Nonhydrostatic effects and the determination of icy satellites’ moment of inertia

We compare the moment of inertia (MOI) of a simple hydrostatic, two layer body as determined by the Radau–Darwin Approximation (RDA) to its exact hydrostatic MOI calculated to first order in the parameter q = Ω²R³/GM, where Ω, R, and M are the spin angular velocity, radius, and mass of the body, and G is the gravitational constant. We show that the RDA is in error by less than 1% for many configurations of core sizes and layer densities congruent with those of solid bodies in the Solar System. We then determine the error in the MOI of icy satellites calculated with the RDA due to nonhydrostatic effects by using a simple model in which the core and outer shell have slight degree 2 distortions away from their expected hydrostatic shapes. Since the hydrostatic shape has an associated stress of order ρΩ²R² (where ρ is density) it follows that the importance of nonhydrostatic effects scales with the dimensionless number σ/ρΩ²R², where σ is the nonhydrostatic stress. This highlights the likely importance of this error for slowly rotating bodies (e.g., Titan and Callisto) and small bodies (e.g., Saturn moons other than Titan). We apply this model to Titan, Callisto, and Enceladus and find that the RDA-derived MOI can be 10% greater than the actual MOI for nonhydrostatic stresses as small as ∼0.1 bars at the surface or ∼1 bar at the core–mantle boundary, but the actual nonhydrostatic stresses for a given shape change depends on the specifics of the interior model. When we apply this model to Ganymede we find that the stresses necessary to produce the same MOI errors as on Titan, Callisto, and Enceladus are an order of magnitude greater due to its faster rotation, so Ganymede may be the only instance where RDA is reliable. We argue that if satellites can reorient to the lowest energy state then RDA will always give an overestimate of the true MOI. Observations have shown that small nonhydrostatic gravity anomalies exist on Ganymede and Titan, at least at degree 3 and presumably higher. If these anomalies are indicative of the nonhydrostatic anomalies at degree 2 then these imply only a small correction to the MOI, even for Titan, but it is possible that the physical origin of nonhydrostatic degree 2 effects is different from the higher order terms. We conclude that nonhydrostatic effects could be present to an extent that allows Callisto and Titan to be fully differentiated.     

Evaluation of stress strain non-uniformities in the laboratory direct simple shear test specimens using 3D discrete element analysis

The direct simple shear (DSS) device is one of the commonly used laboratory element testing tools to characterize the shear behaviour of soil. The interpretation of results from an element test requires understanding of the degree of stress and strain non-uniformities in a given test specimen. So far, studies on stress and strain non-uniformities in the DSS test have been conducted using direct boundary measurements of stresses in laboratory specimens supported by a continuum based analytical approach. Discrete element modelling now provides a means of modelling the soil behaviour in a realistic manner using a particulate approach. Accordingly, the performance of a DSS specimen was modelled using discrete element modelling with emphasis on assessing stress and strain non-uniformities in the specimen during shearing. The approach allowed for the numerical determination of stresses not only at the boundaries, but also within the DSS specimen. It was shown that mobilised stress ratio distribution throughout the shearing phase for the majority of specimen volume at locations near the central planes parallel and perpendicular to the direction of shearing is fairly uniform. Finally, it was noted that the potential for particle slippage at locations near the specimen centre can result in non-uniform shear strain distributions.     

Further examples of ventifacts and unusual patterned ground from the Falkland Islands, South Atlantic

Abstract Examples of ventifacts and forms of unusual patterned ground that differ in situation, characteristics and/or origin to types reported previously are described from the Falkland Islands, South Atlantic. The ventifacts, represented by clasts projecting from an eroding tillite shore platform, have been grooved by the passage of windblown sand. The patterned ground forms comprise stone polygons on clay loam regolith, stone polygons on peat, peat‐filled desiccation cracks on peat, and clusters of on‐edge clasts (stone packings) on a gravel beach. Aeolian transport of particles is considered responsible for the infill of the polygonal cracks. The clusters of on‐edge clasts are thought to have developed as a result of wave action, in particular backwash and/or undertow. Although these features occupy small surface areas they provide useful information about local geomorphic processes and testify to the marked diversity of such features in nature.     

Parametric cubic splines and geologic shape descriptions

Parametric cubic splines provide a versatile means of describing and sampling shapes and curves commonly found in geology. These splines allow the researcher to treat easily curves which are not single-valued in Cartesian or polar coordinates. In addition, they simultaneously provide approximations to positions, slopes, and curvatures of the curve being considered. In conjunction with simple digitizing equipment and a small computer, the method of parametric cubic spline approximation allows the researcher to analyze curves or outlines in cases where the more rapid technique involving video imaging equipment is either not applicable or not available.     

