Editorial     

Eric Pawson  Etienne Nel 《New Zealand geographer》2011,67(1):1-1

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F and G Taylor series solutions to the Stark and Kepler problems with Sundman transformations     

Etienne Pellegrini  Ryan P. Russell  Vivek Vittaldev 《Celestial Mechanics and Dynamical Astronomy》2014,118(4):355-378

The classic $F$ and $G$ Taylor series of Keplerian motion are extended to solve the Stark problem and to use the generalized Sundman transformation. Exact recursion formulas for the series coefficients are derived, and the method is implemented to high order via a symbolic manipulator. The results lead to fast and accurate propagation models with efficient discretizations. The new $F$ and $G$ Stark series solutions are compared to the Modern Taylor Series (MTS) and 8th order Runge–Kutta–Fehlberg (RKF8) solutions. In terms of runtime, the $F$ and $G$ approach is shown to compare favorably to the MTS method up to order 20, and both Taylor series methods enjoy approximate order of magnitude speedups compared to RKF8 implementations. Actual runtime is shown to vary with eccentricity, perturbation size, prescribed accuracy, and the Sundman power law. The method and results are valid for both the Stark and the Kepler problems. The effects of the generalized Sundman transformation on the accuracy of the propagation are analyzed. The Taylor series solutions are shown to be exceptionally efficient when the unity power law from the classic Sundman transformation is applied. An example low-thrust trajectory propagation demonstrates the utility of the $F$ and $G$ Stark series solutions.  相似文献   

50 Myr recovery from the largest negative δ13C excursion in the Ediacaran ocean     

Erwan Le Guerrou  Philip A. Allen  Andrea Cozzi  James L. Etienne  Mark Fanning 《地学学报》2006,18(2):147-153

Sedimentary rocks deposited during the Ediacaran period (～630–542 Ma) contain carbonates whose carbon isotopic ratios show a marked negative excursion consisting of a precipitous drop from +5‰ to ?12‰, followed by a sub‐linear recovery to positive δ¹³C values. Isotopic ages (U/Pb) and thermal subsidence modelling are combined to constrain the excursion in time and indicate an onset at ～600 Ma, and duration of recovery of approximately 50 Myr. The excursion is widely recognized in Oman and has potential correlatives in Ediacaran strata elsewhere, and may thus represent a characteristic feature of the Ediacaran period. The amplitude of this carbon isotope excursion far exceeds those of other Neoproterozoic anomalies. The isotopic trend of negative excursion and long‐term recovery spanned at least one short‐lived glacial episode (at 580 Ma), but appears unrelated to glaciation, which indicates that negative anomalies in the Neoproterozoic marine carbon isotope record are not directly or uniquely linked to ice ages.  相似文献   

Uraniferous bitumen nodules in the Talvivaara Ni–Zn–Cu–Co deposit (Finland): influence of metamorphism on uranium mineralization in black shales     

Andreï Lecomte  Michel Cathelineau  Etienne Deloule  Marc Brouand  Chantal Peiffert  Kirsti Loukola-Ruskeeniemi  Esa Pohjolainen  Hannu Lahtinen 《Mineralium Deposita》2014,49(4):513-533

In the central part of the Fennoscandian Shield, the Talvivaara Ni–Zn–Cu–Co deposit, hosted by Palaeoproterozoic metamorphosed black schists, contains low uranium concentrations ranging from 10 to 30 ppm. The Talvivaara black schists were deposited 2.0–1.9 Ga ago and underwent subsequent metamorphism during the 1.9–1.79 Ga Svecofennian orogeny. Anhedral uraninite crystals rimmed by bitumen constitute the main host of uranium. U–Pb secondary ion mass spectrometry dating indicates that uraninite crystals were formed between 1,878?±?17 and 1,871?±?43 Ma, during peak metamorphism. Rare earth element patterns and high Th content (average 6.38 wt%) in disseminated uraninite crystals indicate that U was concentrated during high temperature metamorphism (>400 °C). The formation of bitumen rims around uraninite may be explained by two distinct scenarios: (a) a transport of U coincident with the migration of hydrocarbons or (b) post-metamorphic formation of bitumen rims, through radiolytic polymerization of gaseous hydrocarbons at the contact with uraninite.  相似文献   

Theoretical study of the local charge compensation and spectroscopic properties of B-type carbonate defects in apatite     

Haohao Yi  Etienne Balan  Christel Gervais  Loïc Ségalen  Marc Blanchard  Michele Lazzeri 《Physics and Chemistry of Minerals》2014,41(5):347-359

