[1] The finite element method (FEM) combined with unstructured meshes forms an elegant and versatile approach capable of dealing with the complexities of problems in Earth science. Practical applications often require high-resolution models that necessitate advanced computational strategies. We therefore developed ''Million a Minute'' (MILAMIN), an efficient MATLAB implementation of FEM that is capable of setting up, solving, and postprocessing two-dimensional problems with one million unknowns in one minute on a modern desktop computer. MILAMIN allows the user to achieve numerical resolutions that are necessary to resolve the heterogeneous nature of geological materials. In this paper we provide the technical knowledge required to develop such models without the need to buy a commercial FEM package, programming compiler-language code, or hiring a computer specialist. It has been our special aim that all the components of MILAMIN perform efficiently individually and as a package. While some of the components rely on readily available routines, we develop others from scratch and make sure that all of them work together efficiently. One of the main technical focuses of this paper is the optimization of the global matrix computations. The performance bottlenecks of the standard FEM algorithm are analyzed. An alternative approach is developed that sustains high performance for any system size. Applied optimizations eliminate Basic Linear Algebra Subprograms (BLAS) drawbacks when multiplying small matrices, reduce operation count and memory requirements when dealing with symmetric matrices, and increase data transfer efficiency by maximizing cache reuse. Applying loop interchange allows us to use BLAS on large matrices. In order to avoid unnecessary data transfers between RAM and CPU cache we introduce loop blocking. The optimization techniques are useful in many areas as demonstrated with our MILAMIN applications for thermal and incompressible flow (Stokes) problems. We use these to provide performance comparisons to other open source as well as commercial packages and find that MILAMIN is among the best performing solutions, in terms of both speed and memory usage. The corresponding MATLAB source code for the entire MILAMIN, including input generation, FEM solver, and postprocessing, is available from the authors (http://www.milamin.org) and can be downloaded as auxiliary material.

A comprehensive study was made of the synthesis of a spectrum of poly(dialkylstannane)s by catalytic dehydropolymerization of dialkylstannanes (dialkyltin dihydrides, R 2 SnH 2 , prepared by reduction of R 2 SnCl 2 ), with R ) ethyl, propyl, butyl, pentyl, hexyl, octyl, and dodecyl. The polymerization reactions were followed by 1 H and 119 Sn NMR spectroscopy, IR spectroscopy (disappearance of the Sn-H vibration), and quantitative measurement of H 2 which evolved during the reaction. Among the numerous metal complexes employed as catalyst, [RhCl(PPh 3 ) 3 ] was found to be particularly suited for the preparation of these inorganic polymers. The reaction parameters temperature, solvent, R 2 SnH 2 concentration, and [RhCl(PPh 3 ) 3 ]/R 2 SnH 2 ratio were varied, with the most prominent influence on the monomer conversion being the temperature. The numberaverage molar masses of the polystannanes were in the range of 1 × 10 4 to 1 × 10 5 g/mol, depending on the reaction conditions. For the generic case of the polymerization of Bu 2 SnH 2 with [RhCl(PPh 3 ) 3 ] as catalyst, it was demonstrated that poly(dibutylstannane) did not form by a random polycondensation, but by growth at a rhodium complex, whereby only a minor part of [RhCl(PPh 3 ) 3 ] was converted to catalytically active species by reaction with tin hydrides. The polymers featured phase transitions into liquid-crystalline states, on occasion at remarkably low temperatures. A particularly high phase transition temperature was observed for poly(dipropylstannane), which also was characterized by a high density, indicative of a particularly favorable packing of the propyl groups.

SUMMARY Using Muskhelishvili's method, we present closed‐form analytical solutions for an isolated elliptical inclusion in general shear far‐field flows. The inclusion is either perfectly bonded to the matrix or, as in the case of a circular inclusion, to a possible intermediate layer. The solutions are valid for incompressible all‐elastic or all‐viscous systems. The actual values of the shear modulus or viscosity in the inclusion, mantle and matrix can be different and no limits are imposed on the possible material property contrasts. The solutions presented are complete 2‐D solutions and the parameters that can be analysed include all kinematic (e.g. stream functions, velocities, strain rates, strains) and dynamic parameters (e.g. pressure, maximum shear stress, etc.). We refrain from giving the tedious derivation of the presented solutions, and instead we focus on how to use the solutions, how to extract the parameters of interest and how to apply and verify them. In order to demonstrate the usefulness of Muskhelishvili's method for slow viscous flow problems, we apply our results to a clast in a shear zone and obtain important new insights, even for simple, circular inclusions. Another important application is the benchmarking of numerical codes for which the presented solutions are most suitable due to the infinite range of viscosity contrasts and the strong local gradients of properties and results. To stimulate a broader use of Muskhelishvili's method, all solutions are implemented in MATLAB and downloadable from the web.

