How fluids bend: the elastic expansion for higher-dimensional black holes

Hydrodynamics can be consistently formulated on surfaces of arbitrary co-dimension in a background space-time, providing the effective theory describing long-wavelength perturbations of black branes. When the co-dimension is non-zero, the system acquires fluid-elastic properties and constitutes what is called a fluid brane. Applying an effective action approach, the most general form of the free energy quadratic in the extrinsic curvature and extrinsic twist potential of stationary fluid brane configurations is constructed to second order in a derivative expansion. This construction generalizes the Helfrich-Canham bending energy for fluid membranes studied in theoretical biology to the case in which the fluid is rotating. It is found that stationary fluid brane configurations are characterized by a set of 3 elastic response coefficients, 3 hydrodynamic response coefficients and 1 spin response coefficient for co-dimension greater than one. Moreover, the elastic degrees of freedom present in the system are coupled to the hydrodynamic degrees of freedom. For co-dimension-1 surfaces we find a 8 independent parameter family of stationary fluid branes. It is further shown that elastic and spin corrections to (non)-extremal brane effective actions can be accounted for by a multipole expansion of the stress-energy tensor, therefore establishing a relation between the different formalisms of Carter, Capovilla-Guven and Vasilic-Vojinovic and between gravity and the effective description of stationary fluid branes. Finally, it is shown that the Young modulus found in the literature for black branes falls into the class predicted by this approach - a relation which is then used to make a proposal for the second order effective action of stationary blackfolds and to find the corrected horizon angular velocity of thin black rings.

Geochemical synthesis for the Effingen Member in boreholes at Oftringen, Gösgen and Küttigen

