A numerical method for obtaining multiple linear regression parameters with physically realistic signs and magnitudes: Applications to the determination of equilibrium constants from solubility data

A common problem in experimental geochemistry is the derivation of equilibrium constants from solubility experiments. A simple method of deriving these equilibrium constants, multiple linear regression, often results in the appearance of negative values. This has been a significant obstacle to continuing research in this field. The problem occurs for the most part because of significant correlations among the “independent” concentration variables. These correlations are an inescapable result of the nature of the experiments and the physical model being fitted. Ridge regression is an appropriate modification to simple linear regression which overcomes this difficulty. Ridge regression results in a simple procedure to obtain physically plausible, yet statistically rigorous stability constants. Of course, other problems may further degrade the quality of derived equilibrium constants, e.g. uncertainty in activity coefficients and no purely statistical method can overcome these types of problems. However, ridge regression is an effective procedure to overcome the multicolinearity which is the main cause of negative equilibrium constants. We demonstrate the use of ridge regression with a general mathematical model and then illustrate its use in the determination of iron-chloro complex equilibrium constants from solubility studies of pyrite-pyrrhotite-magnetite in NaCl solutions at 250°C. Ridge regression may also be of use in other geochemical problems where one must estimate parameters with a physical interpretation and where the independent variables are significantly intercorrelated.     

Peace Parks and jaguar trails: transboundary conservation in a globalizing world

An increasingly utilized strategy for expanding conservation in the developing world has been the promotion of protected areas that supersede national borders. Alternatively known as transfrontier biosphere reserves, transfrontier or transboundary conservation areas, or Peace Parks, these protected areas are aggressively advanced by conservation agencies for their purported ecological and economic benefits. This article provides a comparative assessment of two case studies to understand the various impacts of transboundary conservation. The Great Limpopo Transfrontier Park, which unites protected areas in South Africa, Mozambique and Zimbabwe, is contrasted with efforts to protect jaguars along the United States–Mexico border. We argue that while these cases are promising for the purposes of biodiversity protection, they demonstrate that transboundary conservation can minimize political context, contributes to the hegemony of international conservation agendas, and remains closely linked to economic neoliberalism and decentralization in the developing world.

Resonant oscillations in sunspot umbrae

The Uchida and Sakurai (1975), Thomas and Scheuer (1982), and Scheuer and Thomas (1981) theory of umbral oscillations as resonant modes of magneto-acoustic-gravity waves is re-examined. For an isothermal atmosphere it is found that the quasi-Alfvén approximation is not a good approximation to the complete linearized wave equations. The new results presented here show that 3 min umbral oscillation periods are fairly insensitive to magnetic field strength above some critical value. For a detailed model umbra (Thomas and Scheuer, 1982) the calculations presented here show that 3 min umbral oscillations do not depend to any great extent on the level of forcing of the oscillations for those magnetic field strengths which are observed in sunspot umbras. Modes outside the 3 min range appear, as the lowest mode, as the level of forcing is placed at deeper and deeper levels in the solar atmosphere.     

A multi‐method approach to dating the burial and skeleton of Kiacatoo Man,New South Wales,Australia

Kiacatoo Man, a large, rugged Aboriginal adult buried in the Lachlan riverine plains of southeastern Australia, was discovered in 2011. Laser‐ablation uranium series analysis on bone yielded a minimum age for the burial of 27.4 ± 0.4 ka (2σ). Single‐grain, optically stimulated luminescence ages on quartz sediment in which the grave had been dug gave a weighted mean age of 26.4 ± 1.5 ka (1σ). Luminescence samples from the grave infill and from sediment beneath the grave exhibit overdispersed dose distributions consistent with bioturbation or other disturbance, which has obscured the burial signal. The overlap between the minimum (U‐series) and maximum (luminescence) ages places the burial between 27.0 and 29.4 ka (2σ). Luminescence ages obtained from the channel belt of between 28 ± 2 and 25 ± 3 ka indicate that fluvial sedimentation was occurring before the Last Glacial Maximum, which is consistent with the broader geomorphic setting. Together, these results are internally and regionally consistent, and indicate that Kiacatoo Man was one of the more ancient individuals so far identified in Australia. His remains are important to our understanding of patterns of biological variation and other processes that have shaped people in the Murray‐Darling Basin through time. Copyright © 2019 John Wiley & Sons, Ltd.     

Thermal expansion and crystal structure of FeSi between 4 and 1173 K determined by time-of-flight neutron powder diffraction

The thermal expansion and crystal structure of FeSi has been determined by neutron powder diffraction between 4 and 1173?K. No evidence was seen of any structural or magnetic transitions at low temperatures. The average volumetric thermal expansion coefficient above room temperature was found to be 4.85(5)?×?10^?5?K^?1. The cell volume was fitted over the complete temperature range using Grüneisen approximations to the zero pressure equation of state, with the internal energy calculated via a Debye model; a Grüneisen second-order approximation gave the following parameters: θ_D=445(11)?K, V ₀=89.596(8)?ų, K ₀′=4.4(4) and γ′=2.33(3), where θ_D is the Debye temperature, V ₀ is V at T=0?K, K ₀′ is the first derivative with respect to pressure of the incompressibility and γ′ is a Grüneisen parameter. The thermodynamic Grüneisen parameter, γ_th, has been calculated from experimental data in the range 4–400?K. The crystal structure was found to be almost invariant with temperature. The thermal vibrations of the Fe atoms are almost isotropic at all temperatures; those of the Si atoms become more anisotropic as the temperature increases.     

