First order planetary perturbations with elliptic functions

The differential equations of planetary theory are solved analytically to first order for the two-dimensional case, using only Jacobian elliptic functions and the elliptic integrals of the first and second kind. This choice of functions leads to several new features potentially of importance for planetary theory. The first of these is that the solutions do not require the expansion of the reciprocal of the distance between two planets, even for those variables which depend on two angular arguments. A second result is that the solution is free from small divisors with the exception of two special resonances. In fact, not only are the solutions for resonant orbits free from small divisors, the perturbations for all variables are expressible in closed form. A subset of the resonant orbits maintains this form and in addition has the remarkable feature that the first order perturbations are purely periodic; they contain no secular terms. A solution for the 13 resonance case is given as an example.     

Mid-Pleistocene lavas from the Seguam volcanic center,central Aleutian arc: closed-system fractional crystallization of a basalt to rhyodacite eruptive suite

In contrast to adjacent volcanic centers of the modern central Aleutian arc, Seguam Island developed on strongly extended arc crust. K-Ar dates indicate that mid-Pleistocene, late-Pleistocene, and Holocene eruptive phases constitute Seguam. This study focuses on the petrology of the mid-Pleistocene, 1.07–07 Ma, Turf Point Formation (TPF) which is dominated by an unusual suite of porphyritic basalt and basaltic andesite lavas with subordinate phenocryst-poor andesite to rhyodacite lavas. Increasing whole-rock FeO^*/MgO from basalt to dacite, the anhydrous Plag+Ol+Cpx±Opx±Mt phenocryst assemblage, groundmass pigeonite, and the reaction Ol+Liq=Opx preserved in the mafic lavas indicate a tholeiitic affinity. Thermometry and comparison to published phase equilibria suggests that most TPF basalts crystallized Plag+Ol+Cpx±Mt at 1160°C between about 3–5 kb (±1–2% H₂O), andesites crystallized Plag+Cpx+Opx±Mt at 1000°C between 3–4 kb with 3–5% H₂O, and dacites crystallized Plag +Cpx±Opx±Mt at 1000°C between 1–2 kb with 2–3% H₂O. All lavas crystallized at f _{o 2} close to the NNO buffer. Mineral compositions and textures indicate equilibrium crystallization of the evolved lavas; petrographic evidence of open-system mixing or assimilation is rare. MgO, CaO, Al₂O₃, Cr, Ni, and Sr abundances decrease and K₂O, Na₂O, Rb, Ba, Zr, and Pb increase with increasing SiO₂ (50–71%). LREE enrichment [(Ce/Yb)_n=1.7±0.2] characterizes most TPF lavas; total REE contents increase and Eu anomalies become more negative with increasing SiO₂. Relative to other Aleutian volcanic centers, TPF basalts and basaltic andesites have lower K₂O, Na₂O, TiO₂, Rb, Ba, Sr, Zr, Y, and LREE abundances. ⁸⁷Sr/⁸⁶Sr ratios (0.70361–0.70375) and ratios of ²⁰⁶Pb/²⁰⁴Pb (18.88–18.97), ²⁰⁷Pb/²⁰⁴Pb (15.58–15.62), ²⁰⁸Pb/²⁰⁴Pb (38.46–38.55) are the highest measured for any suite of lavas in the oceanic portion of the Aleutian arc. Conversely, Nd values (+5.8 to+6.7) are among the lowest from the Aleutians. Sr, Nd, and Pb ratios are virtually constant from basalt through rhyodacite, whereas detectable isotopic heterogenity is observed at most other Aleutian volcanic centers. Major and trace element, REE, and Sr, Nd, and Pb isotopic compositions are consistent with the basaltic andesitic, andesitic, dacitic, and rhyodacitic liquids evolving from TPF basaltic magma via closed-system fractional crystallization alone. Fractionation models suggest that removal of 80 wt% cumulate (61% Plag, 17% Cpx, 12% Opx, 7% Ol, and 3% Mt) can produce 20 wt% rhyodacitic residual liquid per unit mass of parental basaltic liquid. Petrologic and physical constraints favor segregation of small batches of basalt from a larger mid-crustal reservoir trapped below a low-density upper crustal lid. In these small magma batches, the degree of cooling, crystallization, and fractionation are functions of the initial mass of basaltic magma segregated, the thermal state of the upper crust, and the magnitude of extension. Tholeiitic magmas erupted at Seguam evolved by substantially different mechanisms than did calc-alkaline lavas erupted at the adjacent volcanic centers of Kanaga and Adak on unextended arc crust. These variable differentiation mechanisms and liquid lines of descent reflect contrasting thermal and mechanical conditions imposed by the different tectonic environments in which these centers grew. At Seguam, intra-arc extension promoted eruption of voluminous basalt and its differentiates, unmodified by interaction with lower crustal or upper mantle wallrocks.     