The Effingen Member is a low-permeability rock unit of Oxfordian age (ca. 160 Ma) that occurs across northern Switzerland. It comprises sandy calcareous marls and (argillaceous) limestones. This report describes the hydrogeochemistry, mineralogy and supporting physical properties of the Effingen Member in three boreholes in the Jura-Südfuss area: Oftringen, Gösgen and Küttigen, where it is 220–240 m thick. The top of the Effingen Member is at 420, 66 and 32 m depths at the three sites. Core materials are available from Oftringen and Gösgen, whereas information from Küttigen is limited to cuttings, in-situ hydrogeological testing and geophysical logging. Hydrogeological boundaries of the Effingen Member vary between locations. Ground-water flows were identified during drilling at the top (Geissberg Member), but not at the base, of the Effingen Member at Oftringen, at the base (Hauptrogenstein Formation) of the Effingen Member at Gösgen, and in a limestone layer (Gerstenhübel unit) within the Effingen Member at Küttigen. The marls and limestones of the Effingen Member have carbonate contents of 46–91 wt.-% and clay-mineral contents of 5–37 wt.-%. Pyrite contents are up to 1.6 wt.-%, but no sulphate minerals were detected by routine analyses. Clay minerals are predominantly mixed-layer illite-smectite, illite and kaolinite, with sporadic traces of chlorite and smectite. Veins filled with calcite ± celestite occur through the Effingen Member at Oftringen but not at Gösgen or Küttigen. They formed at 50–70 ºC from externally derived fluids, probably of Miocene age. Water contents are 0.7–4.2 wt.-%, corresponding to a water-loss porosity range of 1.9–10.8 vol.-%. Specific surface areas, measured by the BET method, are 2–30 m2/g, correlating with clay-mineral contents. Water activity has been measured and yielded surprisingly low values down to 0.8. These cannot be explained by pore-water salinity alone and include other effects, such as changes in the fabric due to stress release or partial saturation. Observed variations in measurements are not fully understood. Cation exchange capacity (CEC) and exchangeable cation populations have been studied by the Ni-en method. CEC, derived from the consumption of the index cation Ni, is 9–99 meq/kgrock at a solid:liquid ratio of 1, correlating with the clay-mineral content. Cation concentrations in Ni-en extract solutions are in the order Na+≥Ca2+>Mg2+>K+>Sr2+. However, the analytical results from the Ni-en extractions have additional contributions from cations originating from pore water and from mineral dissolution reactions that occurred during extraction, and it was not possible to reliably quantify these contributions. Therefore, in-situ cation populations and selectivity coefficients could not be derived. A suite of methods have been used for characterising the chemical compositions of pore waters in the Effingen Member. Advective displacement was used on one sample from each Oftringen and Gösgen and is the only method that produces results that approach complete hydrochemical compositions. Aqueous extraction was used on core samples from these two boreholes and gives data only for Cl- and, in some cases, Br-. Out-diffusion was used on core samples from Oftringen and similarly gives data for Cl- and Br- only. For both aqueous extraction and out-diffusion, reaction of the experimental water with rock affected concentrations of cations, SO42 and alkalinity in experimental solutions. Another method, centrifugation, failed to extract pore water. Stable isotope ratios (δ18O and δ2H) of pore waters in core samples from Oftringen were analysed by the diffusive exchange method and helium contents of pore water in Oftringen samples were extracted for mass spectrometric analysis by quantitative outgassing of preserved core samples. Several lines of evidence indicate that drillcore samples might not have been fully saturated when opened and subsampled in the laboratory. These include comparisons of water-loss porosities with physical porosities, water-activity measurements, and high contents of dissolved gas as inferred from ground-water samples. There is no clear proof of partial saturation and it is unclear whether this might represent in-situ conditions or is due to exsolution of gas due to the pressure release since drilling. Partial saturation would have no impact on the recalculation of pore-water compositions from aqueous extraction experiments using water-loss porosity data. The largest uncertainty in the pore-water Cl- concentrations recalculated from aqueous extraction and out-diffusion experiments is the magnitude of the anion-accessible fraction of water-loss porosity. General experience of clay-mineral rich formations suggests that the anion-accessible porosity fraction is very often about 0.5 and generally in a range of 0.3 to 0.6 and tends to be inversely correlated with clay-mineral contents. Comparisons of the Cl- concentration in pore water obtained by advective displacement with that recalculated from aqueous extraction of an adjacent core sample suggests a fraction of 0.27 for an Oftringen sample, whereas the same procedure for a Gösgen sample suggests a value of 0.64. The former value for anion-accessible porosity fraction is presumed to be unrepresentative given the local mineralogical heterogeneity at that depth. Through-diffusion experiments with HTO and 36Cl- suggest that the anion-accessible porosity fraction in the Effingen Member at Oftringen and Gösgen is around 0.5. This value is proposed as a typical average for rocks of the Effingen Member, bearing in mind that it varies on a local scale in response to the heterogeneity of lithology and pore-space architecture. The substantial uncertainties associated with the approaches to estimating anion-accessible porosity propagate into the calculated values of in-situ pore-water Cl- concentrations. On the basis of aqueous extraction experiments, and using an anion-accessible porosity fraction of 0.5, Cl- concentrations in the Effingen Member at Oftringen reach a maximum of about 14 g/L in the centre. Cl- decreases upwards and downwards from that, forming a curved depth profile. Cl- contents in the Effingen Member at Gösgen increase with depth from about 3.5 g/L to about 14 g/L at the base of the cored profile (which corresponds to the centre of the formation). Out-diffusion experiments were carried out on four samples from Oftringen, distributed through the Effingen Member. Recalculated Cl- concentrations are similar to those from aqueous extraction for 3 out of the 4 samples, and somewhat lower for one sample. Concentrations of other components, i.e. Na+, K+, Ca2+, Mg2+, Sr2+, SO42- and HCO3- cannot be obtained from the aqueous extraction and out-diffusion experimental data because of mineral dissolution and cation exchange reactions during the experiments. Pore-water pH also is not constrained by those extraction experiments. The only experimental approach to obtain complete pore-water compositions for samples from Oftringen and Gösgen is advective displacement of pore water. The sample from Oftringen used for this experiment is from 445 m depth in the upper part of the Effingen Member and gave eluate with 16.5 g/L Cl- whereas aqueous extraction from a nearby sample indicated about 9 g/L Cl-. The sample from Gösgen used for advective displacement is from 123 m depth in the centre of the Effingen Member sequence and gave eluate with about 9 g/L Cl- whereas aqueous extraction gave 11.5 g/L Cl-. In both cases the pore waters have Na-(Ca)-Cl compositions and SO42- concentrations of about 1.1 g/L. The Gösgen sample has a Br/Cl ratio similar to that of sea water, whereas this ratio is lower for the Oftringen sample. Taking account of uncertainties in the applied experimental approaches, it is reasonable to place an upper limit of ca. 20 g/L on Cl- concentration for pore water in the Effingen Member in this area. There are major discrepancies between pore-water SO42- concentrations inferred from aqueous extraction or out-diffusion experiments and those obtained from advective displacement in both the Oftringen and Gösgen cases. A general conclusion is that all or at least part of the discrepancies are attributable to perturbation of the sulphur system and enhancement of SO42- by sulphate mineral dissolution and possibly minor pyrite oxidation during aqueous extraction and out-diffusion. Therefore, data for SO42- calculated from those pore-water sampling methods are considered not to be representative of in-situ conditions. A reference pore-water composition was defined for the Effingen Member in the Jura Südfuss area. It represents the probable upper limits of Cl- contents and corresponding anion and cation concentrations that are reasonably constrained by experimental data. Except for Cl- and possibly Na+ concentrations, this composition is poorly constrained especially with respect to SO42- and Ca2+ concentrations, and pH and alkalinity. Stable isotope compositions, δ18O and δ2H, of pore waters in the Effingen Member at Oftringen plot to the right of the meteoric water line, suggesting that 18O has been enriched by water-rock exchange, which indicates that the pore waters have a long residence time. A long residence time of pore water is supported by the level of dissolved 4He that has accumulated in pore water of the Effingen Member at Oftringen. This is comparable with, or slightly higher than, the amounts of 4He in the Opalinus Clay at Benken. Ground waters were sampled from flowing zones intersected by boreholes at the three locations. The general interpretation is that pore waters and ground-water solutes may have similar origins in Mesozoic and Cenozoic brackish-marine formations waters, but ground-water solutes have been diluted rather more than pore waters by ingress of Tertiary and Quaternary meteoric waters. The available hydrochemical data for pore waters from the Effingen Member at these three locations in the Jura-Südfuss area suggest that the geochemical system evolved slowly over geological periods of time, in which diffusion was an important mechanism of solute transport. The irregularity of Cl- and δ18O profiles and spatial variability of advective ground-water flows in the Malm-Dogger system suggests that palaeohydrogeological and hydrochemical responses to changing tectonic and surface environmental conditions were complex.

