Extension of the solution of Kepler's equation to high eccentricities

The classic Lagrange's expansion of the solutionE(e, M) of Kepler's equation in powers of eccentricity is extended to highly eccentric orbits, 0.6627 ... <e<1. The solutionE(e, M) is developed in powers of (e–e*), wheree* is a fixed value of the eccentricity. The coefficients of the expansion are given in terms of the derivatives of the Bessel functionsJ _n (ne). The expansion is convergent for values of the eccentricity such that |e–e*|<(e*), where the radius of convergence (e*) is a positive real number, which is calculated numerically.     

扬子地台前寒武纪－寒武纪界线地层的微体植物化石群

前寒武纪一寒武纪界线地层在扬子地台发育良好、分布广泛,并有包括微体植物群、海藻、瓶形原生物、具硬体动物及‘澄江动物群’等化石的发现。因而,扬子地台成为研究前寒武纪－寒武纪界线生物地层的代表地区之一。基于对扬子地台前寒武纪－寒武纪界线地层已知微体植物化石记录的回顾和论定,总结概括了下寒武统微体植物化石组合：寒武系最底部硅质磷块岩中的Ｍｉｃｒｈｙｓｔｒｉｄｉｕｍ－Ｐａｒａｃｙｍａｔｉｏｓｐｈａｅｒａ－Ｍｅｇａｔｈｒｉｘ组合和较高层位页岩的Ｓｋｉａｇｉａ－Ａｎｎｕｌｕｍ－Ａｒｃｈａｅｏｄｉｓｃｉｎａ组合。它们分别与Ａｎａｂａｒｉｔｅｓ－Ｃｉｒｃｏｔｈｅｃａ－Ｐｒｏｔｏｈｅｒｔｚｉｎａ小壳动物化石带和Ｐａｒａｂａｄｉｅｌｌａ及Ｅｏｒｅｄｌｉｃｈｉａ三叶虫带相对应。与东欧地台疑源类生物地层相对照,扬子地台Ｍｉｃｒｈｙｓｔｒｉｄｉｕｍ－Ｐａｒａｃｙｍａｔｉｏｓｐｈａｅｒａ－Ｍｅｇａｔｈｒｉｘ组合的纵向分布大体和东欧地台Ａｓｔｅｒｉｄｉｕｍｔｏｒｎａｔｕｍ－Ｃｏｍａｓｐｈａｅｒｉｄｉｕｍｖｅｌｖｅｔｕｍ组合带相一致,而以上两地台的化石组合产出层位可能都略高于纽芬兰东部剖面,依据Ｐｈｙｃｏｄｅｓｐｅｄｕｍ所厘定的寒武系底界?     

Measurements of peroxyacetylnitrate in the marine boundary layer over the Atlantic

The atmospheric concentration of peroxyacetylnitrate (PAN) was measured during a cruise of the R.S. Polarstern from Bremerhaven (Germany) to Rio Grande do Sul (Brazil) in September/ October 1988. The measurements were made in-situ by a combination of electron capture gaschromatography with a cryogenic preconcentration step. The theoretical lower limit of detection (3) was 0.4 ppt. The mixing ratios of PAN varied by more than three orders of magnitude from 2000 ppt in the English Channel to less than 0.4 ppt south of the Azores (38° N). South of 35° N, PAN levels were below the detection limit, except at 30–31° S off the eastern coast of South America. Here, PAN mixing ratios of 10 to 100 ppt were detected in continentally influenced air masses. Detectable levels of PAN were mostly observed in air masses of continental or high northern origin. Changes in the wind directions were usually associated with substantial changes in the PAN mixing ratios.     

