namely to the behaviour of a dry sand (or a saturated sand but in free draining conditions), and to the behaviour of saturated sand in undrained conditions. Some numerical algorithms showing how to deal with those problems are presented and illustrated on the following examples: settlement and pore pressure generation in a soil stratum subjected to an earthquake, settlement of a foundation, pore pressure generation and liquefaction in a sea-bed. The results obtained suggest that the model proposed, as well as a method of dealing with boundary value problems can serve as a useful tool for the analysis of a sandy subsoil subjected to cyclic loadings. 相似文献
Summary. We show that Maslov's extension of the WKBJ method allows an extension of the dynamic ray tracing to wavefields involving caustics of arbitrary form. If the receiver lies off the caustics, then the synthetic seismogram can be obtained by integrating the DRT system along a single ray joining the receiver to the source which may touch caustics. If the receiver-lies in the vicinity of a caustic then DRT has to be carried out along a bunch of rays covering a neighbourhood of the receiver. Our approach encompasses pre-stressed and/or anisotropic media. Initial boundary conditions for a point source embedded in an anisotropic elastic medium are also presented. 相似文献
We report U–Pb single zircon ages from three pre-Variscan granitoids in the NE part of the Bohemian Massif. The Platerówka granodiorite from the Lausitz-Izera Unit, the Polish Sudetes, has been dated at 533±9 Ma. The Bitouchov granite form the SW part of the South Krkonoe Unit, the Czech Sudetes, gave an age of 540+11/–10 Ma, and the Wdroe granodiorite in the Fore-Sudetic Block yielded 548±9 Ma. All these latest Vendian/Early Cambrian granitoids represent the post-tectonic expression of a late Proterozoic Cadomian orogenic cycle and demonstrate the eastward extent of the Cadomian basement into the Variscan orogen. Granodiorites of similar age have so far been reported from Brittany and especially from the Saxo-Thuringian Terrane to the NE and SW of the Elbe Fault Zone. We conclude that the Saxo-Thuringian Terrane extends across the Elbe and Sudetic Marginal Fault Zones into the Fore-Sudetic Block. 相似文献