Development and assessment of an analytical system for the accurate and continual measurement of total dissolved inorganic carbon

An automated coulometric titration system based on that described by Johnson, Sieburth, Williams and Brandstrom (1987, Mar. Chem., 21: 117–133) has been evolved for the accurate and continual measurement of total dissolved inorganic carbon (TCO₂). The instrument achieves an analytical precision (1 SD) of ±0.5–1.0 μmol kg⁻¹ (0.025–0.05%). The accuracy of the system has been examined by a limited comparison with other coulometric-based titrators and with a manometric-based system; agreement was to 1 μmol kg⁻¹. The capability for automatic continual analysis allows surface mapping of TCO₂; a sample rate of 10 analyses h⁻¹ gives a mapping resolution of 1–2 km. Provision for frequent standardization with a liquid substandard has been included in the development. The ability to achieve high-density analyses while maintaining interlaboratory consistency and standardization constitutes a vital contribution to surveys of ocean carbon chemistry (e.g. Joint Global Ocean Flux Study, World Ocean Circulation Experiment).     

Adaptation of the polychaete Neanthes Arenaceodentata to copper

Neanthes arenaceodentata were exposed to 292, 146, 92 and 56 μg litre⁻¹ Cu (measured) and control seawater after a 27-day pre-exposure to a sublethal concentration of Cu (10, 16 and 28 μg litre⁻¹ and control) to determine if the worms increased their tolerance to Cu after the pre-treatment. The worms pre-exposed to 28 μg litre⁻¹ Cu were significantly more resistant to Cu toxicity than control and 10 and 16 μg litre⁻¹ Cu pre-exposed worms. For example, the time to 50 % mortality at 92 μg litre⁻¹ Cu was 18 and 11 days for worms pre-exposed to 28 μg litre⁻¹ Cu and control conditions, respectively. The net rate of Cu uptake during the toxicity test was lower for worms pre-exposed to 28 μg litre⁻¹ Cu than for the control and 10 and 16 μg litre⁻¹ Cu pre-exposed worms. For example, the net rate of Cu uptake at 292 μg litre⁻¹ Cu by worms pre-exposed to 28 μg litre⁻¹ Cu and control conditions was 42 and 102 μg g⁻¹ day ⁻¹, respectively.     

The 12th Workshop on Antarctic Meteorology and Climate

正1.Overview The 12th Workshop on Antarctic Meteorology and Climate(WAMC),formerly known as the Antarctic Meteorological Observation,Modeling,and Forecasting(AMOMF)Workshop(AMOMFW),was held at the National Center for Atmospheric Research(NCAR)in Boulder,Colorado,USA on 26–28 June 2017.The annual workshop dates from 2006,and recent meetings have been the 10th AMOMF Workshop held in 2015 in Cambridge,United Kingdom(Colwell et al.,2016)and the     

Climate change and national security: an agenda for geography

On 4 December 2017 the Australian Foreign Affairs, Defence and Trade References Committee is due to report on its inquiry into the implications of climate change for Australia's national security. Public submissions to the inquiry closed on 4 August 2017 and, at the time of writing, some 59 submissions had been made by researchers, public-interest organisations and members of the public, including a number of geographers. A topic of profound significance, climate change and national security warrants deep and sustained public engagement such as that offered by the Senate Inquiry submission process. In this Thinking Space essay, I urge geographers, working in Australia and internationally, to make ongoing contributions to such engagements. The emerging debate about climate change and national security will likely amplify following the release of the Committee's report. Geographic data and analysis pertaining to various aspects of climate change and security are needed in order to shape policy directions and support evidence-based policy making. My contention here is that contributions ought to extend not just from those working at the coalface of climate change risk, for example in political geography, but from all quarters of the discipline.     

Displacement and strain patterns from naturally occurring shear zone terminations

Strain distribution patterns are described from several naturally occurring ductile shear zone terminations and a two-fold classification is suggested. Type I termination patterns show a symmetrical decrease in strain area and intensity, and are associated with very low shear strain (ψ) values in the main shear zone. The more common Type II termination patterns show a symmetrical increase in strain area with decrease in strain intensity. Some brittle-ductile examples of Type II terminations contain secondary shears that resemble splay faults. All the available evidence suggests that the deformation near the terminations of these shear zones is not plane strain, nor do the observed strain patterns readily fit the existing theoretical models.     

Mass balance calculations with end member compositional variability: applications to petrologic problems

Although end member compositional variability is quite common, most quantitative mass balance procedures cannot accommodate this variability in a systematic manner. By rearranging the traditional mass balance relations, a series of equations can be derived to account for such heterogeneity. While this approach can be applied ton-component systems, the results are difficult to represent graphically. Accordingly, the procedure is most useful for two- and three-component systems. For two components, the concentration of an element in a mixture is: and the isotopic signature is: where pm, hm and 1 refer to parental magma, hybrid magma and component 1, respectively, X is the proportion of parental magma, C is concentration, is isotopic ratio, and the concentration of the denominator isotope in the particular isotopic ratio of interest. These equations describe straight lines, termed isoproportional or IP lines, of fixed mixing proportion in the C_pm−C₁ concentration or planes. Only those IP lines intersecting the rectangle defined by observed end member compositions represent viable mixing proportions. For three-component systems, the mass balance equations are: and: where Y is now the proportion of component 1 and the proportion of component 2, Z, is simply 1 − X − Y. Using major, trace and rare earth element as well as isotopic data, a region of the X-Y plane representing possible mixing combinations can be defined. Due to the compositional variability of most magmatic end members, this new mass balance procedure should be applicable to a diverse range of petrologic problems. This procedure has been applied to three different petrologic processes: Aleutian parental magma genesis, assimilation/contamination, and crust-mantle differentiation.