Large angular motions of tethered surface buoys

A three-dimensional coupled analysis of the interaction of a floating buoy and its mooring is studied. External loads include hydrodynamic forces, tether tensions, wind loads and system weight and buoyancy. Nonlinearities include large rotational and translational motions and non-conservative fluid loads. The mooring problem is formulated as a nonlinear two-point-boundary-value-problem. At each instant in time, the mooring problem is solved by direct integration using a successive iterative algorithm to satisfy boundary conditions. Buoy kinetic and kinematic equations are derived assuming large angles represented by Euler parameters. Coupling between the buoy and the mooring is enforced by matching the velocities of the tether and buoy at the attachment point. A predictor-corrector coupling algorithm is used with multiple sizes of time steps used to provide stability for the separate mooring and buoy models. Numerical results are compared to experimental responses of three types of buoys (sphere, spar and disc) subject to both regular and irregular waves.     

The role of recharge and evapotranspiration as hydraulic drivers of ion concentrations in shallow groundwater on Everglades tree islands,Florida (USA)

Recently, evapotranspiration has been hypothesized to promote the secondary formation of calcium carbonate year‐round on tree islands in the Everglades by influencing groundwater ions concentrations. However, the role of recharge and evapotranspiration as drivers of shallow groundwater ion accumulation has not been investigated. The goal of this study is to develop a hydrologic model that predicts the chloride concentrations of shallow tree island groundwater and to determine the influence of overlying biomass and underlying geologic material on these concentrations. Groundwater and surface water levels and chloride concentrations were monitored on eight constructed tree islands at the Loxahatchee Impoundment Landscape Assessment (LILA) from 2007 to 2010. The tree islands at LILA were constructed predominately of peat, or of peat and limestone, and were planted with saplings of native tree species in 2006 and 2007. The model predicted low shallow groundwater chloride concentrations when inputs of regional groundwater and evapotranspiration‐to‐recharge rates were elevated, while low evapotranspiration‐to‐recharge rates resulted in a substantial increase of the chloride concentrations of the shallow groundwater. Modeling results indicated that evapotranspiration typically exceeded recharge on the older tree islands and those with a limestone lithology, which resulted in greater inputs of regional groundwater. A sensitivity analysis indicated the shallow groundwater chloride concentrations were most sensitive to alterations in specific yield during the wet season and hydraulic conductivity in the dry season. In conclusion, the inputs of rainfall, underlying hydrologic properties of tree islands sediments and forest structure may explain the variation in ion concentration seen across Everglades tree islands. Copyright © 2012 John Wiley & Sons, Ltd.     

Saturn's rings: Particle size distributions for thin layer models

The small physical thickness of Saturn's rings requires that radio occultation observations be interpreted using scattering models with limited amounts of multiple scatter. A new model in which the possible order of near-forward scatter is strictly limited allows for the small physical thickness, and can be used to relate Voyager 1 observations of 3.6-and 13-cm wavelength microwave scatter from Saturn's rings to the ring particle size distribution function n(a), for particles with radius 0.001 ≤ a ≤ 20 m. This limited-scatter model yields solutions for particle size distribution functions for eight regions in Saturn's rings, which exhibit approximately inverse-cubic power-law behavior, with large-size cutoffs in particle radius ranging from about 5 m in ring C to about 10 m in parts of ring A. The power-law index is about 3.1 in ring C, about 2.8 in the Cassini division, and increases systematically with radial location in ring A from 2.7 at 2.10R_s to slightly more than 3.0 at 2.24R_s. Corresponding mass densities are 32–43 kg/m² in ring C, 188 kg/m² in the Cassini division, and 244–344 kg/m² in ring A, under the assumption that the material density of the particles is 0.9 g/cm³. These values are a factor of 1 to 2 lower than first-order mass loading estimates derived from resonance phenomena. In view of the uncertainties in the measurements and in the linear density wave model, and the strong arguments for icy particles with specific gravity not greater than about 1, we interpret this discrepancy as being indicative of possible differences in the regions studied, or systematic errors in the interpretation of the scattering results, the density wave phenomena, or some combination of the above.     