The structure and spectroscopic properties of selected models of B-type carbonate defects in apatite locally compensated by fluoride or hydroxyl ions are investigated using first-principles quantum mechanical calculations. Theoretical infrared absorption spectra and ¹³C, and ¹⁹F nuclear magnetic resonance chemical shifts are determined. Among the investigated models, only the clumped (CO₃ ^2?, F^?) defect, with the carbonate group close to the sloping face of the tetrahedral site and the F^? ion at the remaining apex, corresponds to previous experimental observations performed on carbonate-fluorapatite samples. Although the substitution of hydroxyl by fluoride ions is commonly observed in minerals, the clumped (CO₃ ^2?, OH^?) defects are unlikely to occur in apatite, considering both their theoretical spectroscopic properties and relative stability. Anionic F^? for OH^? exchange between channel and B sites displays a preference of ~20 kJ/mol for the local charge compensation by fluoride ions at the B-site, pointing to a significantly different behavior of F^? and OH^? ions in the charge compensation mechanism. This difference is ascribed to the poor H-bond acceptor character of available oxygen atoms surrounding the apex of the tetrahedral site. The explicit calculation of the infrared absorption spectra of the defect models is also used to interpret the significant difference observed in the linewidth of the ν₂ and ν₃ CO₃ infrared powder absorption bands of carbonated apatite samples. It is shown that for a concentration of 4.4 wt% of CO₂, long-range electrostatic effects already significantly contribute to the broadening of the ν₃ CO₃ bands in apatite.  相似文献   

Methodology for Rare Earth Element Determinations of Uranium Oxides by Ion Microprobe     

Jessica Bonhoure  Philippe Kister  Michel Cuney  Etienne Deloule 《Geostandards and Geoanalytical Research》2007,31(3):209-225

A methodology for the determination of the rare earth elements in uranium oxides by ion microprobe has been set up on a Cameca ims-3f instrument. An uranium oxide reference material from a syn-metamorphic uranium deposit related to albitisation has also been developed for this type of analysis. Applications of the methodology are presented for a series of uranium oxides selected from some major uranium deposit types: from the world's highest grade unconformity-related uranium deposit from the Athabasca Basin (Saskatchewan, Canada; the Shea Creek and the McArthur River examples), a perigranitic vein-type deposit (Pen Ar Ran, Vendée, France) and a volcanic caldera-related deposit (Streltsovkoye, Transbaikalia, Russia). Each type of uranium deposit appears to have a specific REE signature. All REE patterns from the Shea Creek and the McArthur deposits are characterised by bell-shaped patterns centred on Tb-Dy and similar to those already published for uranium oxides from unconformity-related deposits from Australia. Such bell-shaped REE patterns centred on Tb-Dy may therefore be considered as a typical signature of uranium oxides from Mesoproterozoic unconformity-related deposits. A smoother bell shape pattern centred on Eu characterises the syn-metamorphic albitisation related deposit of Mistamisk selected for the reference material. The REE patterns from the Pen Ar Ran deposit show a fractionation from LREE to HREE with anomalously high abundances of Sm, Eu and Gd with respect to the other REEs, similar to the REE patterns of uranium oxides from the volcanic-related deposits of Streltsovkoye.  相似文献   

Insights into the high-pressure behavior of kaolinite from infrared spectroscopy and quantum-mechanical calculations     

Mark?D.?WelchEmail author  Wren?Montgomery  Etienne?Balan  Philippe?Lerch 《Physics and Chemistry of Minerals》2012,39(2):143-151

The high-pressure behavior of Keokuk kaolinite has been studied to 9.5 GPa by infrared spectroscopy using synchrotron radiation. The kaolinite-I → kaolinite-II and kaolinite-II → kaolinite-III transformations have clear spectroscopic expression, with discontinuities coinciding with the transformation pressures bracketed by X-ray diffraction (Welch and Crichton in Am Mineral 95:651–654, 2010). The experimental spectra have been interpreted from band assignments derived from density functional theory for the structures of kaolinite-II and kaolinite-III, using as starting models the ab initio structures reported by Mercier and Le Page (Acta Crystallogr A B64:131–143, 2008, Mater Sci Technol 25:437–442, 2009) and unit-cell parameters from Welch and Crichton (Am Mineral 95:651–654, 2010). The relaxed theoretical structures are very similar to those reported by Mercier and Le Page (Acta Crystallogr A B64:131–143, 2008, Mater Sci Technol 25:437–442, 2009) in their theoretical investigation of kaolinite polytypes at high pressure. The vibrational spectra calculated from the quantum-mechanical analysis allow band assignments of the IR spectra to be made and provide insights into the behavior of different OH environments in the two high-pressure polytypes. The single perpendicular-interlayer OH group of kaolinite-III has a distinctive spectroscopic signature that is diagnostic of this polytype (ν = 3,595 cm⁻¹ at 9.5 GPa) and is sensitive to the compression/expansion of the interlayer space. This OH group also has a distinctive signature in the calculated spectra. The spectra collected on decompression are those of kaolinite-III and persist largely unchanged to 4.6 GPa, except for a continuous blue shift of the 3,595 cm⁻¹ band to 3,613 cm⁻¹. Finally, kaolinite-I is recovered at 0.6 GPa, confirming the kaolinite-III → kaolinite-I transformation previously observed by X-ray diffraction, and the irreversibility of the kaolinite-II → kaolinite-III transformation. The ambient spectra collected at the start and finish of the experiment are those of kaolinite-I, and start/finish band frequencies agree to within 6 cm⁻¹.  相似文献   

