Crystallization conditions and controls on trace element residence in the main minerals from the Pedra Branca Syenite, Brazil: An electron microprobe and LA-ICPMS study

Major and trace-element microanalyses of the main minerals from the 610 Ma Pedra Branca Syenite, southeast Brazil, allow inferences on intensive parameters of magmatic crystallization and on the partition of trace-elements among these minerals, with important implications for the petrogenetic evolution of the pluton. Two main syenite types make up the pluton, a quartz-free syenite with tabular alkali feldspar (laminated silica-saturated syenite, LSS, with Na-rich augite + phlogopite + hematite + magnetite + titanite + apatite) and a quartz-bearing syenite (laminated silica-oversaturated syenite, LSO, with scarce corroded plagioclase plus diopside + biotite +/- hornblende + ilmenite magnetite +/- titanite + apatite). Both types share a remarkable enrichment in incompatible elements as K, Ba, Sr, P and LREE. Apatite saturation temperatures of similar to 1060-1090 degrees C are the best estimates of liquidus, whereas the pressure of emplacement, based on Al-in-hornblende barometry, is estimated as 3.3 to 4.8 khan Although both units crystallized under oxidizing conditions, oxygen fugacity was probably higher in LSS, as shown by higher mg# of the mafic minerals and higher hematite contents in Hem-Ilm(ss). In contrast with the Ca-bearing alkali-feldspar from LSO, which hosts most of the whole-rock Sr and Pb, virtually Ca-free alkali-feldspar from LSS hosts similar to 50% of whole-rock Sr and similar to 80% of Pb, the remainder of these elements being shared by apatite, pyroxene and titanite. This contrast reflects a strong crystal-chemical control, whereby a higher proportion of an element with similar ratio and charge (Ca2+) enhances the residence of Sr and Pb in the M-site of alkali feldspar. The more alkaline character of the LSS magma is inferred to have inhibited zircon saturation; Zr + Hf remained in solution until late in the crystallization, and were mostly accommodated in the structure of Ca-Na pyroxene and titanite, which are one order of magnitude richer in these elements compared to the same minerals in LSO, where most of Zr and Hf are inferred to reside in zircon. The REE, Th and U reside mostly in titanite and apatite; D(REE)Tit/Ap raises steadily from 1 to 6 from La to Tb then remains constant up to Lu in the LSO sample; these values are about half as much in the LSS sample, where lower contents of incompatible elements in titanite are attributed to its greater modal abundance and earlier crystallization. (C) 2012 Elsevier B.V. All rights reserved.

Re-Os isotope and highly siderophile element systematics of the Parana continental flood basalts (Brazil)

Basalts of the Parana continental flood basalt (PCFB) province erupted through dominantly Proterozoic continental crust during the Cretaceous. In order to examine the mantle source(s) of this major flood basalt province, we studied Os, Sr, Nd, and Pb isotope systematics, and highly siderophile element (HSE) abundances in tholeiitic basalts that were carefully chosen to show the minimal effects of crustal contamination. These basalts define a precise Re-Os isochron with an age of 131.6 +/- 2.3 Ma and an initial Os-187/Os-188 of 0.1295 +/- 0.0018 (gamma Os-187 = +2.7 +/- 1.4). This initial Os isotopic composition is considerably more radiogenic than estimates of the contemporary Depleted Mantle (DM). The fact that the Re-Os data define a well constrained isochron with an age similar to Ar-40/Ar-39 age determinations, despite generally low Os concentrations, is consistent with closed-system behavior for the HSE. Neodymium, Sr, and Pb isotopic data suggest that the mantle source of the basalts had been variably hybridized by melts derived from enriched mantle components. To account for the combined Os, Nd, Sr, and Pb isotopic characteristics of these rocks, we propose that the primary melts formed from metasomatized asthenospheric mantle (represented by arc-mantle peridotite) that underwent mixing with two enriched components, EM-I and EM-II. The different enriched components are reflected in minor isotopic differences between basalts from southern and northern portions of the province. The Tristan da Cunha hotspot has been previously suggested to be the cause of the Parana continental flood basalt magmatism. However, present-day Tristan da Cunha lavas have much higher Os-187/Os-188 isotopic compositions than the source of the PCFB. These data, together with other isotopic and elemental data, preclude making a definitive linkage between the Tristan plume and the PCFB. (C) 2012 Elsevier B.V. All rights reserved.