Nitrogen isotopes in the solar system

Measurements of the isotopic composition of nitrogen in the solar system are summarized. We show that the 30% change, during the last 3 to 4 billion years, of ${}^{15}\text{N}{}^{14}\text{N}$ in solar-wind-bearing lunar soils and breccias probably does not reflect changes in this ratio at the solar surface. Such changes, whether by spallation or thermonuclear reactions are ruled out by comparing the yields of ¹⁵N with those of other rare isotopes such as ⁹Be, ¹¹B, ³He or ¹³C, even if an arbitrary degree of solar mixing is introduced. Moreover, we calculate that the solar activity required for producing significant amounts of ¹⁵N by spallation at the solar surface should have resulted in a particle bombardment of the Moon of an intensity that would have produced amounts of spallation isotopes (e.g.¹⁵N, ²¹Ne, ³⁸Ar, ¹³¹Xe) several orders of magnitude in excess of what is actually found in the whole regolith.We argue that accretion of interstellar matter also does not work as a cause for a significant change of the photospheric ${}^{15}\text{N}{}^{14}\text{N}$ ratio. Evidence is presented that the mixing depth at the solar surface on a time scale of ?10⁹ years is (10^?2 ?10^?1) M_⊙ Mixing to this depth renders accretion of interstellar matter as a source of compositional changes at the solar surface inefficient, even if allowance is made for the expected large difference in the accretion rates of condensed and gaseous matter. A quantitative treatment of several alternatives of solar accretion leads to serious contradictions (e.g. with the low Ne abundances in planetary atmospheres or with the amounts of nitrogen that should have been directly accreted by the Moon), and we conclude that accretion during the main sequence life of the Sun is an unlikely source of changes in ${}^{15}\text{N}{}^{14}\text{N}$ at the solar surface.A ratio of ${}^{15}\text{N}{}^{14}\text{N}\text{= (4.0 ± 0.3) × 10}{}^{\mathrm{?3}}$ is our best estimate for average solar system material and for the Sun. We propose that a rare, very light nitrogen component (called LPN) is admixed in varying amounts to planetary matter. Undiluted LPN has not been found in meteorites or planetary atmospheres, but we show that the combined effects of LPN admixture and isotope fractionation can in principle account for the variability of ${}^{15}\text{N}{}^{14}\text{N}$ observed in the planetary system. Determination of the Jovian ${}^{15}\text{N}{}^{14}\text{N}$ ratio with an accuracy of ~10% would crucially test our interpretation of the nitrogen isotope observations.     

Service contracts—An instrument of international logistics supply chain: Under United States and European Union regulatory frameworks

Service contracts have emerged as an important instrument to secure a long-term relationship between carriers in the container shipping industry and shippers requiring scheduled services covering a global market. This contract, entered into largely on an individual and confidential basis, continues to enjoy anti-trust immunity under current United States and European Union regulations. It will continue to be in place even after the EC Council Regulation 4056/86 is repealed in October 2008 although it may operate in a modified way because of the absence of the common external conference tariff. This article examines the implications of this instrument on the international supply chain and explores its future role in defining efficiencies in international trade flows.     

Climate spectra and detecting climate change

Part of the debate over possible climate changes centers on the possibility that the changes observed over the previous century are natural in origin. This raises the question of how large a change could be expected as a result of natural variability. If the climate measurement of interest is modelled as a stationary (or related) Gaussian time series, this question can be answered in terms of (a) the way in which change is estimated, and (b) the spectrum of the time series. These computations are illustrated for 128 years of global temperature data using some simple measures of change and for a variety of possible temperature spectra. The results highlight the time scales on which it is important to know the magnitude of natural variability. The uncertainties in estimates of trend are most sensitive to fluctuations in the temperature series with periods from approximately 50 to 500 years. For some of the temperature spectra, it was found that the standard error of the least squares trend estimate was 3 times the standard error derived under the naïve assumption that the temperature series was uncorrelated. The observed trend differs from zero by more than 3 times the largest of the calculated standard errors, however, and is therefore highly significant.     

Eine Verbesserung von Alsops Methode zur Bestimmung der Reflexions- und Transmissionskoeffizienten von Oberflächenwellen

Zusammenfassung Die Methode von Alsop (1966) für den Durchgang von schräg einfallenden Oberflächenwellen durch eine vertikale Diskontinuität wird durch Verwendung eines neuen Funktionals, das auf der Diskontinuitätsfläche stationär sein soll, verbessert Das modifizierte Funktional hat die Dimension eines Energieflusses und wird durch diejenige Spannungs- und Verschiebungsdiskontinuität charakterisiert, die durch das Oberflächenwellenfeld auf der Diskontinuitätsfläche erzeugt wird. Modellrechnungen für SV-Wellen und Lovewellen zeigen, daß die neue Version von Alsoos Verfahren in jeder Hinsicht konsistentere Ergebnisse als die bisherige liefert.

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An improvement of Alsop's method for the determination of reflection and transmission coefficients of surface waves

Summary Alsop's method (1966) for the non-normal passage of surface waves through a vertical discontinuity is improved by using a new functional to be made stationary on the plane of discontinuity. The modified functional has the dimension of an energy flux and is characterized by the discontinuous surface wave displacements and stresses on the vertical discontinuity. Model calculations which were carried out for SV-waves and Love waves show that the new version of Alsop's method yields in all respects more consistent results than the old one.

     

A determination of the composition of the Saturnian stratosphere using the IUE

We reduced ultraviolet spectra of Saturn from the IUE satellite to produce a geometric albedo of the planet from 1500 to 3000 Å. By matching computer models to the albedo we determined a chemical composition consistent with the data. This model includes C₂H₂ and C₂H₆ with mixing ratios and distributions of (9 ± 3) × 10^?8 in the top 20 mbar of the atmosphere with none below for C₂H₂ and (6 ± 1) × 10^?6 also in the top 20 mbar with none below for C₂H₆. The C₂H₂ and C₂H₆ distributions and the C₂H₆ mixing ratio are taken directly from the Voyager IRIS model [R. Courtin et al., Bull. Amer. Astron. Soc.13, 722 (1981), and private communication]. The Voyager IRIS model also includes PH₃, which is not consistent with the uv albedo from 1800 to 2400 Å. Our model requires a previously unidentified absorber to explain the albedo near 1600 Å. After considering several candidates, we find that the best fit to the data is obtained with H₂O, having a column density of (6 ± 1) × 10^?3 cm-am.