On the periodic solutions of a particular Lame equation

We consider the Hill's equation: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGKbWaaWbaaSqabeaacaaIYaaaaOGaeqOVdGhabaGaamizaiaadsha% daahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaacaWGTbGaai% ikaiaad2gacqGHRaWkcaaIXaGaaiykaaqaaiaaikdaaaGaam4qamaa% CaaaleqabaGaaGOmaaaakiaacIcacaWG0bGaaiykaiabe67a4jabg2% da9iaaicdaaaa!4973!\[\frac{{d^2 \xi }}{{dt^2 }} + \frac{{m(m + 1)}}{2}C^2 (t)\xi = 0\]Where C(t) = Cn (t, {frbuilt|1/2}) is the elliptic function of Jacobi and m a given real number. It is a particular case of theame equation. By the change of variable from t to defined by: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaOWaaiqaaq% aabeqaamaalaaajaaybaGaamizaGGaaiab-z6agbqaaiaadsgacaWG% 0baaaiabg2da9OWaaOaaaKaaGfaacaGGOaqcKbaG-laaigdajaaycq% GHsislkmaaleaajeaybaGaaGymaaqaaiaaikdaaaqcaaMaaeiiaiaa% bohacaqGPbGaaeOBaOWaaWbaaKqaGfqabaGaaeOmaaaajaaycqWFMo% GrcqWFPaqkaKqaGfqaaaqcaawaaiab-z6agjab-HcaOiab-bdaWiab% -LcaPiab-1da9iab-bdaWaaakiaawUhaaaaa!51F5!\[\left\{ \begin{array}{l}\frac{{d\Phi }}{{dt}} = \sqrt {(1 - {\textstyle{1 \over 2}}{\rm{ sin}}^{\rm{2}} \Phi )} \\\Phi (0) = 0 \\\end{array} \right.\]it is transformed to the Ince equation: (1 + · cos(2)) y + b · sin(2) · y + (c + d · cos(2)) y = 0 where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaiaadggacq% GH9aqpcqGHsislcaWGIbGaeyypa0JcdaWcgaqaaiaaigdaaeaacaaI% ZaGaaiilaiaabccacaWGJbGaeyypa0Jaamizaiabg2da9aaacaqGGa% WaaSaaaKaaGfaacaWGTbGaaiikaiaad2gacqGHRaWkcaaIXaGaaiyk% aaqaaiaaiodaaaaaaa!4777!\[a = - b = {1 \mathord{\left/{\vphantom {1 {3,{\rm{ }}c = d = }}} \right.\kern-\nulldelimiterspace} {3,{\rm{ }}c = d = }}{\rm{ }}\frac{{m(m + 1)}}{3}\]In the neighbourhood of the poles, we give the expression of the solutions.The periodic solutions of the Equation (1) correspond to the periodic solutions of the Equation (3). Magnus and Winkler give us a theory of their existence. By comparing these results to those of our study in the case of the Hill's equation, we can find the development in Fourier series of periodic solutions in function of the variable and deduce the development of solutions of (1) in function of C(t).     

Mantle plumes from top to bottom

Hotspots include midplate features like Hawaii and on-axis features like Iceland. Mantle plumes are a well-posed hypothesis for their formation. Starting plume heads provide an explanation of brief episodes of flood basalts, mafic intrusions, and radial dike swarms. Yet the essence of the hypothesis hides deep in the mantle. Tests independent of surface geology and geochemistry to date have been at best tantalizing. It is productive to bare the current ignorance, rather than to dump the plume hypothesis. One finds potentially fruitful lines of inquiry using simple dynamics and observations. Ancient lithospheric xenoliths may reveal heating by plumes and subsequent thermal equilibration in the past. The effect at the base of the chemical layer is modest 50-100 K for transient heating by plume heads. Thinning of nonbuoyant platform lithosphere is readily observed but not directly attributable to plumes. The plume history in Antarctica is ill constrained because of poor geological exposure. This locality provides a worst case on what is known about surface evidence of hotspots. Direct detection of plume tail conduits in the mid-mantle is now at the edge of seismic resolution. Seismology does not provide adequate resolution of the deep mantle. We do not know the extent of a chemically dense dregs layer or whether superplume regions are cooler or hotter than an adiabat in equilibrium with the asthenosphere. Overall, mid-mantle seismology is most likely to give definitive results as plume conduits are the guts of the dynamic hypothesis. Finding them would bring unresolved deep and shallow processes into place.     

Large eddy simulation of hydrocyclone—prediction of air-core diameter and shape

Hydrocyclones are widely used in the mining and chemical industries. An attempt has been made in this study, to develop a CFD (computational fluid dynamics) model, which is capable of predicting the flow patterns inside the hydrocyclone, including accurate prediction of flow split as well as the size of the air-core. The flow velocities and air-core diameters are predicted by DRSM (differential Reynolds stress model) and LES (large eddy simulations) models were compared to experimental results. The predicted water splits and air-core diameter with LES and RSM turbulence models along with VOF (volume of fluid) model for the air phase, through the outlets for various inlet pressures were also analyzed. The LES turbulence model led to an improved turbulence field prediction and thereby to more accurate prediction of pressure and velocity fields. This improvement was distinctive for the axial profile of pressure, indicating that air-core development is principally a transport effect rather than a pressure effect.     

