Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

Sedimentology of the northwestern Weddel Sea continental shelf and slope

Geologie cores on two profiles oriented normaly to the continental shelf and slope, have been investigated to reconstruct the Quaternary sedimentary history of the southeast continental border of South Orkney (NW Weddell Sea). The sediments were described macroscopically and their fabric investigated by use of X-radiographs. Laboratory work comprised detailed grain-size analysis, determination of the watercontent, carbonate, organic carbon and sand fraction.composition. Stable oxygen and carbon isotopes have been measured On planktonic foraminifera. Palaeomagnetism, analysis of 230Th-content and detailed comparison of the lithlogic Parameters with the oxygen isotope stages (Martinson curve) were used for stratigraphic classification of the sediments. The sediment cores from the continental slope comprise a maximum age of 300,000 years B. P.. Bottom currents, ice rafting and biogenic input are the main sources of sediment. Based on lithologic parameters a distinction between glacial and interglacial facies is possible. Silty clays without microfossils and few bioturbation characterise the sediments of the glacial facies. Only small amounts of icerafted debris can be recognized. This type of sediment was accumulated during times of lower sea-level and drastically reduced rate of bottom water production. Based on grain-size distribution, bottom current velocities of 0.01 cmls were calculated. Thick sea-ice coverage reduced biogenic production in the surface water, and as consequence benthic communities were depleted. Because of the reduced benthic life, sediments are only slithly bioturbated. At the beginning of the interglacial Stage, the sea-level rised rapidly, and calving rate of icebergs, combined with input of ice-rafted material, increased considerably. Sediments of this transition facies are silty cliiys with a high proportion of coarse ice-rafted debris, but without microfossils. With the onset of bottom water production in connection with shelf ice water, sediments of interglacial facies were formed. They consist of silty clays to clayey silts with considerable content of sand and gravel. Sediments are strongly bioturbated. Based On the sediment caracteristics, current velocities of the bottom water were calculated to be of 0.96 cmls for interglacials. At the southern slope of a NW/SE-striking ridge, bottom water current is channelized, resulting in a drastic increase of current velocities. Current velocities up to 7.5 cm/s lead to formation of residual sediments. While the continental slope has predominantly fine sediments, the South Orkney shelf are mainly sandy silts and silty sands with a high proportion of gravel. These sediments were formed dominantly by ice-rafting during Brunhes- and Matuyama-Epoch. Currents removed the fine fraction of the sediments. Based on microfossil contents it was not possible to differentiate sediments from glacial to interglacial. In the upper Parts of the cores graded sequences truncated by erosion were observed. These sequences were formed during Brunhes-Epoch by strong currents with velocities decreasing periodically from about 7.5 cm/s to about 1 cm/s. Sediments with a high proportion of siliceous microfossils but barren of foraminifera compose the lower part of the shelf cores. These sediments have formed during the warmer Matuyama-Epoch.

In Situ Observation of the Thermal Decomposition of Weddelite by Heating Stage Environmental Scanning Electron Microscopy

The morphological and chemical changes occurring during the thermal decomposition of weddelite, CaC2O4·2H2O, have been followed in real time in a heating stage attached to an Environmental Scanning Electron Microscope operating at a pressure of 2 Torr, with a heating rate of 10 °C/min and an equilibration time of approximately 10 min. The dehydration step around 120 °C and the loss of CO around 425 °C do not involve changes in morphology, but changes in the composition were observed. The final reaction of CaCO3 to CaO while evolving CO2 around 600 °C involved the formation of chains of very small oxide particles pseudomorphic to the original oxalate crystals. The change in chemical composition could only be observed after cooling the sample to 350 °C because of the effects of thermal radiation.

Thermal decomposition of the synthetic hydrotalcite iowaite

The thermal stability and thermal decomposition pathways for synthetic iowaite have been determined using thermogravimetry in conjunction with evolved gas mass spectrometry. Chemical analysis showed the formula of the synthesised iowaite to be Mg6.27Fe1.73(Cl)1.07(OH)16(CO3)0.336.1H2O and X-ray diffraction confirms the layered structure. Dehydration of the iowaite occurred at 35 and 79°C. Dehydroxylation occurred at 254 and 291°C. Both steps were associated with the loss of CO2. Hydrogen chloride gas was evolved in two steps at 368 and 434°C. The products of the thermal decomposition were MgO and a spinel MgFe2O4. Experimentally it was found to be difficult to eliminate CO2 from inclusion in the interlayer during the synthesis of the iowaite compound and in this way the synthesised iowaite resembled the natural mineral.

Raman spectroscopy of the molybdate minerals chillagite (tungsteinian wulfenite-I4), stolzite, scheelite, wolframite and wulfenite

Raman spectra of chillagite, wulfenite, stolzite, scheelite and wolframite were obtained at 298 and 77 K using a Raman microprobe in combination with a thermal stage. Chillagite is a solid solution of wulfenite and stolzite. The spectra of these molybdate minerals are orientation dependent. The band at 695 cm-1 is interpreted as an antisymmetric bridging mode associated with the tungstate chain. The bands at 790 and 881 cm-1 are associated with the antisymmetric and symmetric Ag modes of terminal WO2 whereas the origin of the 806 cm-1 band remains unclear. The 4(Eg) band was absent for scheelite. The bands at 353 and 401 cm-1 are assigned as either deformation modes or as r(Bg) and (Ag) modes of terminal WO2. The band at 462 cm-1 has an equivalent band in the infrared at 455 cm-1 assigned as as(Au) of the (W2O4)n chain. The band at 508 cm-1 is assigned as sym(Bg) of the (W2O4)n chain.