Wind signatures in the X-ray emission-line profiles of the late-O supergiant ζ Orionis

X-ray line-profile analysis has proved to be the most direct diagnostic of the kinematics and spatial distribution of the very hot plasma around O stars. The Doppler-broadened line profiles provide information about the velocity distribution of the hot plasma, while the wavelength-dependent attenuation across a line profile provides information about the absorption to the hot plasma, thus providing a strong constraint on its physical location. In this paper, we apply several analysis techniques to the emission lines in the Chandra High Energy Transmission Grating Spectrometer (HETGS) spectrum of the late-O supergiant ζ Ori (O9.7 Ib), including the fitting of a simple line-profile model. We show that there is distinct evidence for blueshifts and profile asymmetry, as well as broadening in the X-ray emission lines of ζ Ori. These are the observational hallmarks of a wind-shock X-ray source, and the results for ζ Ori are very similar to those for the earlier O star, ζ Pup, which we have previously shown to be well fit by the same wind-shock line-profile model. The more subtle effects on the line-profile morphologies in ζ Ori, as compared to ζ Pup, are consistent with the somewhat lower density wind in this later O supergiant. In both stars, the wind optical depths required to explain the mildly asymmetric X-ray line profiles imply reductions in the effective opacity of nearly an order of magnitude, which may be explained by some combination of mass-loss rate reduction and large-scale clumping, with its associated porosity-based effects on radiation transfer. In the context of the recent reanalysis of the helium-like line intensity ratios in both ζ Ori and ζ Pup, and also in light of recent work questioning the published mass-loss rates in OB stars, these new results indicate that the X-ray emission from ζ Ori can be understood within the framework of the standard wind-shock scenario for hot stars.     

A three-invariant smooth cap model with mixed hardening

A cap model is presented that uses a multiplicative formulation to define a smooth (continuous derivative) failure surface that includes the third stress invariant. This formulation offers several advantages over previous cap model formulations: elimination of ‘corner’ coding, resulting in a numerical algorithm suitable for vectorization; a three stress invariant implementation that is easily specialized to classical failure surfaces or generalized to represent observed material response; and a framework for easily implementing additional model features such as kinematic hardening as demonstrated.     

Surface composition of magnetic neutron stars

The relative abundances of seven constitutent nuclei, He⁴, C¹², O¹⁶, Ne²⁰, Mg²⁴, Si²⁸ and Fe⁵⁶, are calculated as a function of time for neutron star atmospheres within which exist magnetic fields of the order of 10¹³G. The opacity, equation of state of the electrons, and cooling rate of the magnetic star are discussed, and it is shown to be a reasonable approximation to assume an atmosphere to be isothermal. The effects of particle diffusion are included in the nuclear reaction network. Computations are performed both for a constant mass atmosphere and for an atmosphere in which mass is being ejected. It is found that the final abundances are model independent as long as the initial model contains predominantly He⁴. The relative abundances are compared to the cosmic ray spectrum. For both the constant mass and mass loss atmospheres, nucleosynthesis proceeds virtually completely to Fe⁵⁶. However the outermost layers of the envelope, in which no mass is being ejected, are composed almost entirely of He⁴ with trace amounts of Fe⁵⁶. After the loss of about 10²¹ g, only Fe⁵⁶ is ejected from atmospheres expelling mass.A portion of the research on which this paper was based was performed while L. C. Rosen was present at the Lawrence Radiation Laboratory, Livermore, California.     

W-shaped occultation signatures: Inference of entwined particle orbits in charged planetary ringlets