Characterization and differentiation of body fluids, putrefaction fluid, and blood using Hounsfield unit in postmortem CT

The purpose of the present study was to evaluate the ranges of Hounsfield unit (HU) found in body fluids, putrefaction fluids, and blood on postmortem CT and how these ranges are affected by postmortem interval, temperatures, and CT beam energy. Body fluids, putrefaction fluids, and blood from a total of 53 corpses were analyzed to determine the ranges of HU values from postmortem CT images that were taken prior to autopsy. The fluids measured in CT images were obtained at autopsy and examined in terms of macroscopic and microscopic appearances. Body fluids and blood were also collected in plastic bottles, which were subjected to CT scans at different beam energies (80-130 kV) and at various fluid temperatures (4 to 40 °C). At a postmortem interval of 1 to 4 days, the ranges of HU values of the serous fluids (13-38 HU) and the nonsedimented blood (40-88 HU) did not overlap. In the sedimented blood, the upper serum layer exhibited HU value ranges that overlapped with those of the serous fluids. The putrefaction fluids exhibited a range of HU values between 80 and -130 HU. Elevated HU values were observed in fluids with accretive cell impurities. HU values decreased slightly with increasing temperature and CT beam energy. We concluded that serous fluids and blood in fresh corpses can be characterized and differentiated from each other based on HU value ranges. In contrast, body fluids in decomposed corpses cannot be differentiated by their HU value ranges. Different beam energies and corpse temperatures had only minor influences on HU value ranges and therefore should not be obstacles to the differentiation and characterization of body fluids and blood.

