The solubility of rhenium in silicate melts: Implications for the geochemical properties of rhenium at high temperatures

The solubility of rhenium (Re) in a haplobasaltic melt (anorthite-diopside eutectic composition) has been experimentally determined using the mechanically assisted equilibration technique at 1400°C as a function of oxygen fugacity (10−12 < fO2 ≤ 10−7 bar), imposed by CO-CO2 gas mixtures. Samples were analysed by laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS). This is a true microanalytical technique, which allows small-scale sample heterogeneity to be detected, while providing a limit of detection of 2 ppb Re. Time-resolved LA-ICP-MS spectra revealed the presence of suboptically sized micronuggets of Re in all samples, which, because they are present at the 0.5 to 10 ppm level, dominate the true solubilities of Re (<1 ppm at the conditions of the experiment) in bulk analyses of the samples. Nevertheless, the micronuggets could be filtered out from the time-resolved spectra to reveal accurate values of the true Re solubility. A number of time series of samples were taken at constant fO2 to demonstrate that the solubilities converge to a constant value. In addition, solubilities were measured after increasing and decreasing the imposed fO2. The results show that Re dissolves in the silicate melt as ReO2 (Re4+) and ReO3 (Re6+) species, with the latter predominating at typical terrestrial upper-mantle oxygen fugacities. The total solubility of Re is described by the following expression (fO2 in bars): [Re/ppb] = 9.7(±1.9) × 109 (fO2) + 4.2 (±0.3) × 1014 (fO2)1.5Assuming an activity coefficient for Re in Fe-rich metal of 1, this gives a value of DRemet/sil of 5 × 1010 at log fO2 = IW-2, appropriate for metal-silicate partitioning in an homogenously accreting Earth. Thus, Re is indeed very highly siderophile, and the mantle’s abundance cannot be explained by homogenous accretion

Enhancement of bichromatic high-harmonic generation with a high-frequency field

Using a high-frequency field superposed to a linearly polarized bichromatic laser field composed by a wave with frequency $\omega$ and a wave with frequency $2\omega$, we show it is possible to enhance the intensity of a group of high harmonics in orders of magnitude. These harmonics have frequencies about 30% higher than the monochromatic-cutoff frequency, and, within the three-step-model framework, correspond to a set of electron trajectories for which tunneling ionization is strongly suppressed. Particular features in the observed enhancement suggest that the high-frequency field provides an additional mechanism for the electron to reach the continuum. This interpretation is supported by a time-frequency analysis of the harmonic yield. The additional high frequency field permits the control of this group of harmonics leaving all other sets of harmonics practically unchanged, which is an advantage over schemes involving only bichromatic fields.Comment: 6 pages RevTex, 5 figures (ps files), Changes in text, figures, references and equations include

Chiral Analysis of Quenched Baryon Masses

We extend to quenched QCD an earlier investigation of the chiral structure of the masses of the nucleon and the delta in lattice simulations of full QCD. Even after including the meson-loop self-energies which give rise to the leading and next-to-leading non-analytic behaviour (and hence the most rapid variation in the region of light quark mass), we find surprisingly little curvature in the quenched case. Replacing these meson-loop self-energies by the corresponding terms in full QCD yields a remarkable level of agreement with the results of the full QCD simulations. This comparison leads to a very good understanding of the origins of the mass splitting between these baryons.Comment: 23 pages, 6 figure

Chiral Behaviour of the Rho Meson in Lattice QCD

In order to guide the extrapolation of the mass of the rho meson calculated in lattice QCD with dynamical fermions, we study the contributions to its self-energy which vary most rapidly as the quark mass approaches zero; from the processes $\rho \to \omega \pi$ and $\rho \to \pi \pi$. It turns out that in analysing the most recent data from CP-PACS it is crucial to estimate the self-energy from $\rho \to \pi \pi$ using the same grid of discrete momenta as included implicitly in the lattice simulation. The correction associated with the continuum, infinite volume limit can then be found by calculating the corresponding integrals exactly. Our error analysis suggests that a factor of 10 improvement in statistics at the lowest quark mass for which data currently exists would allow one to determine the physical rho mass to within 5%. Finally, our analysis throws new light on a long-standing problem with the J-parameter.Comment: 13 pages, 7 figures. Full analytic forms of the self-energies are included and a correction in the omega-pi self-energ

Neutrino-Deuteron Scattering in Effective Field Theory at Next-to-Next-to Leading Order