Tectonic relation between northeastern China and the Korean peninsula revealed by interpretation of GRACE satellite gravity data

The major continental blocks in northeastern Asia are the North China block and the South China block, which have collided starting from the Korean peninsula. Geologic and geophysical interpretations reveal a well defined suture zone in northeastern China from Qinling through Dabie to Jiaodong. The discovery of high-pressure metamorphic rocks in the Hongseong area of the Korean peninsula, prominent evidence for the collision zone, indicates extension of the collision zone in northeastern China into the Korean peninsula. Interpretation of the GRACE satellite gravity dataset shows two prominent structural boundaries in the Yellow Sea. One extends from the Jiaodong Belt in eastern China to the Imjingang Belt in the Korean peninsula. The other extends from near Nanjing, eastern China, to Hongseong. Tectonic movement in or near the suture zone may be responsible for seismic activity in the western Korean peninsula and the development of the Yellow Sea sedimentary basin.     

Seismic lamination and anisotropy of the Lower Continental Crust

Seismic lamination in the lower crust associated with marked anisotropy has been observed at various locations. Three of these locations were investigated by specially designed experiments in the near vertical and in the wide-angle range, that is the Urach and the Black Forrest area, both belonging to the Moldanubian, a collapsed Variscan terrane in southern Germany, and in the Donbas Basin, a rift inside the East European (Ukrainian) craton. In these three cases, a firm relationship between lower crust seismic lamination and anisotropy is found. There are more cases of lower-crustal lamination and anisotropy, e.g. from the Basin and Range province (western US) and from central Tibet, not revealed by seismic wide-angle measurements, but by teleseismic receiver function studies with a P–S conversion at the Moho. Other cases of lamination and anisotropy are from exhumed lower crustal rocks in Calabria (southern Italy), and Val Sesia and Val Strona (Ivrea area, Northern Italy). We demonstrate that rocks in the lower continental crust, apart from differing in composition, differ from the upper mantle both in terms of seismic lamination (observed in the near-vertical range) and in the type of anisotropy. Compared to upper mantle rocks exhibiting mainly orthorhombic symmetry, the symmetry of the rocks constituting the lower crust is either axial or orthorhombic and basically a result of preferred crystallographic orientation of major minerals (biotite, muscovite, hornblende). We argue that the generation of seismic lamination and anisotropy in the lower crust is a consequence of the same tectonic process, that is, ductile deformation in a warm and low-viscosity lower crust. This process takes place preferably in areas of extension. Heterogeneous rock units are formed that are generally felsic in composition, but that contain intercalations of mafic intrusions. The latter have acted as heat sources and provide the necessary seismic impedance contrasts. The observed seismic anisotropy is attributed to lattice preferred orientation (LPO) of major minerals, in particular of mica and hornblende, but also of olivine. A transversely isotropic symmetry system, such as expected for sub-horizontal layering, is found in only half of the field studies. Azimuthal anisotropy is encountered in the rest of the cases. This indicates differences in the horizontal components of tectonic strain, which finally give rise to differences in the evolution of the rock fabric.     

Mais comment s'écoule donc un glacier ? Aperçu historique

Ice and snow have often helped physicists understand the world. On the contrary it has taken them a very long time to understand the flow of the glaciers. Naturalists only began to take an interest in glaciers at the beginning of the 19th century during the last phase of glacier advances. When the glacier flow from the upslope direction became obvious, it was then necessary to understand how it flowed. It was only in 1840, the year of the Antarctica ice sheet discovery by Dumont d'Urville, that two books laid the basis for the future field of glaciology: one by Agassiz on the ice age and glaciers, the other one by canon Rendu on glacier theory. During the 19th century, ice flow theories, adopted by most of the leading scientists, were based on melting/refreezing processes. Even though the word ‘fluid’ was first used in 1773 to describe ice, more the 130 years would have to go by before the laws of fluid mechanics were applied to ice. Even now, the parameter of Glen's law, which is used by glaciologists to model ice deformation, can take a very wide range of values, so that no unique ice flow law has yet been defined. To cite this article: F. Rémy, L. Testut, C. R. Geoscience 338 (2006).