Relative Predicativity and dependent recursion in second-order set theory and higher-orders theories

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ω. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).

(Table 1) Trace element/Ca ratios of Orbulina universa shells from late Neogene Mediterranean samples

A Mediterranean composite sedimentary record was analyzed for Ba/Ca ratios on carbonate shells of Orbulina universa planktonic foraminifer (Ba/Ca)carb providing the opportunity to study and assess the extent of freshwater inputs on the basin and possible impacts on its dynamics during the Tortonian to Recent period. A number of scanning electron microscope analyses and auxiliary trace element measurements (Mn, Sr, and Mg), obtained from the same samples, exclude important diagenetic effects on the studied biogenic carbonates and corroborate the reliability of (Ba/Ca)carb ratios in foraminifera calcite as indicators of seawater source components during the studied interval. A long-term trend with (Ba/Ca)carb values shifting from ~7 to 3 µmol/mol from the base of the Tortonian to the top of the Messinian is observed. The interval of the late Messinian salinity crisis, where biogenic carbonates are missing or strongly diagenized, represents a crucial passage not monitored in our record. At the base of the Pliocene, up to about 4.7 Ma, the (Ba/Ca)carb record shows a decreasing trend from ~4 µmol/mol stabilizing itself to an about constant value of 0.9 ± 0.3 µmol/mol for the whole Plio-Pleistocene interval. These results suggest a dramatic change in the continental runoff values, up to ~3-16 times higher during part of the late Neogene (Tortonian-early Pliocene), with a possible profound modification in the physical dynamics of the Mediterranean basin. First-order mass balance equations used to estimate barium and salinity budgets in the Mediterranean Sea during the late Miocene-early Pliocene interval support the hypothesis of an active connection of the basin with the Paratethys region and of a definitive restriction at the base of the Pliocene after about 0.7 Ma from the well-known Messinian Lagomare phase. They also open intriguing scenarios on possible circulation shifts during the Neogene.

Platinum-group, major, and trace element abundances in ODP Leg 183 basalts

Seventeen basalts from Ocean Drilling Program (ODP) Leg 183 to the Kerguelen Plateau (KP) were analyzed for the platinum-group elements (PGEs: Ir, Ru, Rh, Pt, and Pd), and 15 were analyzed for trace elements. Relative concentrations of the PGEs ranged from ~0.1 (Ir, Ru) to ~5 (Pt) times primitive mantle. These relatively high PGE abundances and fractionated patterns are not accounted for by the presence of sulfide minerals; there are only trace sulfides present in thin-section. Sulfur saturation models applied to the KP basalts suggest that the parental magmas may have never reached sulfide saturation, despite large degrees of partial melting (~30%) and fractional crystallization (~45%). First order approximations of the fractionation required to produce the KP basalts from an ~30% partial melt of a spinel peridotite were determined using the PELE program. The model was adapted to better fit the physical and chemical observations from the KP basalts, and requires an initial crystal fractionation stage of at least 30% olivine plus Cr-spinel (49:1), followed by magma replenishment and fractional crystallization (RFC) that included clinopyroxene, plagioclase, and titanomagnetite (15:9:1). The low Pd values ([Pd/Pt]_pm < 1.7) for these samples are not predicted by currently available Kd values. These Pd values are lowest in samples with relatively higher degrees of alteration as indicated by petrographic observations. Positive anomalies are a function of the behavior of the PGEs; they can be reproduced by Cr-spinel, and titanomagnetite crystallization, followed by titanomagnetite resorption during the final stages of crystallization. Our modeling shows that it is difficult to reproduce the PGE abundances by either depleted upper or even primitive mantle sources. Crustal contamination, while indicated at certain sites by the isotopic compositions of the basalts, appears to have had a minimal affect on the PGEs. The PGE abundances measured in the Kerguelen Plateau basalts are best modeled by melting a primitive mantle source to which was added up to 1% of outer core material, followed by fractional crystallization of the melt produced. This reproduces both the abundances and patterns of the PGEs in the Kerguelen Plateau basalts. An alternative model for outer core PGE abundances requires only 0.3% of outer core material to be mixed into the primitive mantle source. While our results are clearly model dependent, they indicate that an outer core component may be present in the Kerguelen plume source.

