Element Partitioning between Immiscible Carbonatite and Silicate Melts for Dry and H2O-bearing Systems at 1-3 GPa

Carbonatite and silicate rocks occurring within a single magmatic complex may originate through liquid immiscibility. We thus experimentally determined carbonatite/silicate melt partition coefficients (Dcarbonate melt/silicate melt, hereafter D) for 45 elements to understand their systematics as a function of melt composition and to provide a tool for identifying the possible conjugate nature of silicate and carbonatite magmas. Static and, when necessary, centrifuging piston cylinder experiments were performed at 1-3 GPa, 1150-1260°C such that two well-separated melts resulted. Bulk compositions had Na K, Na ∼ K, and Na K; for the latter we also varied bulk H2O (0-4 wt %) and SiO2 contents. Oxygen fugacities were between iron-wüstite and slightly below hematite-magnetite and were not found to exert significant control on partitioning. Under dry conditions alkali and alkaline earth elements partition into the carbonatite melt, as did Mo and P (DMo >8, DP= 1·6-3·3). High field strength elements (HFSE) prefer the silicate melt, most strongly Hf (DHf = 0·04). The REE have partition coefficients around unity with DLa/Lu = 1·6-2·3. Transition metals have D < 1 except for Cu and V (DCu ∼ 1·3, DV = 0·95-2). The small variability of the partition coefficients in all dry experiments can be explained by a comparable width of the miscibility gap, which appears to be flat-topped in our dry bulk compositions. For all carbonatite and silicate melts, Nb/Ta and Zr/Hf fractionate by factors of 1·3-3·0, in most cases much more strongly than in silicate-oxide systems. With the exception of the alkalis, partition coefficients for the H2O-bearing systems are similar to those for the anhydrous ones, but are shifted in favour of the carbonatite melt by up to an order of magnitude. An increase of bulk silica and thus SiO2 in the silicate melt (from 35 to 69 wt %) has a similar effect. Two types of trace element partitioning with changing melt composition can be observed. The magnitude of the partition coefficients increases for the alkalis and alkaline earths with the width of the miscibility gap, whereas partition coefficients for the REE shift by almost two orders of magnitude from partitioning into the silicate melt (DLa = 0·47) to strongly partitioning into the carbonatite melt (DLa = 38), whereas DLa/DLu varies by only a factor of three. The partitioning behavior can be rationalized as a function of ionic potential (Z/r). Alkali and alkaline earth elements follow a trend, the slope of which depends on the K/Na ratio and H2O content. Contrasting the sodic and potassic systems, alkalis have a positive correlation in D vs Z/r space in the potassic case and Cs to K partition into the silicate melt in the presence of H2O. For the divalent third row transition metals on the one hand and for the tri- and tetravalent REE and HFSE on the other, two trends of negative correlation of D vs Z/r can be defined. Nevertheless, the highest ionic strength network-modifying cations (V, Nb, Ta, Ti and Mo) do not follow any trend; understanding their behavior would require knowledge of their bonding environment in the carbonatite melt. Strong partitioning of REE into the carbonatite melt (DREE = 5·8-38·0) occurs only in H2O-rich compositions for which carbonatites unmix from evolved alkaline melts with the conjugate silicate melt being siliceous. We thus speculate that upon hydrous carbonatite crystallization, the consequent saturation in fluids may lead to hydrothermal systems concentrating REE in secondary deposit

An Improved High Order Finite Difference Method for Non-conforming Grid Interfaces for the Wave Equation

This paper presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators being norm-contracting, which is satisfied by the second and fourth order operators, but not by the sixth order operator. We construct new penalty terms to impose interface conditions such that the stability proof does not require the norm-contracting condition. As a consequence, the sixth order accurate scheme is also provably stable. Numerical experiments demonstrate the improved stability and accuracy property

Piston-ring film thickness: theory and experiment compared

A review of the published literature has demonstrated a large variability and discrepancies in the measured and predicted values of piston-ring lubricating film thickness in internal combustion engines. Only 2 papers have been found that compare experiments in firing engines directly with outputs from sophisticated ring-pack lubrication models. The agreement between theory and experiment in these comparisons was limited, possibly because of inadequacies in the models and/ or inaccuracies of measurement. This paper seeks to contribute to the literature by comparing accurately calibrated experimental measurements of piston-ring film thickness in a firing engine with predictions from an advanced, commercial software package alongside details of the systematic analysis of the measurement errors in this process. Suggestions on how measurement accuracy could be further improved are also given. Measurements of oil film thickness with an error (standard deviation) of +/-15% have been achieved. It is shown that this error can be reduced further, by changes in the design and installation of the sensors. Detailed experimental measurements of film thickness under the top compression ring in a firing petrol engine have been made and compared with the predictions from a commercial, state-of-the art modelling package. The agreement between theory and experiment is excellent throughout the stroke in most cases, but some significant differences are observed at the lower load conditions. These differences are as yet unexplained, but may be due to the sensor topography influencing the hydrodynamic lubrication, lubricant availability, out-of-roundness in the cylinder, or squeeze effects. This a topic that requires further stud

Boundary Effects on Spectral Properties of Interacting Electrons in One Dimension

