Continuous Self-Similarity and SS-Duality

We study the spherically symmetric collapse of the axion/dilaton system coupled to gravity. We show numerically that the critical solution at the threshold of black hole formation is continuously self-similar. Numerical and analytical arguments both demonstrate that the mass scaling away from criticality has a critical exponent of $\gamma = 0.264$.Comment: 17 pages, harvmac, six figures uuencoded in separate fil

Volatiles beneath mid-ocean ridges: deep melting, channelised transport, focusing, and metasomatism

Deep-Earth volatile cycles couple the mantle with near-surface reservoirs. Volatiles are emitted by volcanism and, in particular, from mid-ocean ridges, which are the most prolific source of basaltic volcanism. Estimates of volatile extraction from the asthenosphere beneath ridges typically rely on measurements of undegassed lavas combined with simple petrogenetic models of the mean degree of melting. Estimated volatile fluxes have large uncertainties; this is partly due to a poor understanding of how volatiles are transported by magma in the asthenosphere. Here, we assess the fate of mantle volatiles through numerical simulations of melting and melt transport at mid-ocean ridges. Our simulations are based on two-phase, magma/mantle dynamics theory coupled to idealised thermodynamic model of mantle melting in the presence of water and carbon dioxide. We combine simulation results with catalogued observations of all ridge segments to estimate a range of likely volatile output from the global mid-ocean ridge system. We thus predict global MOR crust production of 66-73 Gt/yr (22-24 km3/yr) and global volatile output of 52-110 Mt/yr, corresponding to mantle volatile contents of 100--200~ppm. We find that volatile extraction is limited: up to half of deep, volatile-rich melt is not focused to the axis but is rather deposited along the LAB. As these distal melts crystallise and fractionate, they metasomatise the base of the lithosphere, creating rheological heterogeneity that could contribute to the seismic signature of the LAB.Comment: 42 pages; 8 figures; 2 appendices (incl 1 table); 7 suppl. figures; 1 suppl. tabl

High-pressure Partial Melting of Mafic Lithologies in the Mantle

We review experimental phase equilibria associated with partial melting of mafic lithologies (pyroxenites) at high pressures to reveal systematic relationships between bulk compositions of pyroxenite and their melting relations. An important aspect of pyroxenite phase equilibria is the existence of the garnet-pyroxene thermal divide, defined by the enstatite-Ca-Tschermaks pyroxene-diopside plane in CaO-MgO-Al2O3-SiO2 projections. This divide appears at pressures above ∼2 GPa in the natural system where garnet and pyroxenes are the principal residual phases in pyroxenites. Bulk compositions that reside on either side of the divide have distinct phase assemblages from subsolidus to liquidus and produce distinct types of partial melt ranging from strongly nepheline-normative to quartz-normative compositions. Solidus and liquidus locations are little affected by the location of natural pyroxenite compositions relative to the thermal divide and are instead controlled chiefly by bulk alkali contents and Mg-numbers. Changes in phase volumes of residual minerals also influence partial melt compositions. If olivine is absent during partial melting, expansion of the phase volume of garnet relative to clinopyroxene with increasing pressure produces liquids with high Ca/Al and low MgO compared with garnet peridotite-derived partial melt

Critical Collapse of the Massless Scalar Field in Axisymmetry

We present results from a numerical study of critical gravitational collapse of axisymmetric distributions of massless scalar field energy. We find threshold behavior that can be described by the spherically symmetric critical solution with axisymmetric perturbations. However, we see indications of a growing, non-spherical mode about the spherically symmetric critical solution. The effect of this instability is that the small asymmetry present in what would otherwise be a spherically symmetric self-similar solution grows. This growth continues until a bifurcation occurs and two distinct regions form on the axis, each resembling the spherically symmetric self-similar solution. The existence of a non-spherical unstable mode is in conflict with previous perturbative results, and we therefore discuss whether such a mode exists in the continuum limit, or whether we are instead seeing a marginally stable mode that is rendered unstable by numerical approximation.Comment: 11 pages, 8 figure

Anhydrous Partial Melting Experiments on MORB-like Eclogite: Phase Relations, Phase Compositions and Mineral-Melt Partitioning of Major Elements at 2-3 GPa

