Metal–silicate partitioning of W and Mo and the role of carbon in controlling their abundances in the bulk silicate earth

The liquid metal–liquid silicate partitioning of molybdenum and tungsten during core formation must be well-constrained in order to understand the evolution of Earth and other planetary bodies, in particular because the Hf–W isotopic system is used to date early planetary evolution. The partition coefficients DMo and DW have been suggested to depend on pressure, temperature, silicate and metal compositions, although previous studies have produced varying and inconsistent models. Additionally, the high cationic charges of W and Mo in silicate melts make their partition coefficients particularly sensitive to oxygen fugacity. We combine 48 new high pressure and temperature experimental results with a comprehensive database of previous experiments to re-examine the systematics of Mo and W partitioning, and produce revised partitioning models from the large combined dataset. W partitioning is particularly sensitive to silicate and metallic melt compositions and becomes more siderophile with increasing temperature. We show that W has a 6+ oxidation state in silicate melts over the full experimental fO2 range of ΔIW −1.5 to −3.5. Mo has a 4+ oxidation state, and its partitioning is less sensitive to silicate melt composition but also depends on metallic melt composition. DMo stays approximately constant with increasing depth in Earth. Both W and Mo become more siderophile with increasing C content of the metal: we therefore performed experiments with varying C concentrations and fit epsilon interaction parameters:  = −7.03 ± 0.30 and  = −7.38 ± 0.57. W and Mo along with C are incorporated into a combined N-body accretion and core–mantle differentiation model, which already includes the major rock-forming elements as well as S, and moderately and highly siderophile elements. In this model, oxidation and volatility gradients extend through the protoplanetary disk so that Earth accretes heterogeneously. These gradients, as well as the metal–silicate equilibration pressure, are fitted using a least squares optimisation so that the model Earth-like planet reproduces the composition of the bulk silicate Earth (BSE) in terms of 17 simulated element concentrations (Mg, Fe, Si, Ni, Co, Nb, Ta, V, Cr, S, Pt, Pd, Ru, Ir, W, Mo, and C). The effects of the interaction of W and Mo with Si, S, O, and C in metal are included. Using this model with six separate terrestrial planet accretion simulations, we show that W and Mo require the early accreting Earth to be sulfur-depleted and carbon-enriched so that W and Mo are efficiently partitioned into Earth’s core and do not accumulate in the mantle. When this is the case, the produced Earth-like planets possess mantle compositions matching the BSE for all simulated elements. However, there are two distinct groups of estimates of the bulk mantle’s C abundance in the literature: low (∼100 ppm) and high (∼800 ppm), and all six models are consistent with the higher estimated carbon abundance. The low BSE C abundance would be achievable when the effects of the segregation of dispersed metal droplets produced in deep magma oceans by the disproportionation of Fe2+ to Fe3+ plus metallic Fe is included

Leibniz algebras constructed by Witt algebras

We describe infinite-dimensional Leibniz algebras whose associated Lie algebra is the Witt algebra and we prove the triviality of low-dimensional Leibniz cohomology groups of the Witt algebra with the coefficients in itself

Deformation of Codimension-2 Surface and Horizon Thermodynamics

The deformation equation of a spacelike submanifold with an arbitrary codimension is given by a general construction without using local frames. In the case of codimension-1, this equation reduces to the evolution equation of the extrinsic curvature of a spacelike hypersurface. In the more interesting case of codimension-2, after selecting a local null frame, this deformation equation reduces to the well known (cross) focusing equations. We show how the thermodynamics of trapping horizons is related to these deformation equations in two different formalisms: with and without introducing quasilocal energy. In the formalism with the quasilocal energy, the Hawking mass in four dimension is generalized to higher dimension, and it is found that the deformation of this energy inside a marginal surface can be also decomposed into the contributions from matter fields and gravitational radiation as in the four dimension. In the formalism without the quasilocal energy, we generalize the definition of slowly evolving future outer trapping horizons proposed by Booth to past trapping horizons. The dynamics of the trapping horizons in FLRW universe is given as an example. Especially, the slowly evolving past trapping horizon in the FLRW universe has close relation to the scenario of slow-roll inflation. Up to the second order of the slowly evolving parameter in this generalization, the temperature (surface gravity) associated with the slowly evolving trapping horizon in the FLRW universe is essentially the same as the one defined by using the quasilocal energy.Comment: Latex, 61 pages, no figures; v2, type errors corrected; v3, references and comments are added, English is improved, to appear in JHE

The prevalence and risk of immune restoration disease in HIV-infected patients treated with highly active antiretroviral therapy

