Contractivity-preserving explicit multistep Hermite–Obrechkoff series differential equation solvers

New optimal, contractivity-preserving (CP), explicit, d-derivative, k-step Hermite–Obrechkoff series methods of order p up to \(p=20\), denoted by CP HO(d, k, p), with nonnegative coefficients are constructed. These methods are used to solve nonstiff first-order initial value problems \(y'=f(t,y)\), \(y(t_0)=y_0\). The upper bound \(p_u\) of order p of HO(d, k, p) can reach, approximately, as high as 2.4 times the number of derivatives d. The stability regions of HO(d, k, p) have generally a good shape and grow with decreasing \(p-d\). We, first, note that three selected CP HO methods: 4-derivative 7-step HO of order 13, denoted by HO(4, 7, 13), 5-derivative 6-step HO of order 13, denoted by HO(5, 6, 13), and 9-derivative 2-step HO of order 13, denoted by CMDAHO(13) compare favorably with Adams–Cowell of order 13, denoted by AC(13), in solving standard N-body problems over an interval of 1000 periods on the basis of the relative error of energy as a function of the CPU time. Next, the three HO methods compare positively with AC(13) in solving standard N-body problems on the basis of the growth of relative positional error and relative energy error over 10, 000 periods of integration. Finally, these three methods compare also well with P-stable methods of Cash and Franco et al. on some quasi periodic, second-order linear and nonlinear problems. The coefficients of selected HO methods are listed in the appendix.     

In situ U–Pb dating of micro-baddeleyite by secondary ion mass spectrometry

We introduce a technique for U–Pb dating of baddeleyite using secondary ion mass spectrometry (SIMS) in situ analysis of ng-mass crystals that cannot be efficiently extracted by conventional mineral separation techniques. Average ²⁰⁷Pb/²⁰⁶Pb ages for Precambrian baddeleyite crystals are within < 0.3% of the respective isotope dilution thermal ionization mass spectrometry (ID-TIMS) ages. ²⁰⁶Pb/²³⁸U ratios are corrected for instrumental fractionation calibrated through linear regression in a Pb/U relative sensitivity vs. UO₂⁺/U⁺ calibration plot. Calibration is performed on separated baddeleyite crystals (～ 100–200 μm in maximum dimension) mounted in random crystallographic orientation. ²⁰⁶Pb/²³⁸U ages for baddeleyite from Duluth gabbro (FC4b) and Kovdor are accurate within 1–2% when averaging 15–30 individual spot analyses and relative sensitivities calibrated on Phalaborwa baddeleyite. The relative difference of ²⁰⁶Pb/²³⁸U between large crystals and micro-baddeleyite from FC4b is within ～ 1%. Comparison between silicate glass and baddeleyite, as well as replicate analysis of the same grains in different orientations relative to the incidence direction of the primary beam support previous evidence for bias in Pb/U sensitivity in baddeleyite due to variable crystal orientations. We successfully utilized oxygen flooding and a UO₂⁺/U⁺-based calibration to significantly reduce orientation dependent bias.     

In situ U–Pb SIMS (IN-SIMS) micro-baddeleyite dating of mafic rocks: Method with examples

An in situ U–Pb SIMS (IN-SIMS) method to date micro-baddeleyite crystals as small as 3 μm is presented with results from three samples that span a variety of ages and geologic settings. The method complements ID-TIMS geochronology by extending the range of dateable crystals to sizes smaller than can be recovered by physical separation. X-ray mapping and BSE imaging are used to locate target grains in thin section, followed by SIMS analysis on a CAMECA ims 1270, using the field aperture in the transfer column to screen out ions from host phases. Internal age precisions for the method are anticipated to range from 0.1% for Precambrian rocks to 3–7% for Phanerozoic rocks. Results establish a 2689 ± 5 Ma age for mafic dikes in the Wyoming craton, USA, a 1540 ± 30 Ma age for a subaerial lava flow from the Thelon Basin of northern Canada, and a 457 ± 34 Ma age for mafic dikes in the platform sequence of southeastern Siberia. The method is ideal for relatively non-destructive dating of small samples such as extraterrestrial rocks and precious terrestrial samples.     

An EPR study of native radiation-induced paramagnetic defects in sudoite (di–trioctahedral Al–Mg chlorite) from the alteration halo related to unconformity-type uranium deposits

Natural radiation-induced defects were identified in specimens of sudoite (Al–Mg di-trioctahedral chlorite) related to unconformity-type uranium deposits at the base of the Athabasca Group (Saskatchewan, Canada), using electron paramagnetic resonance (EPR) spectroscopy at X- and Q-band frequencies. X-band spectra indicate the presence of a main native defect, named the A_s-center, whose EPR signal is dominated by an axially distorted spectrum with apparent principal components as follows: g _// = 2,051 and g _⊥ = 2,005, and a secondary defect with apparent component g = 2,025. The study of oriented specimens shows that the main defect has its g _// component perpendicular to the (ab) plane of sudoite. The A_s-center corresponds to an electron hole located on oxygen atoms of the structure and is likely associated with Si, according to the lack of hyperfine structure. The A_s-center in sudoite has EPR parameters similar to the A-center in kaolinite and dickite, and the A_i-center in illite. The saturation behavior of EPR spectra as a function of power demonstrates that native defects of sudoite are different from those known in other clays, such as kaolinite, dickite or smectite, but are similar to those of illite. The isochronal annealing data suggest that the main defect in sudoite is stable to more than 300°C. The corresponding defects characterized in sudoite may have the potential for tracing past radionuclide migration around unconformity-type uranium deposits.     