We present melt and mineral compositions from nominally anhydrous partial melting experiments at 2-3 GPa on a quartz eclogite composition (G2) similar to average oceanic crust. Near-solidus partial melts at 3 GPa, determined with melt traps of vitreous carbon spheres, have 55-57 wt % SiO2, rather less silica than the dacitic compositions that are generally assumed for near-solidus eclogite partial melts. At 2 GPa, equivalent near-solidus partial melts are less silicic (≤52 wt % SiO2). The 3 GPa near-solidus partial melts (up to melt fractions of ∼3%) are saturated in rutile and have 5·7-6·7 wt % TiO2. The G2 composition is K2O-poor (0·03 wt %), but a modified composition with 0·26 wt % K2O (G2K) produces dacitic near-solidus melts with 61-64 wt % SiO2. Rutile saturation for G2K extends to higher melt fraction (∼13%) and occurs at lower TiO2 melt contents (3·3 wt %) than for G2. These results can be understood in terms of a simplified thermodynamic model in which alkalis increase the SiO2 content of liquids saturated in quartz, which in turn diminishes the TiO2 concentrations required to maintain rutile saturation. Additionally, the mode of residual garnet and generation of silicic liquids by partial melting of anhydrous eclogite are linked, as garnet is required to mass-balance formation of appreciable SiO2-rich melt. Partitioning of Na between clinopyroxene and melt shows significant increases with pressure, but only modest shifts with changing temperature. In contrast, partitioning of Ti between cpx and melt, as well as between cpx and garnet, shows pronounced dependence on temperature for compositions relevant to anhydrous partial melting of eclogite. Mixtures between partial melts of eclogite and primitive picritic Hawaiian magmas are similar to magnesian, SiO2-rich compositions inferred from melt inclusions from the Koolau volcano. However, in detail, no eclogitic partial melt has been identified that is capable of explaining all of the compositional features of the exotic Koolau component. Based on phase compositions in our experiments, the calculated density of near-solidus eclogite is 3440 kg/m3, notably less than commonly assumed. Therefore, the excess temperature required for a plume to support a given proportion of eclogite in the upper mantle may be less than previously assume

Minimal model for double Weyl points, multiband quantum geometry, and singular flat band inspired by LK-99

Two common difficulties in the design of topological quantum materials are that the desired features lie too far from the Fermi level and are spread over a too large energy range. Doping-induced states at the Fermi level provide a solution, where non-trivial topological properties are enforced by the doping-reduced symmetry. To show this, we consider a regular placement of dopants in a lattice of space group (SG) 176 (P6$\text{}_3$/m), which reduces the symmetry to SG 143 (P3). Our two- and four-band models feature symmetry-enforced double Weyl points at $\Gamma$ and A with Chern bands for $k_z\neq 0,\pi$, Van Hove singularities, nontrivial multiband quantum geometry due to mixed orbital character, and a singular flat band. The excellent agreement with density-functional theory (DFT) calculations on copper-doped lead apatite ('LK-99') provides evidence that minimal topological bands at the Fermi level can be realized in doped materials.Comment: Shortened for peer-review, phase convention adjusted, recent literature adde

Perturbations and Critical Behavior in the Self-Similar Gravitational Collapse of a Massless Scalar Field

This paper studies the perturbations of the continuously self-similar critical solution of the gravitational collapse of a massless scalar field (Roberts solution). The perturbation equations are derived and solved exactly. The perturbation spectrum is found to be not discrete, but occupying continuous region of the complex plane. The renormalization group calculation gives the value of the mass-scaling exponent equal to 1.Comment: 12 pages, RevTeX 3.1, 1 figur

A revised model for activity–composition relations in solid and molten FePt alloys and a preliminary model for characterization of oxygen fugacity in high-pressure experiments

We present new models for the activity of iron (γFe) in solid face-centered cubic (fcc) and liquid FePt alloy at high temperature and pressure to facilitate their use as sliding buffer redox sensors under extreme conditions. Numerous experimental studies of γFe in FePt alloy at 100 kPa have produced a wide spread of values. By favoring high-temperature studies that are more likely to have produced equilibrium measurement and excluding experiments for compositions and temperatures that probably encountered ordered or unmixed low-temperature phases, we regress an asymmetric Margules activity–composition model with parameters WFePtfcc=-121.5±2.1 kJ mol−1 and WPtFefcc=-93.3±4.3 kJ mol−1. These values are close to the widely used model of Kessel et al. (2001), but for Pt-rich compositions they predict larger Fe activities and correspondingly more reduced oxygen fugacities. Activity–composition relations in liquid FePt are calibrated from direct measurements of activities and, most sensitively, from the trace of the Fe–Pt liquidus. Together, these yield asymmetric Margules parameters of WFePtliq=-124.5 kJ mol−1 and WPtFeliq=-94.0 kJ mol−1. The effects of pressure on both fcc and liquid FePt alloy are considered from excess-volume relations. Both solid and liquid alloy display significant positive excess volumes of mixing. Extraction of the excess volume of mixing for fcc FePt alloy requires filtering data for ordered low-temperature phases and corrections for the effects of magnetostriction on Fe-rich compositions which exhibit “Invar” behavior. Applied at high temperatures and pressures, both solid and liquid FePt alloys have strongly negative deviations from ideality at low pressure, which become closer to ideal at high pressure. These models provide a provisional basis for the calculation of aFe in high-temperature, high-pressure experiments that, when combined with estimates of aFeO, allow characterization of fO2 under conditions relevant to magma oceans, core formation, and differentiation processes in the lower mantle of Earth or on other terrestrial planets. Improvements in these models require new constraints on the equation of state of FePt fcc alloy and documentation of the high-pressure melting relations in the system Fe–Pt.</p