Kobyashevite, Cu5(SO4)2(OH)6·4H2O, a new devilline-group mineral from the Vishnevye Mountains, South Urals, Russia

A new mineral kobyashevite, Cu₅(SO₄)₂(OH)₆·4H₂O (IMA 2011–066), was found at the Kapital’naya mine, Vishnevye Mountains, South Urals, Russia. It is a supergene mineral that occurs in cavities of a calcite-quartz vein with pyrite and chalcopyrite. Kobyashevite forms elongated crystals up to 0.2 mm typically curved or split and combined into thin crusts up to 1?×?2 mm. Kobyashevite is bluish-green to turquoise-coloured. Lustre is vitreous. Mohs hardness is 2½. Cleavage is {010} distinct. D(calc.) is 3.16 g/cm³. Kobyashevite is optically biaxial (?), α 1.602(4), β 1.666(5), γ 1.679(5), 2 V(meas.) 50(10)°. The chemical composition (wt%, electron-microprobe data) is: CuO 57.72, ZnO 0.09, FeO 0.28, SO₃ 23.52, H₂O(calc.) 18.39, total 100.00. The empirical formula, calculated based on 18 O, is: Cu_4.96Fe_0.03Zn_0.01S_2.01O_8.04(OH)_5.96·4H₂O. Kobyashevite is triclinic, $ P\overline{\,1 } $ , a 6.0731(6), b 11.0597(13), c 5.5094(6)?Å, α 102.883(9)°, β 92.348(8)°, γ 92.597(9)°, V 359.87(7)?ų, Z?=?1. Strong reflections of the X-ray powder pattern [d,Å-I(hkl)] are: 10.84–100(010); 5.399–40(020); 5.178–12(110); 3.590–16(030); 2.691–16(20–1, 040, 002), 2.653–12(04–1, 02–2), 2.583–12(2–11, 201, 2–1–1), 2.425–12(03–2, 211, 131). The crystal structure (single-crystal X-ray data, R?=?0.0399) сontains [Cu₄(SO₄)₂(OH)₆] corrugated layers linked via isolated [CuO₂(H₂O)₄] octahedra; the structural formula is CuCu₄(SO₄)₂(OH)₆·4H₂O. Kobyashevite is a devilline-group member. It is named in memory of the Russian mineralogist Yuriy Stepanovich Kobyashev (1935–2009), a specialist on mineralogy of the Urals.     

Comparison of forms of the viscous shallow-water equations in the boundary-fitted coordinates

In order to determine robustness of the models based on the viscous shallow-water equations in the boundary-fitted coordinates the solution characteristics of the boundary-value problem are compared for different forms of equations in contravariant, covariant and Cartesian presentations of the velocity. Distinctions between these forms associated with presentation of advection and eddy viscosity in their approximation on a curvilinear grid are established. A boundary-value problem for the tidal dynamics computation in the Strait of Messina (Mediterranean Sea) is formulated with use of different forms of equations in the boundary-fitted coordinates. An estimation and comparison of the modelling results are performed.     

Certification of ERM‐EB400, the First Matrix Reference Material for Lead Isotope Amount Ratios,and ERM‐AE142, a Lead Solution Providing a Lead Isotopic Composition at the Edge of Natural Variation