Major element chemistr yof fallout tephra from ODP Hole 125-782A

New and published analyses of major element oxides (SiO2, TiO2, Al2O3, FeO*, MnO, MgO, CaO, K2O, Na2O and P2O5) from the central Izu Bonin and Mariana arcs (IBM) were compiled in order to investigate the evolution of the IBM in terms of major elements since arc inception at ~49 million years ago. The database comprises ?3500 volcanic glasses of distal tephra fallout and ?500 lava samples, ranging from the Quaternary to mid-Eocene in age. The data were corrected to 4 wt% MgO in order to display the highly resolved temporal trends. These trends show that the IBM major elements have always been "arc-like" and clearly distinct from N-MORB. Significant temporal variations of some major element oxides are apparent. The largest variations are displayed by K4.0. The data support a model wherein the K2O variability is caused by the addition of slab component with strongly differing K2O contents to a fairly depleted subarc mantle; variable extents of melting, or mantle heterogeneity, appear to play a negligible role. The other major element oxides are controlled by the composition and processes of the subarc mantle wedge. The transition from the boninitic and tholeiitic magmatism of the Eocene and Oligocene to the exclusively tholeiitic magmatism of the Neogene IBM is proposed to reflect a change in the composition of the subarc mantle wedge. The early boninitic magmas originate from an ultra-depleted subarc mantle, that is residual to either the melting of E-MORB mantle, or of subcontinental lithospheric mantle. During the Eocene and Oligocene, this residual mantle is gradually replaced by Indian MORB mantle advected from the backarc regions. The Indian MORB mantle is more radiogenic in Nd isotope ratios but also more fertile with respect to major and trace elements. Therefore the Neogene tholeiites have higher Al2O3 and TiO2 contents and lower mg# numbers at given SiO2 content. After the subarc mantle replacement was complete in the late Oligocene or early Miocene, the Neogene IBM entered a "steady state" that is characterized by the continuous advection of Indian MORB mantle from the reararc, which is fluxed by fluids and melt components from slab. The thickness of the IBM crust must have grown with time, but any effects of crustal thickening on the major element chemistry of the IBM magmas appear to be minor relative to the compositional changes that are related to source composition. Therefore next to the processes of melting, the composition of the mantle sources must play a major role in creating substantiative heterogeneities in the major element chemistry of the arc crust.

A second order in time modified Lagrange-Galerkin finite element method for the incompressible Navier-Stokes equations

We introduce a second order in time modified Lagrange--Galerkin (MLG) method for the time dependent incompressible Navier--Stokes equations. The main ingredient of the new method is the scheme proposed to calculate in a more efficient manner the Galerkin projection of the functions transported along the characteristic curves of the transport operator. We present error estimates for velocity and pressure in the framework of mixed finite elements when either the mini-element or the $P2/P1$ Taylor--Hood element are used.

Adaptation Strategies for Discontinuous Galerkin Spectral Element Methods by means of Truncation Error Estimations