Background It is becoming increasingly clear that, during successful highly active antiretroviral therapy (HAART), a proportion of treated patients develop opportunistic infections (OIs), referred to in this setting as immune restoration disease (IRD). We examined the risk of developing IRD in HAART-treated HIV-infected patients. Methods A retrospective study of a cohort including all 389 patients treated with HAART between I January 1998 and 31 May 2004 in our HIV unit was performed to evaluate the occurrence of and risk factors for IRD during HAART. Baseline and follow-up values of CD4 T-cell counts and plasma viral loads (pVLs) were compared to assess the success of HAART. Results During successful HAART (significant increase in CD4 T-cell counts and decrease in pVL), at least one IRD episode occurred in 65 patients (16.7%). The median time to IRD was 4.6 months (range 212 months). IRDs included dermatomal herpes zoster (26 patients), pulmonary tuberculosis (four patients), tuberculous exudative pericarditis (two patients), tuberculous lymphadenitis (two patients), cerebral toxoplasmosis (one patient), progressive multifocal leucoencephalopathy (PML) (one patient), inflamed molluscum (one patient), inflamed Candida albicans angular cheilitis (three patients), genital herpes simplex (two patients), tinea corporis (two patients), cytomegalovirus (CMV) retinitis (two patients), CMV vitritis (one patient) and hepatitis B (three patients) or C (fifteen patients). A baseline CD4 T-cell count below 100 cells/mu L was shown to be the single predictor [odds ratio (OR) 2.5, 95% confidence interval (CI) 0.9-6.4] of IRD, while a CD4 T-cell count increase to gt 400 cells/mu L, but not undetectable pVL, was a negative predictor of IRD (OR 0.3, 95% CI 0.1-0.8). Conclusions To avoid IRD in advanced patients, HAART should be initiated before the CD4 T-cell count falls below 100 cells/mu L

Hamiltonian dynamics for Einstein's action in G→\rightarrow0 limit

The Hamiltonian analysis for the Einstein's action in $G\to 0$ limit is performed. Considering the original configuration space without involve the usual $ADM$ variables we show that the version $Gto 0$ for Einstein's action is devoid of physical degrees of freedom. In addition, we will identify the relevant symmetries of the theory such as the extended action, the extended Hamiltonian, the gauge transformations and the algebra of the constraints. As complement part of this work, we develop the covariant canonical formalism where will be constructed a closed and gauge invariant symplectic form. In particular, using the geometric form we will obtain by means of other way the same symmetries that we found using the Hamiltonian analysis

Critical Overview of Loops and Foams

This is a review of the present status of loop and spin foam approaches to quantization of four-dimensional general relativity. It aims at raising various issues which seem to challenge some of the methods and the results often taken as granted in these domains. A particular emphasis is given to the issue of diffeomorphism and local Lorentz symmetries at the quantum level and to the discussion of new spin foam models. We also describe modifications of these two approaches which may overcome their problems and speculate on other promising research directions.Comment: 75 page

Traditional electrosurgery and a low thermal injury dissection device yield different outcomes following bilateral skin-sparing mastectomy: a case report

<p>Abstract</p> <p>Introduction</p> <p>Although a skin- and nipple-sparing mastectomy technique offers distinct cosmetic and reconstructive advantages over traditional methods, partial skin flap and nipple necrosis remain a significant source of post-operative morbidity. Prior work has suggested that collateral thermal damage resulting from electrocautery use during skin flap development is a potential source of this complication. This report describes the case of a smoker with recurrent ductal carcinoma <it>in situ </it>(DCIS) who experienced significant unilateral skin necrosis following bilateral skin-sparing mastectomy while participating in a clinical trial examining mastectomy outcomes with two different surgical devices. This unexpected complication has implications for the choice of dissection devices in procedures requiring skin flap preservation.</p> <p>Case presentation</p> <p>The patient was a 61-year-old Caucasian woman who was a smoker with recurrent DCIS of her right breast. As part of the clinical trial, each breast was randomized to either the standard of care treatment group (a scalpel and a traditional electrosurgical device) or treatment with a novel, low thermal injury dissection device, allowing for a direct, internally controlled comparison of surgical outcomes. Post-operative follow-up at six days was unremarkable for both operative sites. At 16 days post-surgery, the patient presented with a significant wound necrosis in the mastectomy site randomized to the control study group. Following debridement and closure, this site progressively healed over 10 weeks. The contralateral mastectomy, randomized to the alternative device, healed normally.</p> <p>Conclusion</p> <p>We hypothesize that thermal damage to the subcutaneous microvasculature during flap dissection may have contributed to this complication and that the use of a low thermal injury dissection device may be advantageous in select patients undergoing skin- and nipple-sparing mastectomy.</p

Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v

Using Simulations as a Starting Point for Constructing Meaningful Learning Games

For many school administrators and decision makers, the term “video games” holds numerous cultural associations which make their adoption in the education space challenging. Additionally, the term is so broad that it can sometimes be difficult to communicate explicitly a desire to build learning experiences that go beyond the Drill and Kill edutainment titles that currently dominate most people’s perceptions of educational games. By contrast, the term “simulations” is often well respected among educators, particularly in the natural sciences. With “simulation” already being a full genre of video games, it would seem natural that researchers are beginning to explore the overlaps between simulation games and pedagogical goals that go beyond those found in Drill and Kill games. In this chapter, we survey some of the relevant research concerning both simulations and video games and outline practical pathways through which we can leverage the interest and frameworks designed for simulation construction to facilitate the introduction of video game concepts and experiences into the classroom environment. In particular, we report on the use of Starlogo TNG, a graphical programming environment in which kids themselves can create simulation-based video games, for deepening children’s understanding of scientific concepts