Experimental and theoretical study of the vibrational properties of diaspore (α-AlOOH)     

Simon?Delattre  Etienne?BalanEmail author  Michele?Lazzeri  Marc?Blanchard  Maxime?Guillaumet  Olivier?Beyssac  Eiken?Haussühl  Bj?rn?Winkler  Ekhard?K.?H.?Salje  Georges?Calas 《Physics and Chemistry of Minerals》2012,39(2):93-102

Vibrational properties of diaspore, α-AlOOH, have been re-investigated using room-temperature single-crystal Raman spectroscopy and low-temperature powder infrared (IR) transmission spectroscopy. First-principles harmonic calculations based on density functional theory provide a convincing assignment of the major Raman peaks and infrared absorption bands. The large width of the Raman band related to OH stretching modes is ascribed to mode–mode anharmonic coupling due to medium-strength H-bonding. Additional broadening in the powder IR spectrum arises from depolarization effects in powder particles. The temperature dependence of the IR spectrum provides a further insight into the anharmonic properties of diaspore. Based on their frequency and temperature behavior, narrow absorption features at ~2,000 cm⁻¹ and anti-resonance at ~2,966 cm⁻¹ in the IR spectrum are interpreted as overtones of fundamental bending bands.  相似文献   

Site effect assessment using KiK-net data: part 2—site amplification prediction equation based on f<Subscript>0</Subscript> and Vsz     

Cadet Héloïse  Anne-Marie Duval  Etienne Bertrand 《Bulletin of Earthquake Engineering》2012,10(2):451-489

This paper presents empirical correlations between amplification factors and simple site parameters derived from a large subset of the KiK-net data. The amplification factor is estimated from the ratios between the surface and down-hole horizontal response spectra, corrected for the varying depths and impedance of the down-hole sites (Cadet et al. in Site effect assessment using KiK-net data—part 1—a simple correction procedure for surface/downhole spectral ratios, 2011). Several site parameters are selected on the basis of their simplicity and availability at relatively low cost. They are the shallow time-average velocities V_SZ, with z equal to 5, 10, 20 and 30 m, and the fundamental frequency f₀. The amplification factors are then correlated with each of the individual site parameters; four other “twin-parameter”—couples (f₀, V_SZ)—are also considered and the correlation with amplification factors is performed through a normalization of the frequencies by each site fundamental frequency. The quality of the correlations is given by a misfit compared with the original data variance. The largest variance reduction is obtained with twin-parameter characterizations, out of which the couple (f₀, V_S30) proves to provide the lower misfit. The performance of single parameter correlations is relatively lower; however, the best single parameter proves to be the fundamental frequency, which provides smaller misfit than the Vsz parameters. A comparison is also performed with the amplification factors recommended in European regulations, showing that it is possible right now to significantly improve both the site characterization criteria and the associated amplification factors, for use in building codes and microzonation studies.  相似文献   

Fluid flow dynamics under location uncertainty     

Etienne Mémin 《地球物理与天体物理流体动力学》2014,108(2):119-146

We present a derivation of a stochastic model of Navier Stokes equations that relies on a decomposition of the velocity fields into a differentiable drift component and a time uncorrelated uncertainty random term. This type of decomposition is reminiscent in spirit to the classical Reynolds decomposition. However, the random velocity fluctuations considered here are not differentiable with respect to time, and they must be handled through stochastic calculus. The dynamics associated with the differentiable drift component is derived from a stochastic version of the Reynolds transport theorem. It includes in its general form an uncertainty dependent subgrid bulk formula that cannot be immediately related to the usual Boussinesq eddy viscosity assumption constructed from thermal molecular agitation analogy. This formulation, emerging from uncertainties on the fluid parcels location, explains with another viewpoint some subgrid eddy diffusion models currently used in computational fluid dynamics or in geophysical sciences and paves the way for new large-scales flow modeling. We finally describe an applications of our formalism to the derivation of stochastic versions of the Shallow water equations or to the definition of reduced order dynamical systems.  相似文献