Postmortem quantitative 1.5-T MRI for the differentiation and characterization of serous fluids, blood, CSF, and putrefied CSF.

The purpose of the present study was to investigate whether serous fluids, blood, cerebrospinal fluid (CSF), and putrefied CSF can be characterized and differentiated in synthetically calculated magnetic resonance (MR) images based on their quantitative T 1, T 2, and proton density (PD) values. Images from 55 postmortem short axis cardiac and 31 axial brain 1.5-T MR examinations were quantified using a quantification sequence. Serous fluids, fluid blood, sedimented blood, blood clots, CSF, and putrefied CSF were analyzed for their mean T 1, T 2, and PD values. Body core temperature was measured during the MRI scans. The fluid-specific quantitative values were related to the body core temperature. Equations to correct for temperature differences were generated. In a 3D plot as well as in statistical analysis, the quantitative T 1, T 2 and PD values of serous fluids, fluid blood, sedimented blood, blood clots, CSF, and putrefied CSF could be well differentiated from each other. The quantitative T 1 and T 2 values were temperature-dependent. Correction of quantitative values to a temperature of 37 °C resulted in significantly better discrimination between all investigated fluid mediums. We conclude that postmortem 1.5-T MR quantification is feasible to discriminate between blood, serous fluids, CSF, and putrefied CSF. This finding provides a basis for the computer-aided diagnosis and detection of fluids and hemorrhages.

The mobility of Nb in rutile-saturated NaCl- and NaF-bearing aqueous fluids from 1-6.5 GPa and 300-800 °C

Rutile (TiO2) is an important host phase for high field strength elements (HFSE) such as Nb in metamorphic and subduction zone environments. The observed depletion of Nb in arc rocks is often explained by the hypothesis that rutile sequesters HFSE in the subducted slab and overlying sediment, and is chemically inert with respect to aqueous fluids evolved during prograde metamorphism in the forearc to subarc environment. However, field observations of exhumed terranes, and experimental studies, indicate that HFSE may be soluble in complex aqueous fluids at high pressure (i.e., >0.5 GPa) and moderate to high temperature (i.e., >300 degrees C). In this study, we investigated experimentally the mobility of Nb in NaCl- and NaF-bearing aqueous fluids in equilibrium with Nb-bearing rutile at pressure-temperature conditions applicable to fluid evolution in arc environments. Niobium concentrations in aqueous fluid at rutile saturation were measured directly by using a hydrothermal diamond-anvil cell (HDAC) and synchrotron X-ray fluorescence (SXRF) at 2.1 to 6.5 GPa and 300-500 degrees C, and indirectly by performing mass loss experiments in a piston-cylinder (PC) apparatus at similar to 1 GPa and 700-800 degrees C. The concentration of Nb in a 10 wt% NaCl aqueous fluid increases from 6 to 11 mu g/g as temperature increases from 300 to 500 degrees C, over a pressure range from 2.1 to 2.8 GPa, consistent with a positive temperature dependence. The concentration of Nb in a 20 wt% NaCl aqueous fluid varies from 55 to 150 mu g/g at 300 to 500 degrees C, over a pressure range from 1.8 to 6.4 GPa; however, there is no discernible temperature or pressure dependence. The Nb concentration in a 4 wt% NaF-bearing aqueous fluid increases from 180 to 910 mu g/g as temperature increases from 300 to 500 degrees C over the pressure range 2.1 to 6.5 GPa. The data for the F-bearing fluid indicate that the Nb content of the fluid exhibits a dependence on temperature between 300 and 500 degrees C at >= 2 GPa, but there is no observed dependence on pressure. Together, the data demonstrate that the hydrothermal mobility of Nb is strongly controlled by the composition of the fluid, consistent with published data for Ti. At all experimental conditions, however, the concentration of Nb in the fluid is always lower than coexisting rutile, consistent with a role for rutile in moderating the Nb budget of arc rocks.