Mobility of metals in nickel mine spoil materials

An understanding of the biogeochemical behaviour of metals in mine spoil materials is a prerequisite to rehabilitate Ni mining sites. The objective of this study was to characterize the fate of metals in different Ni ore spoil materials as influenced by hydrological conditions and fertilisation practices. In tropical ultramafic complexes, the different stages of lateritic weathering lead to two types of ores, and therefore, to two spoil types. They are mainly either a clay-rich saprolite, so-called “garnierite”, enriched in phyllosilicates, or a limonitic material, enriched in Fe oxides. Lysimeter columns were designed to monitor leaching waters through both spoil materials. The garnieritic spoil released higher concentrations of Mg (mean = 2.25 mg L⁻¹), Ni (0.39 mg L⁻¹) and Cr (1.19 mg L⁻¹) than the limonitic spoil (Mg = 0.5 mg L⁻¹; Ni = 0.03 mg L⁻¹ and Cr = 0.25 mg L⁻¹). Chromium was mainly in an anionic form in leaching solutions. As exchangeable pools of Cr(VI) in limonite (980 mg kg⁻¹ of KH₂PO₄-extractable Cr) are considerable its release in water may still occur in the case of a pH increase. In mixed spoil, metal concentrations were almost as low as in the limonitic one. The effect of mineral-N fertilisation was a strong release of cations (Ni, Mg) into the leachate. Phosphate amendment did not affect the soil solution composition under experimental conditions.     

The recording of floods and earthquakes in Lake Chichój,Guatemala during the twentieth century

Laguna Chichój (Lake Chichój) is the only deep permanent lake in the central highlands of Guatemala. The lake is located in the boundary zone between the North American and Caribbean plates. The lake has been struck by devastating earthquakes and tropical cyclones in historical times. We investigated the imprint of twentieth century extreme events on the sedimentary record of this tropical lake using a bathymetric survey of the lake, coring the lake floor, and providing a chronology of sediment accumulation. The lake occupies a series of circular depressions likely formed by the rapid dissolution of a buried body of gypsum. ²¹⁰Pb and ¹³⁷Cs inventories and varve counting indicate high rates of sedimentation (1–2 cm year^?1). The annually layered sediment is interrupted by turbidites of two types: a darker-colored turbidite, enriched in lake-derived biogenic constituents, and interpreted as a seismite, and a lighter-colored type, enriched in catchment-derived constituents, interpreted as a flood layer. Comparison of our ¹³⁷Cs-determined layer ages with a catalog of twentieth century earthquakes shows that an earthquake on the Motagua fault in 1976 generated a conspicuous darker-colored turbidite and slumped deposits in separate parts of the lake. The entire earthquake inventory further reveals that mass movements in the lake are triggered at Modified Mercalli Intensities higher than V. Tropical cyclonic depressions known to have affected the lake area had limited effect on the lake, including Hurricane Mitch in 1998. One storm however produced a significantly thicker flood layer in the 1940s. This storm is reportedly the only event to have generated widespread slope failures in the lake catchment. It is thus inferred that abundant landsliding provided large amounts of concentrated sediment to the lake, through hyperpycnal flows.     

Spatio-temporal variability of currents over a mobile dune field in the Dover Strait

A one month field campaign featuring two spring–neap tide cycles and three strong storms has been performed in a mobile dune area located in the central part of the Dover Strait. These dunes are known to move in a complex manner as their migration direction varies in space and time (Le Bot et al., 2000, Le Bot, 2001, Le Bot and Trentesaux, 2004). In order to gain some insights into the dune motion processes we present an analysis of the spatio-temporal variability of currents in the area emphasizing the relative influence of tides and storms. A total of eight different hydro-meteorological regimes have been distinguished during the experiment duration. The analysis of the currents measurements at five locations in the area shows that the eight hydro-meteorological regimes induce very different current responses at the bottom. The residual tidal currents exhibit a significant spatial variability both in direction and in intensity. A numerical model of tidal currents over the Dover Strait confirms the strong spatio-temporal variability of the residual tidal currents featuring three singular points. Amongst them, a saddle point is located just south of the I-dune at the convergence of opposite direction residual tidal currents. The wind-induced currents are almost uniform in space, their intensity and direction however strongly depends on the wind regime and thus on time. The mean total current feature a spatial pattern which can be tidal of wind-induced currents dominated, or either in balance, depending on the regime considered. At the PERMOD campaign time scale, the total current is dominated by the residual tidal current. These results proved to give valuable insights to explain the complex dynamics of dune motion observed in this area by Le Bot et al., 2000, Le Bot, 2001, Le Bot and Trentesaux, 2004 at short and long time scales.