The single electron Green's function of the one-dimensional Tomonaga-Luttinger model in the presence of open boundaries is calculated with bosonization methods. We show that the critical exponents of the local spectral density and of the momentum distribution change in the presence of a boundary. The well understood universal bulk behavior always crosses over to a boundary dominated regime for small energies or small momenta. We show this crossover explicitly for the large-U Hubbard model in the low-temperature limit. Consequences for photoemission experiments are discussed.Comment: revised and reformatted paper to appear in Phys. Rev. Lett. (Feb. 1996). 5 pages (revtex) and 3 embedded figures (macro included). A complete postscript file is available from http://FY.CHALMERS.SE/~eggert/luttinger.ps or by request from [email protected]

Back-reaction and effective acceleration in generic LTB dust models

We provide a thorough examination of the conditions for the existence of back-reaction and an "effective" acceleration (in the context of Buchert's averaging formalism) in regular generic spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. By considering arbitrary spherical comoving domains, we verify rigorously the fulfillment of these conditions expressed in terms of suitable scalar variables that are evaluated at the boundary of every domain. Effective deceleration necessarily occurs in all domains in: (a) the asymptotic radial range of models converging to a FLRW background, (b) the asymptotic time range of non-vacuum hyperbolic models, (c) LTB self-similar solutions and (d) near a simultaneous big bang. Accelerating domains are proven to exist in the following scenarios: (i) central vacuum regions, (ii) central (non-vacuum) density voids, (iii) the intermediate radial range of models converging to a FLRW background, (iv) the asymptotic radial range of models converging to a Minkowski vacuum and (v) domains near and/or intersecting a non-simultaneous big bang. All these scenarios occur in hyperbolic models with negative averaged and local spatial curvature, though scenarios (iv) and (v) are also possible in low density regions of a class of elliptic models in which local spatial curvature is negative but its average is positive. Rough numerical estimates between -0.003 and -0.5 were found for the effective deceleration parameter. While the existence of accelerating domains cannot be ruled out in models converging to an Einstein de Sitter background and in domains undergoing gravitational collapse, the conditions for this are very restrictive. The results obtained may provide important theoretical clues on the effects of back-reaction and averaging in more general non-spherical models.Comment: Final version accepted for publication in Classical and Quantum Gravity. 47 pages in IOP LaTeX macros, 12 pdf figure

Anomalous Spin Dynamics observed by High Frequency ESR in Honeycomb Lattice Antiferromagnet InCu2/3V1/3O3

High-frequency ESR results on the S=1/2 Heisenberg hexagonal antiferromagnet InCu2/3V1/3O3 are reported. This compound appears to be a rare model substance for the honeycomb lattice antiferromagnet with very weak interlayer couplings. The high-temperature magnetic susceptibility can be interpreted by the S=1/2 honeycomb lattice antiferromagnet, and it shows a magnetic-order-like anomaly at TN=38 K. Although, the resonance field of our high-frequency ESR shows the typical behavior of the antiferromagnetic resonance, the linewidth of our high-frequency ESR continues to increase below TN, while it tends to decrease as the temperature in a conventional three-dimensional antiferromagnet decreases. In general, a honeycomb lattice antiferromagnet is expected to show a simple antiferromagnetic order similar to that of a square lattice antiferromagnet theoretically because both antiferromagnets are bipartite lattices. However, we suggest that the observed anomalous spin dynamics below TN is the peculiar feature of the honeycomb lattice antiferromagnet that is not observed in the square lattice antiferromagnet.Comment: 5 pages, 5 figure

Weighed scalar averaging in LTB dust models, part I: statistical fluctuations and gravitational entropy

We introduce a weighed scalar average formalism ("q-average") for the study of the theoretical properties and the dynamics of spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models models. The "q-scalars" that emerge by applying the q-averages to the density, Hubble expansion and spatial curvature (which are common to FLRW models) are directly expressible in terms of curvature and kinematic invariants and identically satisfy FLRW evolution laws without the back-reaction terms that characterize Buchert's average. The local and non-local fluctuations and perturbations with respect to the q-average convey the effects of inhomogeneity through the ratio of curvature and kinematic invariants and the magnitude of radial gradients. All curvature and kinematic proper tensors that characterize the models are expressible as irreducible algebraic expansions on the metric and 4-velocity, whose coefficients are the q-scalars and their linear and quadratic local fluctuations. All invariant contractions of these tensors are quadratic fluctuations, whose q-averages are directly and exactly related to statistical correlation moments of the density and Hubble expansion scalar. We explore the application of this formalism to a definition of a gravitational entropy functional proposed by Hosoya et al (2004 Phys. Rev. Lett. 92 141302). We show that a positive entropy production follows from a negative correlation between fluctuations of the density and Hubble scalar, providing a brief outline on its fulfillment in various LTB models and regions. While the q-average formalism is specially suited for LTB and Szekeres models, it may provide a valuable theoretical insight on the properties of scalar averaging in inhomogeneous spacetimes in general.Comment: 27 pages in IOP format, 1 figure. Matches version accepted for publication in Classical and Quantum Gravit

Ising Spin Glasses in a Magnetic Field

Ground states of the three dimensional Edwards-Anderson spin glass are computed in the presence of an external magnetic field. Our algorithm is sufficiently powerful for us to treat systems with up to 600 spins. We perform a statistical analysis of how the ground state changes as the field is increased, and reach the conclusion that the spin glass phase at zero temperature does not survive in the presence of any finite field. This is in agreement with the droplet model or scaling predictions, but in sharp disagreement with the mean field picture. For comparison, we also investigate a dilute mean field spin glass model where an Almeida-Thouless line is present.Comment: 4 pages, 4 figures, Revte