Approximation of the Velocity by Coupling Discontinuous Galerkin and Mixed Finite Element Methods for Flow Problems

In this paper, we show how to couple the local discontinuous Galerkin method and the Raviart–Thomas mixed finite element method for elliptic equations modeling flow problems. We then show that the approximation of the velocity converges with the optimal order of k when we take the local discontinuous Galerkin that uses polynomials of degree k and the Raviart–Thomas space of polynomials of degree k?1.     

‘You can get away with loads because there’s no one here’: Discourses of regulation and non-regulation in English rural spaces

Using qualitative data from a research project investigating contemporary rural identities in England this paper examines the apparently contradictory discursive claims that are made on rural spaces. It looks in particular at the ways in which these are narrated - through the notions of rural space as a site of safety, orderliness and community on the one hand and as a site of freedom, anti-order and non-regulation on the other. While the former is a familiar, entrenched and critiqued representation of rurality, the latter narrative has a more marginal and ambivalent place in the dominant rural imaginary. Drawing on Foucault’s concepts of panopticism and heterotopia the paper demonstrates the ways in which the rural is a highly labile concept and emphasises its continual ‘unfinishedness’. However, alongside this, the paper suggests that the tensions and contradictions of the orderly and anti-orderly discourses are underpinned by a particular coherency that is driven by senses of community, belonging and self-regulation. While these do not resolve the contradictions of the discursive claims the potency of such drivers are sufficient to produce a particular inclusive spatiality which is able to accommodate and incorporate the different discursive positions and the practices that are associated with each.     

Extensional neotectonics around the bend of the Western/Central Alps: an overview

The Western Alps’ active tectonics is characterized by ongoing widespread extension in the highest parts of the belt and transpressive/compressive tectonics along its borders. We examine these contrasting tectonic regimes using a multidisciplinary approach including seismotectonics, numerical modeling, GPS, morphotectonics, fieldwork, and brittle deformation analysis. Extension appears to be the dominant process in the present-day tectonic activity in the Western Alps, affecting its internal areas all along the arc. Shortening, in contrast, is limited to small areas located along at the outer borders of the chain. Strike-slip is observed throughout the Alpine realm and in the foreland. The stress-orientation pattern is radial for σ3 in the inner, extensional zones, and for σ1 in the outer, transcurrent/tranpressional ones. Extensional areas can be correlated with the parts of the belt with the thickest crust. Quantification of seismic strain in tectonically homogeneous areas shows that only 10–20% of the geodesy-documented deformation can be explained by the Alpine seismicity. We propose that, Alpine active tectonics are ruled by isostasy/buoyancy forces rather than the ongoing shortening along the Alpine Europe/Adria collision zone. This interpretation is corroborated by numerical modeling. The Neogene extensional structures in the Alps formed under increasingly brittle conditions. A synthesis of paleostress tensors for the internal parts of the West-Alpine Arc documents major orogen-parallel extension with a continuous change in σ3 directions from ENE–WSW in the Simplon area, to N–S in the Vanoise area and to NNW–SSE in the Briançon area. Minor orogen-perpendicular extension increases from N to S. This second signal correlates with the present-day geodynamics as revealed by focal-plane mechanisms analysis. The orogen-parallel extension could be related to the opening of the Ligurian Sea during the Early-Middle Miocene and to compression/rotation of the Adriatic indenter inducing lateral extrusion.     

The Holocene Storegga Slide tsunami in the United Kingdom

All currently known sites in the United Kingdom with evidence for the Holocene Storegga Slide tsunami are described. Information on the altitude, distribution, stratigraphical context, age, particle size profile and microfossil characteristics of the deposits is presented. The tsunami involved a greater area than previously described, reaching a coastline over 600 km long. The ubiquitous sand layer which forms the main deposit associated with the event is shown to exhibit a consistent morphology and a particle size profile marked by fining-upwards sequences. An analysis of new and previously published radiocarbon dates indicates that from evidence in the United Kingdom, the event took place sometime around 7100 radiocarbon years BP (7900 calibrated years BP). A new isobase model for mainland Scotland and adjacent areas, providing a preliminary estimate of land uplift since the tsunami, is presented. The model estimates contemporary sea surface level offshore at 14 m below the present day mean high water spring tides. Tsunami sediment run-up is greatest in inlets, where it reaches at least 25 m on Shetland and at least 5 m along the mainland coastline to the south, and run-up of the tsunami would have exceeded these values. The tsunami sediments identified here are considered particularly valuable as a synchronous marker horizon.     

A fertile harzburgite–garnet lherzolite transition: possible inferences for the roles of strain and metasomatism in upper mantle peridotites

Porphyroclastic enstatite in a garnet lherzolite xenolith from the Monastery Mine kimberlite, South Africa, has exsolved pyrope garnet, Cr-diopside and Al-chromite, and the specimen is interpreted as representing a transition from fertile harzburgite, (containing high Ca-Al-Cr enstatite) to granular garnet lherzolite. Although the exsolved phases occur in morphologically different forms (fine and coarse lamellae; equant, ripened grains), indicating textural disequilibrium, the exsolved grains are very constant in composition, indicating chemical equilibrium. Theoretically, the exsolution could have been due to a fall in temperature, but the close association of exsolution and deformation of the host enstatite suggests that exsolution was also aided by straining of the enstatite lattice. The phase compositions can be broadly matched with those in other mantle peridotites, except that all phases are characterised by a virtual absence of Ti. In the garnet and diopside Ti, Co, Zr and most of the REE are lower than in published analyses of garnet and diopside in both granular and sheared garnet lherzolites from Southern African kimberlites, and diopside/garnet partitioning for Sr and the REE is higher. Comparison with the trace element chemistry of an enstatite from a fertile harzburgite indicates that, except for Nb, the trace element content and distribution found in the Monastery phases could arise by isochemical exsolution from such an enstatite. On the assumption that (a) the Monastery specimen represents a transition from harzburgite to garnet lherzolite, and (b) many garnet lherzolites are of exsolution origin (as suggested by their modal compositions), the inference is that most garnet lherzolites, and not just the sheared variety, have been subject to varying degrees of Ti, Zr, Sr and REE metasomatism.     

Aspects of the mineralogy of alnöitic breccia,Malaita, Solomon Islands; comparison with continental kimberlites

Megacrysts of titanian pyrope, high-Ti bronzite, sub-calcic diopside to augite, and phlogopite in an alnöitic breccia, Malaita, Solomon Islands, have compositional features which distinguish them from silicates in kimberlites. Particularly important is the high content of Al₂O₃ in the Malaita silicates, which may reflect the higher Al₂O₃ content of alnöite than kimberlite. The phlogopite megacrysts fall into two populations, one richer in Mg and Cr, and lower in Ti, than the other. The pyroxenes may also fall into two groups characterized by high and low Mg, Cr and Ni. Two stages of crystallization may be responsible.     

Primary ionization coefficients for dry and moist air; secondary ionization coefficients for a water surface

Summary A comparison has been made between the Townsend primary ionization coefficient, , for dry air and for air with humidities typical of those in the atmosphere. is defined as the number of new electrons produced by an electron per centimeter of drift in a field. A range of field/pressure ratios,E/p ₀, of 40 to 100 V (cm torr)^–1 was employed. The variation of with humidity is very small.Over the range ofE/p ₀ from 50 to 100 V (cm torr)^–1, the secondary ionization coefficient, , of a water surface has been found from sparking potential data to be typically 2×10^–4. represents the fraction of primary ionizing collisions that ultimately result in the production of additional electrons at the surface.