Neoproterozoic geodynamic evolution of SW-Gondwana: a southern African perspective

Our current understanding of the tectonic history of the principal Pan-African orogenic belts in southwestern Africa, reaching from the West Congo Belt in the north to the Lufilian/Zambezi, Kaoko, Damara, Gariep and finally the Saldania Belt in the south, is briefly summarized. On that basis, possible links with tectono-stratigraphic units and major structures on the eastern side of the Rio de la Plata Craton are suggested, and a revised geodynamic model for the amalgamation of SW-Gondwana is proposed. The Rio de la Plata and Kalahari Cratons are considered to have become juxtaposed already by the end of the Mesoproterozoic. Early Neoproterozoic rifting led to the fragmentation of the northwestern (in today`s coordinates) Kalahari Craton and the splitting off of several small cratonic blocks. The largest of these ex-Kalahari cratonic fragments is probably the Angola Block. Smaller fragments include the Luis Alves and Curitiba microplates in eastern Brazil, several basement inliers within the Damara Belt, and an elongate fragment off the western margin, named Arachania. The main suture between the Kalahari and the Congo-So Francisco Cratons is suspected to be hidden beneath younger cover between the West Congo Belt and the Lufilian/Zambezi Belts and probably continues westwards via the Cabo Frio Terrane into the Goias magmatic arc along the Brasilia Belt. Many of the rift grabens that separated the various former Kalahari cratonic fragments did not evolve into oceanic basins, such as the Northern Nosib Rift in the Damara Belt and the Gariep rift basin. Following latest Cryogenian/early Ediacaran closure of the Brazilides Ocean between the Rio de la Plata Craton and the westernmost fragment of the Kalahari Craton, the latter, Arachania, became the locus of a more than 1,000-km-long continental magmatic arc, the Cuchilla Dionisio-Pelotas Arc. A correspondingly long back-arc basin (Marmora Basin) on the eastern flank of that arc is recognized, remnants of which are found in the Marmora Terrane-the largest accumulation of oceanic crustal material known from any of the Pan-African orogenic belts in the region. Corresponding foredeep deposits that emerged from the late Ediacaran closure of this back-arc basin are well preserved in the southern areas, i.e. the Punta del Este Terrane, the Marmora Terrane and the Tygerberg Terrane. Further to the north, present erosion levels correspond with much deeper crustal sections and comparable deposits are not preserved anymore. Closure of the Brazilides Ocean, and in consequence of the Marmora back-arc basin, resulted from a change in the Rio de la Plata plate motion when the Iapetus Ocean opened between the latter and Laurentia towards the end of the Ediacaran. Later break-up of Gondwana and opening of the modern South Atlantic would have followed largely along the axis of the Marmora back-arc basin and not along major continental sutures.

Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

ENO adaptive method for solving one-dimensional conservation laws

In this work an efficient third order non-linear finite difference scheme for solving adaptively hyperbolic systems of one-dimensional conservation laws is developed. The method is based oil applying to the solution of the differential equation an interpolating wavelet transform at each time step, generating a multilevel representation for the solution, which is thresholded and a sparse point representation is generated. The numerical fluxes obtained by a Lax-Friedrichs flux splitting are evaluated oil the sparse grid by an essentially non-oscillatory (ENO) approximation, which chooses the locally smoothest stencil among all the possibilities for each point of the sparse grid. The time evolution of the differential operator is done on this sparse representation by a total variation diminishing (TVD) Runge-Kutta method. Four classical examples of initial value problems for the Euler equations of gas dynamics are accurately solved and their sparse solutions are analyzed with respect to the threshold parameters, confirming the efficiency of the wavelet transform as an adaptive grid generation technique. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

Let M be a compact, connected non-orientable surface without boundary and of genus g >= 3. We investigate the pure braid groups P,(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 -> P(m)(M \ {x(1), ..., x(n)}) hooked right arrow P(n+m)(M) (P*) under right arrow P(n)(M) -> 1, where m, n >= 1, and p* is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p: F(n+m)(M) -> F(n)(M) of configuration spaces, defined by p((x(1), ..., x(n), x(n+1), ..., x(n+m))) = (x(1), ..., x(n)). We show that p and p* admit a section if and only if n = 1. Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups. (C) 2009 Elsevier B.V. All rights reserved.