In this work a p-adaptation (modification of the polynomial order) strategy based on the minimization of the truncation error is developed for high order discontinuous Galerkin methods. The truncation error is approximated by means of a truncation error estimation procedure and enables the identification of mesh regions that require adaptation. Three truncation error estimation approaches are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. Fine solutions, which are obtained by enriching the polynomial order, are required to solve the numerical problem with adequate accuracy. For the three truncation error estimation methods the former needs time converged solutions, while the last two rely on non-converged solutions, which lead to faster computations. Based on these truncation error estimation methods, algorithms for mesh adaptation were designed and tested. Firstly, an isotropic adaptation approach is presented, which leads to equally distributed polynomial orders in different coordinate directions. This first implementation is improved by incorporating a method to extrapolate the truncation error. This results in a significant reduction of computational cost. Secondly, the employed high order method permits the spatial decoupling of the estimated errors and enables anisotropic p-adaptation. The incorporation of anisotropic features leads to meshes with different polynomial orders in the different coordinate directions such that flow-features related to the geometry are resolved in a better manner. These adaptations result in a significant reduction of degrees of freedom and computational cost, while the amount of improvement depends on the test-case. Finally, this anisotropic approach is extended by using error extrapolation which leads to an even higher reduction in computational cost. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier-Stokes equations. The main result is that the two quasi-a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of a factor of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively. RESUMEN En este trabajo se ha desarrollado una estrategia de adaptación-p (modificación del orden polinómico) para métodos Galerkin discontinuo de alto orden basada en la minimización del error de truncación. El error de truncación se estima utilizando el método tau-estimation. El estimador permite la identificación de zonas de la malla que requieren adaptación. Se distinguen tres técnicas de estimación: a posteriori, quasi a priori y quasi a priori con correción. Todas las estrategias requieren una solución obtenida en una malla fina, la cual es obtenida aumentando de manera uniforme el orden polinómico. Sin embargo, mientras que el primero requiere que esta solución esté convergida temporalmente, el resto utiliza soluciones no convergidas, lo que se traduce en un menor coste computacional. En este trabajo se han diseñado y probado algoritmos de adaptación de malla basados en métodos tau-estimation. En primer lugar, se presenta un algoritmo de adaptacin isótropo, que conduce a discretizaciones con el mismo orden polinómico en todas las direcciones espaciales. Esta primera implementación se mejora incluyendo un método para extrapolar el error de truncación. Esto resulta en una reducción significativa del coste computacional. En segundo lugar, el método de alto orden permite el desacoplamiento espacial de los errores estimados, permitiendo la adaptación anisotropica. Las mallas obtenidas mediante esta técnica tienen distintos órdenes polinómicos en cada una de las direcciones espaciales. La malla final tiene una distribución óptima de órdenes polinómicos, los cuales guardan relación con las características del flujo que, a su vez, depenen de la geometría. Estas técnicas de adaptación reducen de manera significativa los grados de libertad y el coste computacional. Por último, esta aproximación anisotropica se extiende usando extrapolación del error de truncación, lo que conlleva un coste computational aún menor. Las estrategias se verifican y se comparan en téminors de precisión y coste computacional utilizando las ecuaciones de Euler y Navier Stokes. Los dos métodos quasi a priori consiguen una reducción significativa del coste computacional en comparación con aumento uniforme del orden polinómico. En concreto, para una capa límite viscosa, obtenemos una mejora en tiempo de computación de 6.6 y 7.6 respectivamente, para las aproximaciones quasi-a priori y quasi-a priori con corrección.

Trace element abundance, and Sr and Nd isotope ratios of dust samples in the Pacific Ocean (Table 2)

Eolian dust preserved in deep-sea sediment cores provides a valuable indicator of past atmospheric circulation and continental paleoclimate. In order to identify the provenance of eolian dust, Nd and Sr isotopic compositions and Rb, Sr and rare earth element (REE) concentrations have been determined for the silicate fractions of deep-sea sediments from the north and central Pacific Ocean. Different regions of the Pacific Ocean are characterized by distinct air-borne inputs, producing a large range in epsolin-Nd (-10 to +1), 87Sr/86Sr (0.705-0.721), La/Yb (5-15), EuN/EuN* (0.6-1.0) and Sr/Nd (4-33). The average Nd isotopic composition of Pacific deep-sea sediments (epsilon-Nd = -6), is more radiogenic than the average from the Atlantic (epsilon-Nd = -8). In contrast, the average147Sm/144Nd ratio for Pacific sediments (0.114) is identical to that of Atlantic sediments and to that of global average riverine suspended material. The values of epsilon-Nd and147Sm/144Nd are positively correlated for the Pacific samples but negatively correlated for Atlantic samples, reflecting a fundamental difference between the dominant components in the end members with radiogenic Nd (island-arc components in the Pacific and LREE-enriched intraplate ocean island components in the Atlantic). Samples from the north central Pacific have distinctive unradiogenic epsilon-Nd values of -10, 87Sr/86Sr > 0.715, high La/Yb (> 12), and low EuN/EuN* (0.6) and Sr/Nd (3-6). These data are virtually identical to the values for loess from Asia and endorse the use of these sediments as indicators of Asian paleoclimate and paleowind directions. Island-arc contributions appear to dominate in the northwest Pacific, resulting in higher epsilon Nd (-1 to +1) and lower 87Sr/86Sr (~ 0.705) and La/Yb (~ 5). Sediments from the eastern Pacific tend to have intermediate Sr and Nd isotopic compositions but regionally variable Sr/Nd and REE patterns; they appear to be derived from the west margin of the North and South American continents, rather than from Asia. Our results confirm that dust provenance can be constrained by isotopic and geochemical analyses, which will facilitate reconstructions of past atmospheric circulation and continental paleoclimate.