We present tectonic models of progressive basin formation in the south‐west Barents Sea derived as part of the PETROBAR project (Petroleum‐related studies of the Barents Sea region). The basin architecture developed as a multi‐stage rift preceding the creation of the sheared/transtensional margin conjugate to NE Greenland. N‐ to NNE‐striking basins, with sediment thicknesses in places exceeding 15 km, are separated by basement highs. We use two basin analysis approaches, BMT™ backstripping and TecMod™time‐forward modelling, to determine stretching factors through time along the profile PETROBAR‐07. This 550 km‐long profile derived from wide‐angle reflection/refraction seismic data acquired in 2007, coincident with deep multichannel seismic reflection data. Detailed stratigraphic analysis of the reflection profile, in concert with a dense grid of 2D profiles tied to wells, provides timing and water depth constraint for the models. Velocity analysis of the wide‐angle data provides constraint on the cumulative crustal stretching. The north‐west trending cross‐section extends from continental craton, at the Varanger Peninsula, to within 16 km of the interpreted continent–ocean boundary. Rifting along the profile was episodic, with four distinct phases of basin formation during the Carboniferous, the Late Permian–Triassic, the Late Jurassic–Early Cretaceous and the Late Cretaceous–Eocene. Collectively, the basins exhibit a general trend of younging, narrowing, and deepening oceanward, suggesting a gradual focusing of rifting prior to final breakup. Cumulative stretching factors derived from BMT and TecMod correlate well with observed crustal thinning, and the two models provide uncertainty bounds for stretching factors for the separate rift phases. In contrast to orthogonally rifted margins, stretching is relatively minor immediately prior to transform breakup, with greater stretching occurring during earlier rift phases.

Vent structures are intimately associated with sill intrusions in sedimentary basins globally and are thought to have been formed contemporaneously due to overpressure generated by gas generation during thermogenic breakdown of kerogen or boiling of water. Methane and other gases generated during this process may have driven catastrophic climate change in the geological past. In this study, we present a 2D FEM/FVM model that accounts for 'explosive' vent formation by fracturing of the host rock based on a case study in the Harstad Basin, offshore Norway. Overpressure generated by gas release during kerogen breakdown in the sill thermal aureole causes fracture formation. Fluid focusing and overpressure migration towards the sill tips results in vent formation after only few tens of years. The size of the vent depends on the region of overpressure accessed by the sill tip. Overpressure migration occurs in self-propagating waves before dissipating at the surface. The amount of methane generated in the system depends on TOC content and the type of kerogen present in the host rock. Generated methane moves with the fluids and vents at the surface through a single, large vent structure at the main sill tip matching first-order observations. Violent degassing takes place within the first couple of hundred years and occurs in bursts corresponding to the timing of overpressure waves. The amount of methane vented through a single vent is only a fraction (between 5 and 16%) of the methane generated at depth. Upscaling to the Vøring and Møre Basins, which are a part of the North Atlantic Igneous Province, and using realistic host rock carbon content and kerogen values results in a smaller amount of methane vented than previously estimated for the PETM. Our study, therefore, suggests that the negative carbon isotope excursion (CIE) observed in the fossil record could not have been caused by intrusions within the Vøring and Møre Basins alone and that a contribution from other regions in the NAIP is also required to drive catastrophic climate change.

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[1] The conditions permitting mantle serpentinization during continental rifting are explored within 2-D thermotectonostratigraphic basin models, which track the rheological evolution of the continental crust, account for sediment blanketing effects, and allow for kinetically controlled mantle serpentinization processes. The basic idea is that the entire extending continental crust has to be brittle for crustal scale faulting and mantle serpentinization to occur. The isostatic and latent heat effects of the reaction are fully coupled to the structural and thermal solutions. A systematic parameter study shows that a critical stretching factor exists for which complete crustal embrittlement and serpentinization occurs. Increased sedimentation rates shift this critical stretching factor to higher values as sediment blanketing effects result in higher crustal temperatures. Sediment supply has therefore, through the temperature-dependence of the viscous flow laws, strong control on crustal strength and mantle serpentinization reactions are only likely when sedimentation rates are low and stretching factors high. In a case study for the Norwegian margin, we test whether the inner lower crustal bodies (LCB) imaged beneath the Mïre and Vïring margin could be serpentinized mantle. Multiple 2-D transects have been reconstructed through the 3-D data set by Scheck-Wenderoth and Maystrenko (2011). We find that serpentinization reactions are possible and likely during the Jurassic rift phase. Predicted thicknesses and locations of partially serpentinized mantle rocks fit to information on LCBs from seismic and gravity data. We conclude that some of the inner LCBs beneath the Norwegian margin may be partially serpentinized mantle.