Feasibility of using in situ fusion for the determination of Co, Cr and Mn in Portland cement by direct solid sampling graphite furnace atomic absorption spectrometry

In situ fusion on the boat-type graphite platform has been used as a sample pretreatment for the direct determination of Co, Cr and Mn in Portland cement by solid sampling graphite furnace atomic absorption spectrometry (SS-GF AAS). The 3-field Zeeman technique was adopted for background correction to decrease the sensitivity during measurements. This strategy allowed working with up to 200 mu g of sample. The in situ fusion was accomplished using 10 mu L of a flux mixture 4.0% m/v Na(2)CO(3) + 4.0% m/v ZnO + 0.1% m/v Triton (R) X-100 added over the cement sample and heated at 800 degrees C for 20 s. The resulting mould was completely dissolved with 10 mu L of 0.1% m/v HNO(3). Limits of detection were 0.11 mu g g(-1) for Co, 1.1 mu g g(-1) for Cr and 1.9 mu g g(-1) for Mn. The accuracy of the proposed method has been evaluated by the analysis of certified reference materials. The values found presented no statistically significant differences compared to the certified values (Student`s t-test, p<0.05). In general, the relative standard deviation was lower than 12% (n = 5). (C) 2009 Elsevier B.V. All rights reserved.

Direct determination of iron in sand using solid sampling graphite furnace atomic absorption spectrometry

A fast and reliable method for the direct determination of iron in sand by solid sampling graphite furnace atomic absorption spectrometry was developed. A Zeeman-effect 3-field background corrector was used to decrease the sensitivity of spectrometer measurements. This strategy allowed working with up to 200 mu g of samples, thus improving the representativity. Using samples with small particle sizes (1-50 mu m) and adding 5 mu g Pd as chemical modifier, it was possible to obtain suitable calibration curves with aqueous reference solutions. The pyrolysis and atomization temperatures for the optimized heating program were 1400 and 2500 degrees C, respectively. The characteristic mass, based on integrated absorbance, was 56 pg, and the detection limits, calculated considering the variability of 20 consecutive measurements of platform inserted without sample was 32 pg. The accuracy of the procedure was checked with the analysis of two reference materials (IPT 62 and 63). The determined concentrations were in agreement with the recommended values (95% confidence level). Five sand samples were analyzed, and a good agreement (95% confidence level) was observed using the proposed method and conventional flame atomic absorption spectrometry. The relative standard deviations were lower than 25% (n = 5). The tube and boat platform lifetimes were around 1000 and 250 heating cycles, respectively.

Application of solid sampling device for direct determination of chromium and nickel in lubricating oils by graphite furnace atomic absorption spectrometry

One method using a solid sampling device for the direct determination of Cr and Ni in fresh and used lubricating oils by graphite furnace atomic absorption spectrometry are proposed. The high organic content in the samples was minimized using a digestion step at 400 degrees C in combination with an oxidant mixture 1.0% (v v(-1)) HNO3+15% (v v(-1)) H2O2+0.1% (m v(-1)) Triton X-100 for the in situ digestion. The 3-field mode Zeeman-effect allowed the spectrometer calibration up to 5 ng of Cr and Ni. The quantification limits were 0.86 mu g g(-1) for Cr and 0.82 mg g(-1) for Ni, respectively. The analysis of reference materials showed no statistically significant difference between the recommended values and those obtained by the proposed methods.

Interfacial Electron Transfer Dynamics Following Laser Flash Photolysis of [Ru(bpy)(2)((4,4 `-PO(3)H(2))(2)bpy)](2+) in TiO(2) Nanoparticle Films in Aqueous Environments

Nanosecond laser flash photolysis has been used to investigate injection and back electron transfer from the complex [(Ru-(bpy)(2)(4,4`-(PO(3)H(2))(2)bpy)](2+) surface-bound to TiO(2) (TiO(2)-Ru(II)). The measurements were conducted under conditions appropriate for water oxidation catalysis by known single-site water oxidation catalysts. Systematic variations in average lifetimes for back electron transfer, - were observed with changes in pH, surface coverage, incident excitation intensity, and applied bias. The results were qualitatively consistent with a model involving rate-limiting thermal activation of injected electrons from trap sites to the conduction band or shallow trap sites followed by site-to-site hopping and interfacial electron transfer, TiO(2)(e(-))-Ru(3+) -> TiO(2)-Ru(2+). The appearance of pH-dependent decreases in the efficiency of formation of TiO(2)-Ru(3+) and in incident-photon-to-current efficiencies with the added reductive scavenger hydroquinone point to pH-dependent back electron transfer processes on both the sub-nanosecond and millisecond-microsecond time scales, which could be significant in limiting long-term storage of multiple redox equivalents.