We study the four channels associated with neutrino-deuteron breakup reactions at next-to-next to leading order in effective field theory. We find that the total cross-section is indeed converging for neutrino energies up to 20 MeV, and thus our calculations can provide constraints on theoretical uncertainties for the Sudbury Neutrino Observatory. We stress the importance of a direct experimental measurement to high precision in at least one channel, in order to fix an axial two-body counterterm.Comment: 32 pages, 14 figures (eps

Chiral extrapolation of lattice data for B-meson decay constant

The B-meson decay constant fB has been calculated from unquenched lattice QCD in the unphysical region. For extrapolating the lattice data to the physical region, we propose a phenomenological functional form based on the effective chiral perturbation theory for heavy mesons, which respects both the heavy quark symmetry and the chiral symmetry, and the non-relativistic constituent quark model which is valid at large pion masses. The inclusion of pion loop corrections leads to nonanalytic contributions to fB when the pion mass is small. The finite-range regularization technique is employed for the resummation of higher order terms of the chiral expansion. We also take into account the finite volume effects in lattice simulations. The dependence on the parameters and other uncertainties in our model are discussed.Comment: 11 pages, 3 Postscript figures, accepted for publication in EPJ

Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees

We present examples of rooted tree graphs for which the Laplacian has singular continuous spectral measures. For some of these examples we further establish fractional Hausdorff dimensions. The singular continuous components, in these models, have an interesting multiplicity structure. The results are obtained via a decomposition of the Laplacian into a direct sum of Jacobi matrices

Anthropic Explanation of the Dark Matter Abundance

I use Bousso's causal diamond measure to make a statistical prediction for the dark matter abundance, assuming an axion with a large decay constant f_a >> 10^{12} GeV. Using a crude approximation for observer formation, the prediction agrees well with observation: 30% of observers form in regions with less dark matter than we observe, while 70% of observers form in regions with more dark matter. Large values of the dark matter ratio are disfavored by an elementary effect: increasing the amount of dark matter while holding fixed the baryon to photon ratio decreases the number of baryons inside one horizon volume. Thus the prediction is rather insensitive to assumptions about observer formation in universes with much more dark matter than our own. The key assumption is that the number of observers per baryon is roughly independent of the dark matter ratio for ratios near the observed value.Comment: 10 pages; v3: published version, references adde

Investigation into high-frequency-vibration assisted micro-blanking of pure copper foils

The difficulties encountered during the manufacture of microparts are often associated with size effects relating to material, process and tooling. Utilizing acoustoplastic softening, achieved through a high-frequency vibration assisted micro-blanking process, was introduced to improve the surface finish in micro-blanking. A frequency of 1.0 kHz was chosen to activate the longitudinal vibration mode of the horn tip, using a piezoelectric actuator. A square hole with dimensions of 0.5 mm × 0.5 mm was made, successfully, from a commercial rolled T2 copper foil with 100 μm in thickness. It was found that the maximum blanking force could be reduced by 5% through utilizing the high-frequency vibration. Proportion of the smooth, burnished area in the cut cross-section increases with an increase of the plasticity to fracture, under the high-frequency vibration, which suggests that the vibration introduced is helpful for inhibiting evolution of the crack due to its acoustoplastic softening effect. During blanking, roughness of the burnished surface could be reduced by increasing the vibration amplitude of the punch, which played a role as surface polishing. The results obtained suggest that the high-frequency vibration can be adopted in micro-blanking in order to improve quality of the microparts

Infrared Behavior of the Gluon Propagator on a Large Volume Lattice

The first calculation of the gluon propagator using an order a^2 improved action with the corresponding order a^2 improved Landau gauge fixing condition is presented. The gluon propagator obtained from the improved action and improved Landau gauge condition is compared with earlier unimproved results on similar physical lattice volumes of 3.2^3 \times 6.4 fm^4. We find agreement between the improved propagator calculated on a coarse lattice with lattice spacing a = 0.35 fm and the unimproved propagator calculated on a fine lattice with spacing a = 0.10 fm. This motivates us to calculate the gluon propagator on a coarse large-volume lattice 5.6^3 \times 11.2 fm^4. The infrared behavior of previous studies is confirmed in this work. The gluon propagator is enhanced at intermediate momenta and suppressed at infrared momenta. Therefore the observed infrared suppression of the Landau gauge gluon propagator is not a finite volume effect.Comment: 8 pages, 4 figures, minor typos corrected and repsonse to referees comment