The effect of Ca-Tschermaks component on trace element partitioning between clinopyroxene and silicate melt

We have studied the influence of Ca-Tschermaks (Calcium Tschermaks or CaTs) content of clinopyroxene on the partitioning of trace elements between this phase and silicate melt at fixed temperature and pressure. Ion probe analyses of experiments carried out in the system Na₂O–CaO–MgO–Al₂O₃–SiO₂, at 0.1 MPa and 1218°C, produced crystal-melt partition coefficients (D) of 36 trace elements (Li, Cl, Sc, Ti, V, Cr, Fe, Co, Ge, Sr, Y, Zr, Nb, Mo, Ru, Rh, In, Sn, Sb, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta and W), for clinopyroxene compositions between 10 and 32 mol% CaTs. Partition coefficients for 2+ to 5+ cations show, for each charge, a near parabolic dependence of log D on ionic radius of the substituting cation, for partitioning into both the M1 and M2 sites of clinopyroxene. Fitting the results to the elastic strain model of Blundy and Wood [Blundy, J.D., Wood, B.J., 1994. Prediction of crystal-melt partition coefficients from elastic moduli. Nature 372, 452–454] we obtain results for the strain-free partition coefficients of theoretical cations (D₀), with site radius r₀, and for the site's Young's Modulus (E).

In agreement with earlier data our results show that increasing ^ivAl concentration in cpx is matched by increasing D, E_M1, E_M2 and D₀ for tri-, tetra- and pentavalent cations. The degree of fractionation between chemically similar elements (i.e. Ta/Nb, Zr/Hf) also increases. In contrast, D values for mono-, di- and hexavalent cations decrease with increasing ^ivAl in the cpx. The large suite of trace elements used has allowed us to study the effects of cation charge on D₀, r₀ and E. We have found that D₀ and r₀ decrease with increasing cation charge, e.g. r₀=0.66 Å for 4+ cations and 0.59 Å for 5+ cations substituting into M1. Values of E_M1 and E_M2 increase with cation charge as well as with increasing ^ivAl content. The increase in E_M2 is linear and close to the trend set by Hazen and Finger [Hazen, R.M., Finger, L.W., 1979. Bulk modulus-volume relationship for cation–anion polyhedra. J. Geophys. Res. 84 (10) 6723–6728] for oxides. E_M1 values are much higher and do not fit the trend predicted by the Hazen and Finger relationship.     

Formation of chondritic refractory inclusions: The astrophysical setting

This study attempts to identify the astrophysical setting in which properties of the Ca,Al-rich inclusions (CAIs) found in chondritic meteorites are best understood. Importance is attached to the short time period in which most or all of the CAIs were formed (<∼0.5 Myr, corresponding to the observed dispersion of values of initial ²⁶Al/²⁷Al about the canonical value of ∼5 × 10⁻⁵), a constraint that has been overlooked. This period is dissimilar to the time scale of evolution of T Tauri stars, ∼10 Myr; it corresponds instead to the time scale of Class 0 and Class I young stellar objects, protostars as they exist during the massive infall of interstellar material that creates stars. The innermost portion of the sun’s rapidly accreting nebular disk, kept hot during that period by viscous dissipation, is the most plausible site for CAI formation. Once condensed, CAIs must be taken out of that hot zone rather promptly in order to preserve their specialized mineralogical compositions, and they must be transported to the radial distance of the asteroid belt to be available for accretion into the chondrites that contain them today. Though this paper is critical of some aspects of the x-wind model of CAI formation, something akin to the x-wind may be the best way of understanding this extraction and transport of CAIs.     

Reaction relationships of chrome-spinels in igneous rocks — further evidence from the layered intrusions of Rhum and Mull,Inner Hebrides,Scotland

Compositions of chrome-spinels in peridotites from the layered igneous rocks of Rhum and of the Ben Buie intrusion, Mull, show evidence of post-depositional reaction relationships with the cumulus olivine and/or the intercumulus liquid. Some seam-forming spinels in the Ben Buie intrusion are highly aluminous, more so than those in the Rhum intrusion. Occasional zoned spinels, in both intrusions, show enrichment in Al towards their rims. The evidence suggests that the spinel reaction trend involving Cr-Al exchange proceeds in the direction of Al-enrichment. Equilibrium between chrome-spinel and cumulus olivine appears to have been attained rarely, thus limiting the application of the olivine-spinel geothermometer.     

Fluid convection and mass transfer in porous sandstones—a theoretical model

When porous, fluid-saturated, bodies of geologic dimensions are subjected to temperature gradients on the order of the normal geothermal gradient (25°C/km) it is shown that large (km) scale eddy currents will spontaneously arise and persist in these bodies. The velocity of these fluid currents is on the order of 1 meter per year, but taken over a period of several million years, the mass flux accompanying the fluid flow is large enough to produce significant porosity changes. It is shown that diffusive mass transfer is generally a negligible component of the total mass flux when characteristic distances are greater than grain diameters and it is concluded that most post-depositional reservoir cementation is due to slowly circulating fluids. In terms of a broad perspective, reservoir diagenesis can be regarded as a low heat flow analogue of hydrothermal alteration, occupying the low fluid flow regime of the spectrum, and passing into the hydrothermal regime as the heat flow and fluid velocities increase.