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1. The Viscosity and Atomic Structure of Volatile-Bearing Melilititic Melts at High Pressure and Temperature and the Transport of Deep Carbon

   https://doi.org/10.3390/min10030267  

   Stagno, Vincenzo ; Stopponi, Veronica ; Kono, Yoshio ; D’Arco, Annalisa ; Lupi, Stefano ; Romano, Claudia ; Poe, Brent T. ; Foustoukos, Dionysis I. ; Scarlato, Piergiorgio ; Manning, Craig E. ( March 2020 , Minerals)

   Understanding the viscosity of mantle-derived magmas is needed to model their migration mechanisms and ascent rate from the source rock to the surface. High pressure–temperature experimental data are now available on the viscosity of synthetic melts, pure carbonatitic to carbonate–silicate compositions, anhydrous basalts, dacites and rhyolites. However, the viscosity of volatile-bearing melilititic melts, among the most plausible carriers of deep carbon, has not been investigated. In this study, we experimentally determined the viscosity of synthetic liquids with ~31 and ~39 wt% SiO2, 1.60 and 1.42 wt% CO2 and 5.7 and 1 wt% H2O, respectively, at pressures from 1 to 4.7 GPa and temperatures between 1265 and 1755 °C, using the falling-sphere technique combined with in situ X-ray radiography. Our results show viscosities between 0.1044 and 2.1221 Pa·s, with a clear dependence on temperature and SiO2 content. The atomic structure of both melt compositions was also determined at high pressure and temperature, using in situ multi-angle energy-dispersive X-ray diffraction supported by ex situ microFTIR and microRaman spectroscopic measurements. Our results yield evidence that the T–T and T–O (T = Si,Al) interatomic distances of ultrabasic melts are higher than those for basaltic melts known from similar recent studies. Based on our experimentalmore »data, melilititic melts are expected to migrate at a rate ~from 2 to 57 km·yr−1 in the present-day or the Archaean mantle, respectively.« less
2. High-temperature Stability of an Iron-rich Smectite: Implications for Smectite Formation on Mars

   Jenkins, D.M. ; DePasquale, B.M. ( December 2020 , American Geophysical Union meeting, Fall 2020 Meeting)

   Iron-rich phyllosilicates on Mars comprise nearly 90% of the H2O- and OH-bearing phases observed directly by rovers and remotely by orbiters (Chemtob et al., 2017, JGR). Theories concerning the possible origin of Fe-rich smectite during Mars’ earliest history (phyllosian) are hard to test because of limited knowledge of the upper-thermal stability of Fe-rich phyllosilicates. In this study we present data on the upper-thermal stability of a pure-iron smectite to put some minimum constraints on its possible high-temperature origin early in Mars history either from a primordial atmosphere or by hydrothermal activity. Smectite coexisting with quartz and magnetite was synthesized from the oxides in the system Na2O-FeO-Fe2O3-Al2O3-SiO2-H2O at 500°C and 2 kbar and fO2 near FMQ. Reversal experiments involved mixtures with equal portions of the smectite-synthesis and breakdown products (quartz, fayalite, albite, magnetite (mt) treated in the presence of about 10 wt% H2O over the range of 1-3 kbar and 530-640°C. The average composition (electron microprobe) of smectite formed both in synthesis and in reversal experiments was Na0.35(Fe2+2.28Fe3+0.31Al0.41)(Al1.07Si2.93)O10(OH)2·nH2O, where ferric iron was calculated by summing the octahedral cations to 3.0. Reversals for the reaction smec+mt1 = fayalite+albite+mt2+quartz+H2O were obtained at 538±8, 590±10, and 610±10°C at 1, 2, and 3 kbar, respectively,more »where mt1 and mt2 have the approximate compositions Fe2.8Si0.2O4 and Fe2.8Al0.1O4, respectively, with all other phases being pure. This smectite has up to 2 interlayer H2O at 25°C (and high humidity), losing 1 H2O at <50°C, and the second at 125 ± 25°C. Thermodynamic modeling of this reaction was used to extrapolate the upper-thermal stability of this Fe-smectite down to 10 bars and approximately 239°C. Applications of these results indicate the maximum temperature for forming Fe-smectite from a dense primordial atmosphere of 100 bars is 390 ± 25°C. Crustal storage of water in Fe-smectite ranges up to a maximum of 10.7 wt% at ~2 km and 40°C, 7.4 wt% at 6 km and 120°C, and 3.8 wt% H2O at 32 km and 625°C for a Noachian geotherm of 20°C/km. Plain language summary: This study presents experimental limits on the temperatures at which the clay mineral smectite might form on Mars, either from a dense primordial atmosphere (390°C at 100 bars) or by high-temperature hydrothermal activity (625°C at 32 km). Because this study deals with iron end-member clay, these are minimum temperatures; any solid solution with magnesium will increase these temperatures.« less
3. Ensemble-based estimates of eigenvector error for empirical covariance matrices

   https://doi.org/10.1093/imaiai/iay010  

   Taylor, Dane ; Restrepo, Juan G ; Meyer, François G ( July 2018 , Information and Inference: A Journal of the IMA)

