Mutual gravitational potential and torque of solid bodies via inertia integrals

The mutual gravitational potential and the mutual gravitational torque of two bodies of arbitrary shape are expanded to the fourth order. The derivations are based on Cartesian coordinates, inertia integrals with relation to the principal reference frames of each body, and the relative rotation matrix. The current formulation is convenient to utilize in high precision problems in rotational dynamics.     

Tidal interactions and disruptions of giant planets on highly eccentric orbits

We calculate the evolution of planets undergoing a strong tidal encounter using smoothed particle hydrodynamics (SPH), for a range of periastron separations. We find that outside the Roche limit, the evolution of the planet is well-described by the standard model of linear, non-radial, adiabatic oscillations. If the planet passes within the Roche limit at periastron, however, mass can be stripped from it, but in no case do we find enough energy transferred to the planet to lead to complete disruption. In light of the three new extrasolar planets discovered with periods shorter than two days, we argue that the shortest-period cases observed in the period-mass relation may be explained by a model whereby planets undergo strong tidal encounters with stars, after either being scattered by dynamical interactions into highly eccentric orbits, or tidally captured from nearly parabolic orbits. Although this scenario does provide a natural explanation for the edge found for planets at twice the Roche limit, it does not explain how such planets will survive the inevitable expansion that results from energy injection during tidal circularization.     

High-pressure behavior of natural single-crystal epidote and clinozoisite up to 40 GPa

The comparative compressibility and high-pressure stability of a natural epidote (0.79 Fe-total per formula unit, Fe_tot pfu) and clinozoisite (0.40 Fe_tot pfu) were investigated by single-crystal X-ray diffraction and Raman spectroscopy. The lattice parameters of both phases exhibit continuous compression behavior up to 30 GPa without evidence of phase transformation. Pressure–volume data for both phases were fitted to a third-order Birch–Murnaghan equation of state with V ₀ = 461.1(1) ų, K ₀ = 115(2) GPa, and \(K_{0}^{'}\) = 3.7(2) for epidote and V ₀ = 457.8(1) ų, K ₀ = 142(3) GPa, and \(K_{0}^{'}\) = 5.2(4) for clinozoisite. In both epidote and clinozoisite, the b-axis is the stiffest direction, and the ratios of axial compressibility are 1.19:1.00:1.15 for epidote and 1.82:1.00:1.19 for clinozoisite. Whereas the compressibility of the a-axis is nearly the same for both phases, the b- and c-axes of the epidote are about 1.5 times more compressible than in clinozoisite, consistent with epidote having a lower bulk modulus. Raman spectra collected up to 40.4 GPa also show no indication of phase transformation and were used to obtain mode Grüneisen parameters (γ _i) for Si–O vibrations, which were found to be 0.5–0.8, typical for hydrous silicate minerals. The average pressure coefficient of Raman frequency shifts for M–O modes in epidote, 2.61(6) cm^?1/GPa, is larger than found for clinozoisite, 2.40(6) cm^?1/GPa, mainly due to the different compressibility of FeO₆ and AlO₆ octahedra in M3 sites. Epidote and clinozoisite contain about 2 wt% H₂O are thus potentially important carriers of water in subducted slabs.     

Using Soil Magnetic Properties to Determine the Onset of Pleistocene Human Settlement at Gledswood Shelter 1, Northern Australia

In regions that lack built structures or stratified open archaeological sites, such as precolonial Australia, rockshelters are a major source of detailed information for understanding the nature and timing of human occupation. A key concern is that the proposed ages for the earliest archaeological sites are based on luminescence dating of sediments, rather than directly of cultural materials, leaving the association between the sediments and evidence of human activity questionable. Here, we present evidence of magnetic enhancement associated with cultural horizons within the deposits of a Pleistocene rockshelter in interior northern Queensland. Soil magnetic studies combined with experimental burning show that magnetically enhanced sediments in Gledswood Shelter 1 are the result of anthropogenic burning of hearth fires, which burn hotter and for a longer time than natural wild fires. These techniques appear to work in this setting because of the nature of the local geology and the geological antiquity of the landscape. Susceptibility and frequency dependence of susceptibility signatures provide a critical tool to resolve that human occupation starts at 2.2 m depth within a stratigraphic section. In conjunction with luminescence dating, soil magnetic studies provide an opportunity for archaeologists to resolve the timing of human settlement in Australia and other intracratonic plate settings.     

U-Th-Pb and Trace Element Evaluation of Existing Titanite and Apatite LA-ICP-MS Reference Materials and Determination of 208Pb/232Th-206Pb/238U Date Discordance in Archaean Accessory Phases

The last decade has seen a marked increase in U-Th-Pb petrochronological studies focused on titanite and apatite. This has motivated the need for detailed, phase-specific method development and well-characterised reference materials with a wide variety of ages and chemical compositions. This study presents new U-Th-Pb isotope and major-, minor- and trace-element mass fraction data for ten titanite and five apatite reference materials based on integrated EPMA, LA-ICP-MS and isotope-dilution (ID) multi-collector (MC)-ICP-MS characterisation. Cross-comparison of EPMA and LA-ICP-MS data for the same titanite reference material suite demonstrates that careful selection of EPMA primary reference materials is necessary to minimise inaccuracies. We further identify a significant X-ray interference when measuring low Ce abundances in Ti-bearing phases and outline a method for its correction. New ID-MC-ICP-MS and LA-ICP-MS data suggest tri-concordance (defined as concordant ages for the ²³⁸U-²⁰⁶Pb, ²³⁵U-²⁰⁷Pb and ²³²Th-²⁰⁸Pb decay systems) of the MKED-1 titanite reference material and demonstrate the reproducibility of ²⁰⁸Pb/²³²Th measurements in some secondary titanite reference materials. Integration of ²⁰⁸Pb/²³²Th results with U-Pb geochronology provides a meaningful tool to help interpret complex U-Th-Pb isotopic age spectra. We provide example applications of ²⁰⁸Pb/²³²Th LA-ICP-MS measurements toward interpreting Archaean titanite ages from the Acasta Gneiss Complex, Northwest Territories, Canada.     

Hierarchical livelihood outcomes among co-managed fisheries

Collaborative management arrangements are increasingly being used in fisheries, yet critical questions remain about the conditions under which these are most successful. Here, we conduct one of the first comprehensive tests of Elinor Ostrom's diagnostic framework for analyzing social–ecological systems to examine how 16 socioeconomic and institutional conditions are related the livelihood outcomes in 42 co-management arrangements in five countries across the Indo-Pacific. We combine recent developments in both theory and modeling to address three key challenges among comparative studies of social–ecological systems: the presence of a large number of explanatory mechanisms, variables operating at multiple scales, and the potential for interactions among socio-economic and institutional factors. We find that resource users were more likely to perceive benefits from co-management when they are more involved in decisions, were aware that humans are causal agents of change in marine systems, were wealthier, were not migrants, were in villages with smaller populations and older co-management arrangements, and had clearly established boundaries. Critically, we quantify a number of key interactions between: wealth, dependence on marine resources, involvement in decision-making, and population size that have strong implications for co-management success in terms of livelihood benefits. This study demonstrates that context plays a critical but identifiable role in co-management success.