Lead isotope amount ratios are commonly used in diverse fields such as archaeometry, geochemistry and forensic science. Currently, five reference materials with certified lead isotope amount ratios are available, namely NIST SRM 981, 982 and 983, GBW‐04442 and NMIJ 3681‐a. Only NIST SRM 981 and NMIJ 3681‐a have approximately natural isotopic compositions, and NIST SRM 981 is predominantly used for correcting mass discrimination/mass fractionation in the applied mass spectrometric procedures. Consequently, there is no other certified reference material available to be used for validation and/or quality control of the analytical procedures applied to lead isotope amount ratio measurements. To fill this gap, two new reference materials have been produced and certified for their lead isotope amount ratios. For both certified reference materials, complete uncertainty budgets have been calculated and SI traceability has been established. This provides the users with independent means for validating and verifying their analytical procedures and for conducting quality control measures. ERM‐EB400 is a bronze material with a nominal lead mass fraction of 45 mg kg^?1 and certified lead isotope amount ratios of n(²⁰⁶Pb)/n(²⁰⁴Pb) = 18.072(17) mol mol^?1, n(²⁰⁷Pb)/n(²⁰⁴Pb) = 15.578(18) mol mol^?1 and n(²⁰⁸Pb)/n(²⁰⁴Pb) = 38.075(46) mol mol^?1 with the associated expanded uncertainties (k = 2) given in brackets. ERM‐AE142 is a high‐purity solution of lead in 2% nitric acid with a nominal mass fraction of 100 mg kg^?1 and certified Pb isotope amount ratios of n(²⁰⁶Pb)/n(²⁰⁴Pb) = 21.114(17) mol mol^?1, n(²⁰⁷Pb)/n(²⁰⁴Pb) = 15.944(17) mol mol^?1 and n(²⁰⁸Pb)/n(²⁰⁴Pb) = 39.850(44) mol mol^?1 with the associated expanded uncertainties (k = 2) given in brackets. Both materials are specifically designed to fall within the natural lead isotopic variation and to assist users with the validation and verification of their analytical procedures. Note that while one of these reference materials requires the chemical separation of Pb from its matrix (ERM‐EB400), the other does not (ERM‐AE142). As additional information, δ^208/206Pb_{NIST SRM981} values are provided for both materials. For ERM‐AE142, a delta value of δ^208/206Pb_{NIST SRM981} = ?28.21(30)‰ was obtained, and for ERM‐EB400, a delta value of δ^208/206Pb_NIST SRM981= ?129.47(38)‰ was obtained, with the associated expanded uncertainties (k = 2) given in brackets.     

Comparison of Star Formation Rate Estimates from Hα, FIR and Radio Data

We use three indicators of massive star formation, H_α, FIR and non-thermal radio luminosities, to compare estimates of the star formation rate (SFR) for a sample of 34 spiral galaxies. To adjust the SFR values obtained from these indicators, we considered the slope, α, and/or the upper mass limit M _up of the initial mass function (IMF) as free parameters. The best agreement between the indicators is found for M _up≈ 60-100 M⊙ and α ≈–3.1 at the high-mass end of the IMF (M>10 M⊙.Parallelwith the SFR we also estimated the FIR excess X _FIR, defined as the fraction of the observed FIR not directly related to young massive stars. X _FIR is found to be well correlated with types of spiral galaxies and their colours (B-V): the redder a galaxy, the higher its FIR excess. We conclude that for any parameters of the IMF the observed FIR flux of early-type spiral galaxies needs an additional source of energy apart from massive star radiation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Lebedev scheme for the numerical simulation of wave propagation in 3D anisotropic elasticity‡

This paper presents a Lebedev finite difference scheme on staggered grids for the numerical simulation of wave propagation in an arbitrary 3D anisotropic elastic media. The main concept of the scheme is the definition of all the components of each tensor (vector) appearing in the elastic wave equation at the corresponding grid points, i.e., all of the stresses are stored in one set of nodes while all of the velocity components are stored in another. Meanwhile, the derivatives with respect to the spatial directions are approximated to the second order on two‐point stencils. The second‐order scheme is presented for the sake of simplicity and it is easy to expand to a higher order. Another approach, widely‐known as the rotated staggered grid scheme, is based on the same concept; therefore, this paper contains a detailed comparative analysis of the two schemes. It is shown that the dispersion condition of the Lebedev scheme is less restrictive than that of the rotated staggered grid scheme, while the stability criteria lead to approximately equal time stepping for the two approaches. The main advantage of the proposed scheme is its reduced computational memory requirements. Due to a less restrictive dispersion condition and the way the media parameters are stored, the Lebedev scheme requires only one‐third to two‐thirds of the computer memory required by the rotated staggered grid scheme. At the same time, the number of floating point operations performed by the Lebedev scheme is higher than that for the rotated staggered grid scheme.     

Statistical Analysis of Fracture-Length Distribution Sampled Under the Truncation and Censoring Effects

The present paper addresses statistical analysis and estimation of fracture-length distributions at scales influenced by the truncation and censoring effects. The computational method employed here uses fracture-length distributions of a given set of measurements and information about observational constraints (i.e., window of observation) to estimate the probability density of the truncated and censored parts of fracture data sets. The results are benchmarked against power-law based maximal likelihood estimations commonly used for the same purpose. The relationship between the accuracy of estimates and size of the window of observation is studied. The utility of employing statistical models with arbitrary probability distributions of fracture lengths in order to provide a valid statistical model approximation is also considered. A verification of the suggested approximation using the Kolmogorov–Smirnov test applied to truncated and censored data is proposed. Numerical computations show that the proposed method can represent an essential improvement compared to other commonly employed techniques.