Stability of outer planetary orbits around binary stars: A comparison of Hill's and Laplace's stability criteria

A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and co-workers and the general, numerically integrated results of Laplace's method by Graziani and Black are compared for varying values of the mass parameter =m ₂/(m ₁+m ₂). For 00.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For >0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of .     

Spatial Modeling of Geometallurgical Properties: Techniques and a Case Study

High-resolution spatial numerical models of metallurgical properties constrained by geological controls and more extensively by measured grade and geomechanical properties constitute an important part of geometallurgy. Geostatistical and other numerical techniques are adapted and developed to construct these high-resolution models accounting for all available data. Important issues that must be addressed include unequal sampling of the metallurgical properties versus grade assays, measurements at different scale, and complex nonlinear averaging of many metallurgical parameters. This paper establishes techniques to address each of these issues with the required implementation details and also demonstrates geometallurgical mineral deposit characterization for a copper–molybdenum deposit in South America. High-resolution models of grades and comminution indices are constructed, checked, and are rigorously validated. The workflow demonstrated in this case study is applicable to many other deposit types.     

Stress fields of the San Andreas and Queen Charlotte transform faults

Analytic solutions to the stress fields resulting from the San Andreas and Queen Charlotte transform faults may be found by applying conformal mappings to the generalized plane stress solution of stresses in a half-plane. The mean stress fields (one-half the trace of the stress tensor) found in this manner show a similarity to the deformation found in western Canada and the western United States. The results refute the hypothesis that Alaska acts as a continental buttress against deformation of the Canadian Cordillera. Moreover, these results imply that the differences in the tectonics of major transform boundaries are caused primarily by differences in lithospheric structure and differences in stress distribution along the plate boundaries.     

Area and volume computation of longitude–latitude grids and three‐dimensional meshes

Longitude–latitude grids are commonly used for surface analyses and data storage in GIS. For volumetric analyses, three‐dimensional meshes perpendicularly raised above or below the gridded surface are applied. Since grids and meshes are defined with geographic coordinates, they are not equal area or volume due to convergence of the meridians and radii. This article compiles and presents known geodetic considerations and relevant formulae needed for longitude–latitude grid and mesh analyses in GIS. The effect of neglecting these considerations is demonstrated on area and volume calculations of ecological marine units.     

The Proterozoic evolution of northern Siberian Craton margin: a comparison of U–Pb–Hf signatures from sedimentary units of the Taimyr orogenic belt and the Siberian platform

Identifying the cratonic affinity of Neoproterozoic crust that surrounds the northern margin of the Siberian Craton (SC) is critical for determining its tectonic evolution and placing the Craton in Neoproterozoic supercontinental reconstructions. Integration of new U–Pb–Hf detrital zircon data with regional geological constraints indicates that distinct Neoproterozoic arc-related magmatic belts can be identified within the Taimyr orogen. Sedimentary rocks derived from 970 to 800 Ma arc-related suites reveal abundant Archean and Paleoproterozoic detritus, characteristic of the SC. The 720–600 Ma arc-related zircon population from the younger Cambrian sedimentary rocks is also complemented by an exotic juvenile Mesoproterozoic zircon population and erosional products of older arc-related suites. Nonetheless, numerous evidences imply that both arcs broadly reworked Siberian basement components. We suggest that the early Neoproterozoic (ca. 970–800 Ma) arc system of the Taimyr orogen evolved on the active margin of the SC and probably extended along the periphery of Rodinia into Valhalla orogen of NE Laurentia. We also suggest the late Neoproterozoic (750–550 Ma) arc system could have been part of the Timanian orogen, which linked Siberia and Baltica at the Precambrian/Phanerozoic transition.     

Variation in DOC and trace metal concentration along the heavily urbanized basin in Kathmandu Valley,Nepal

Water samples were analyzed for DOC and trace metals from Bagmati River within Kathmandu valley, Nepal, to understand the variation trends of DOC and trace metals and their relationship along the drainage network. The variability in organic matter and wastewater input within the Bagmati drainage basin appeared to control DOC and most of the trace metal concentration. The large input of organic matter and wastewater creates anoxic condition by consuming dissolved oxygen and releasing higher concentrations of DOC, trace elements such as nickel, arsenic, barium, cadmium, and copper with downstream distance. Concentrations of DOC and trace metals like barium and zinc showed strong relationships with human population density and suggest that human activities have strong control on these parameters along the drainage network. The DOC and most of the trace metal concentration increased with downstream distance and appeared to be directly associated with human activities. The variation trends of most of the trace metals appeared to be the same; however, concentration varied widely. Inputs of organic matter and wastewater due to human activities appeared directly to be associated for the variation of DOC and trace metals along the Bagmati drainage network within Kathmandu valley.     

Scales of nutrient-limited phytoplankton productivity in Chesapeake Bay

The scales on which phytoplankton biomass vary in response to variable nutrient inputs depend on the nutrient status of the plankton community and on the capacity of consumers to respond to increases in phytoplankton productivity. Overenrichment and associated declines in water quality occur when phytoplankton growth rate becomes nutrient-saturated, the production and consumption of phytoplankton biomass become uncoupled in time and space, and phytoplankton biomass becomes high and varies on scales longer than phytoplankton generation times. In Chesapeake Bay, phytoplankton growth rates appear to be limited by dissolved inorganic phosphorus (DIP) during spring when biomass reaches its annual maximum and by dissolved inorganic nitrogen (DIN) during summer when phytoplankton growth rates are highest. However, despite high inputs of DIN and dissolved silicate (DSi) relative to DIP (molar ratios of N∶P and Si∶P>100), seasonal accumulations of phytoplankton biomass within the salt-intruded-reach of the bay appear to be limited by riverine DIN supply while the magnitude of the spring diatom bloom is governed by DSi supply. Seasonal imbalances between biomass production and consumption lead to massive accumulations of phytoplankton biomass (often>1,000 mg Chl-a m^?2) during spring, to spring-summer oxygen depletion (summer bottom water <20% saturation), and to exceptionally high levels of annual phytoplankton production (>400 g m^?2 yr^?1). Nitrogen-dependent seasonal accumulations of phytoplankton biomass and annual production occur as a consequence of differences in the rates and pathways of nitrogen and phosphorus cycling within the bay and underscore the importance of controlling nitrogen inputs to the mesohaline and lower reaches of the bay.