   Abstract Covariance matrices are fundamental to the analysis and forecast of economic, physical and biological systems. Although the eigenvalues $\{\lambda _i\}$ and eigenvectors $\{\boldsymbol{u}_i\}$ of a covariance matrix are central to such endeavours, in practice one must inevitably approximate the covariance matrix based on data with finite sample size $n$ to obtain empirical eigenvalues $\{\tilde{\lambda }_i\}$ and eigenvectors $\{\tilde{\boldsymbol{u}}_i\}$, and therefore understanding the error so introduced is of central importance. We analyse eigenvector error $\|\boldsymbol{u}_i - \tilde{\boldsymbol{u}}_i \|^2$ while leveraging the assumption that the true covariance matrix having size $p$ is drawn from a matrix ensemble with known spectral properties—particularly, we assume the distribution of population eigenvalues weakly converges as $p\to \infty $ to a spectral density $\rho (\lambda )$ and that the spacing between population eigenvalues is similar to that for the Gaussian orthogonal ensemble. Our approach complements previous analyses of eigenvector error that require the full set of eigenvalues to be known, which can be computationally infeasible when $p$ is large. To provide a scalable approach for uncertainty quantification of eigenvector error, we consider a fixed eigenvalue $\lambda $ and approximate the distribution of the expected square error $r= \mathbb{E}\left [\| \boldsymbol{u}_i - \tilde{\boldsymbol{u}}_i \|^2\right ]$ across themore »matrix ensemble for all $\boldsymbol{u}_i$ associated with $\lambda _i=\lambda $. We find, for example, that for sufficiently large matrix size $p$ and sample size $n> p$, the probability density of $r$ scales as $1/nr^2$. This power-law scaling implies that the eigenvector error is extremely heterogeneous—even if $r$ is very small for most eigenvectors, it can be large for others with non-negligible probability. We support this and further results with numerical experiments.« less
4. A Fast and Effective Memristor-Based Method for Finding Approximate Eigenvalues and Eigenvectors of Non-negative Matrices

   https://doi.org/10.1109/ISVLSI.2018.00108  

   Wang, Chenghong ; Jalali, Zeinab S. ; Ding, Caiwen ; Wang, Yanzhi ; Soundarajan, Sucheta ( July 2018 , 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI))

   Throughout many scientific and engineering fields, including control theory, quantum mechanics, advanced dynamics, and network theory, a great many important applications rely on the spectral decomposition of matrices. Traditional methods such as the power iteration method, Jacobi eigenvalue method, and QR decomposition are commonly used to compute the eigenvalues and eigenvectors of a square and symmetric matrix. However, these methods suffer from certain drawbacks: in particular, the power iteration method can only find the leading eigen-pair (i.e., the largest eigenvalue and its corresponding eigenvector), while the Jacobi and QR decomposition methods face significant performance limitations when facing with large scale matrices. Typically, even producing approximate eigenpairs of a general square matrix requires at least O(N^3) time complexity, where N is the number of rows of the matrix. In this work, we exploit the newly developed memristor technology to propose a low-complexity, scalable memristor-based method for deriving a set of dominant eigenvalues and eigenvectors for real symmetric non-negative matrices. The time complexity for our proposed algorithm is O(N^2 /Δ) (where Δ governs the accuracy). We present experimental studies to simulate the memristor-supporting algorithm, with results demonstrating that the average error for our method is within 4%, while its performance is upmore »to 1.78X better than traditional methods.« less
5. Anomalous elastic behavior of phase egg, AlSiO3(OH), at high pressures

   Mookherjee, Mainak ; Panero, Wendy R. ; Wunder, Bernd ; Jahn, Sandro ( January 2019 , The American mineralogist)

   Phase egg, [AlSiO3(OH)], is an aluminosilicate hydrous mineral that is thermodynamically stable in lithological compositions represented by Al2O3-SiO2-H2O (ASH) ternary, i.e., a simplified ternary for the mineralogy of subducted sediments and continental crustal rocks. High-pressure and high-temperature experiments on lithological compositions resembling hydrated sedimentary layers in subducting slabs show that phase egg is stable up to pressures of 20–30 GPa, which translates to the transition zone to lower mantle depths. Thus, phase egg is a potential candidate for transporting water into the Earth’s mantle transition zone. In this study, we use first-principles simulations based on density functional theory to explore the pressure dependence of crystal structure and how it influences energetics and elasticity. Our results indicate that phase egg exhibits anomalous behavior of the pressure dependence of the elasticity at mantle transition zone depths (~15 GPa). Such anomalous behavior in the elasticity is related to changes in the hydrogen bonding O-H···O configurations, which we delineate as a transition from a low-pressure to a high-pressure structure of phase egg. Full elastic constant tensors indicate that phase egg is very anisotropic resulting in a maximum anisotropy of compressional wave velocity, AvP ≈ 30% and of shear wave velocity, AvS ≈ 17% atmore »zero pressures. Our results also indicate that the phase egg has one of the fastest bulk sound velocities (vP and vS) compared to other hydrous aluminous phases in the ASH ternary, which include topaz-OH, phase Pi, and d-AlOOH. However, the bulk sound velocity of phase egg is slower than that of stishovite. At depths corresponding to the base of mantle transition zone, phase egg decomposes to a mixture of d-AlOOH and stishovite. The changes in compressional DvP and shear DvS velocity associated with the decomposition is ~0.42% and –1.23%, respectively. Although phase egg may be limited to subducted sediments, it could hold several weight percentages of water along a normal mantle geotherm.« less