Observed W-shaped occultation signatures of certain narrow ringlets in the ring systems of Saturn and Uranus imply a concentration of material near their inner and outer radial edges. A model is proposed where edge bunching is a natural consequence of particles in entwined elliptical orbits, with the same particles alternately defining both edges. While such orbits cross over in radius, collisions would not occur if they have small inclinations, the same fixed argument of periapse ω, and other parameters whereby the particles would “fly in formation” along compressed helical paths relative to the core of the ringlet, which is taken to be a circle in the equatorial plane. For this model to match the observed ring thickness and ringlet widths, orbit inclinations i must be much smaller than their eccentricities e, which themselves would be very small compared to unity. Thus, the meridional cross section of the resultant torus would be a very thin ellipse of thickness proportional to i∣cos ω∣, tilted slightly from the equatorial plane by (i/e)∣sin ω∣ radians. However, gravitational perturbations due to the oblateness of the planet would cause a secular change in ω so that this cross section would collapse periodically to a tilted line, and collisions would then occur. If this collapse could be prevented, the torus could remain in a continuous state of nearly zero viscosity. Stabilization against collapse appears possible due to several remarkable characteristics that are added to the model when the particles are electrically charged. First, because of inherent features of the torus structure, a weak electric force could counter the key effect of the vastly larger oblateness force. Second, because the electric perturbation also affects i, there is a large region in ω,i space where stability against cross-sectional collapse is automatic. For this region, the thickness of the elliptical cross section would expand and contract in concert with the way that the major axis of the ellipse rocks back and forth relative to the equatorial plane. The period of these “rocking and breathing” changes would be from 1 to 3 weeks for a torus in the C ring of Saturn, for example. The electric effects could change considerably without driving the parameters of the torus from the stable domain where cross-sectional collapse does not occur. While specialized and in several important ways still incomplete, the proposed model could account for the W-shaped patterns and explain how very dense ringlets might endure without energy loss due to collisions. It also appears to be capable of explaining the observed sorting of particles by size within a ringlet. Several characteristics of the model suggest definitive tests of its applicability, including its prediction that a nonsymmetrical W-shaped occultation signature could be reversed a half orbit away, and that grazing solar illumination of tilted ringlets might cast shadows that change with time in a prescribed way.     

Petrology and provenance of a very‐low‐titanium picrite clast in lunar highland regolith breccia 15295

Clast 100 in regolith breccia 15295 could be a key to resolving the relationship(s) between mare basalts and lunar picritic glasses. The clast is basaltic, with texture, mineralogy, mineral compositions, and calculated bulk composition suggesting that it crystallized in a thick lava flow or shallow intrusive body from a very‐low‐titanium (VLT) basaltic magma. The estimated bulk composition of clast 15295,100 is primitive (i.e., magnesian) compared to those of known VLT basalts, and is very close to those of VLT picritic green glasses, especially the Apollo 14 A green glass. From these similarities, we infer that clast 15295,100 is a crystalline product of a picritic magma similar to the Apollo 14 A glass. Clementine and M³ remotely sensed data of the lunar surface were used to find areas that have chemical compositions consistent with those of clast 15295,100, not only near the Apollo 15 site, but in a broad region surrounding the site. Two regions are consistent with clast's 15295,100 compositional data. The larger region is in southern Mare Imbrium, and a smaller region is in the eastern half of Sinus Aestuum. These locations should be considered as candidates for future missions focusing on sample science.     

Mining soil databases for landscape‐scale patterns in the abundance and size distribution of hillslope rock fragments

Landscape‐scale variation in rock fragments on soil‐mantled hillslopes is poorly understood, despite the potential importance of rock fragments in soil weathering and coarse sediment supply to river networks. We explored the utility of soil survey databases for data mining, with the goals of identifying landscape‐scale patterns in the abundance and size distribution of rock fragments (diameter D > 2 mm) and potential controls on grain size production. We focus on data from three regions: the Hawaiian Islands, and the Sierra Nevada and Cascade Mountains, where elevation transects span a range of environmental conditions. We selected pedons from pits dug on hillslopes with active soil production and transport. For the 27 pedons selected, we constructed depth‐averaged grain size distributions and calculated the mass fraction of rock fragments (F_RF) and the median rock fragment grain size (D_50RF). We also categorized as bimodal, size distributions with a clear ‘breakpoint’ between fine and coarse modes. Several strong patterns emerge from the data. We find rock fragments in 85% of the pedons, primarily in distinct coarse modes within bimodal size distributions. Values of F_RF and D_50RF are strongly correlated, although the best‐fit power law scaling between F_RF and D_50RF differs between the warmer Hawaiian, and colder Sierra Nevada and Cascade Mountain sites. We also find a regional contrast in the variation in F_RF with elevation; F_RF declines with elevation in Hawaii, but increases in the mainland sites. Although this contrast could be an artifact of variable lithology, precipitation may influence many patterns in the data. Lower mean‐annual precipitation correlates with higher F_RF, dominantly bimodal distributions and surface enrichment in the vertical distribution of rock fragments. These observations may be useful in refining models of coarse sediment supply to rivers, and suggest opportunities for future work to test mechanistic hypotheses for rock fragment production on soil‐mantled hillslopes. Copyright © 2011 John Wiley & Sons, Ltd.