Fibre laser using a microchannel based loss tuning element for refractive index sensing

We have proposed and demonstrated a fibre laser system using a microchannel as a cavity loss tuning element for surrounding medium refractive index (SRI) sensing. A ~6µm width microchannel was created by femtosecond (fs) laser inscription assisted chemical etching in the cavity fibre, which offers a direct access to the external liquids. When the SRI changes, the microchannel behaves as a loss tuning element, hence modulating the laser cavity loss and output power. The results indicate that the presented laser sensing system has a linear response to the SRI with a sensitivity in the order of 10-5. Using higher pump power and more sensitive photodetector, the SRI sensitivity could be further enhanced.

On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is to show that well–known error estimates, established for the finite element approximation of elliptic EVPs with classical BCs, hold for the present types of EVPs too. Some attention is also paid to the computational aspects of the resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial numerical examples, the exact eigenpairs of which can be determined.

Fibre laser using a microchannel based loss tuning element for refractive index sensing

We have proposed and demonstrated a fibre laser system using a microchannel as a cavity loss tuning element for surrounding medium refractive index (SRI) sensing. A ~6µm width microchannel was created by femtosecond (fs) laser inscription assisted chemical etching in the cavity fibre, which offers a direct access to the external liquids. When the SRI changes, the microchannel behaves as a loss tuning element, hence modulating the laser cavity loss and output power. The results indicate that the presented laser sensing system has a linear response to the SRI with a sensitivity in the order of 10-5. Using higher pump power and more sensitive photodetector, the SRI sensitivity could be further enhanced.

(Table 1) Major element composition of core 5022-2CP, Laguna Potrok Aike, southern Patagonia

Total organic carbon, total inorganic carbon, biogenic silica content and total organic carbon/total nitrogen ratios of the Laguna Potrok Aike lacustrine sediment record are used to reconstruct the environmental history of south-east Patagonia during the past 51 ka in high resolution. High lake level conditions are assumed to have prevailed during the Last Glacial, as sediments are carbonate-free. Increased runoff linked to permafrost and reduced evaporation due to colder temperatures and reduced influence of Southern Hemispheric Westerlies (SHW) may have caused these high lake levels with lake productivity being low and organic matter mainly of algal or cyanobacterial origin. Aquatic moss growth and diatom blooms occurred synchronously with southern hemispheric glacial warming events such as the Antarctic A-events, the postglacial warming following the LGM and the Younger Dryas chronozone. During these times, a combination of warmer climatic conditions with related thawing permafrost could have increased the allochthonous input of nutrients and in combination with warmer surface waters increased aquatic moss growth and diatom production. The SHW were not observed to affect southern Patagonia during the Last Glacial. The Holocene presents a completely different lacustrine system because (a) permafrost no longer inhibits infiltration nor emits meltwater pulses and (b) the positioning of the SHW over the investigated area gives rise to strong and dry winds. Under these conditions total organic carbon, total organic carbon/total nitrogen ratios and biogenic silica cease to be first order productivity indicators. On the one hand, the biogenic silica is influenced by dissolution of diatoms due to higher salinity and pH of the lake water under evaporative stress characterizing low lake levels. On the other hand, total organic carbon and total organic carbon/total nitrogen profiles are influenced by reworked macrophytes from freshly exposed lake level terraces during lowstands. Total inorganic carbon remains the most reliable proxy for climatic variations during the Holocene as high precipitation of carbonates can be linked to low lake levels and high autochthonous production. The onset of inorganic carbon precipitation has been associated with the southward shift of the SHW over the latitudes of Laguna Potrok Aike. The refined age-depth model of this record suggests that this shift occurred around 9.4 cal. ka BP.