Satellite resonance with longitude-dependent gravity—III. Inclination changes for close satellites

The longitude-dependent part of the geopotential can give rise to significant changes in inclination for a close satellite when its mean motion is commensurable with the Earth's rotation. For a decaying satellite passing through resonance, the total change in inclination depends on the value of a resonant variable at exact commensurability, which is an essentially random quantity. Many different gravity coefficients may contribute significantly, with relative amplitudes which are highly dependent on inclination. The equations for general $\text{β}\text{α}$ resonance also reveal a basic distinction between (βt- α) even and odd.When the drag significantly exceeds the resonance forces, an approximate solution can be found in terms of Fresnel integrals. This shows that the inclination is almost equally likely to increase or decrease, and that the total change is proportional to (drag)${}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, i.e. to the time taken to pass through resonance.The effect offers a way of deriving gravity coefficients of medium order (e.g. m=15) from the observed magnitude and shape of the variation in inclination. The magnitudes of even higher order gravity coefficients obtained from some resonance with α=2 (e.g. $\text{29}\text{2}$) or even with α=3 (e.g. $\text{44}\text{3}$) might yield information on the depth of the sources of the high order gravity field.The effect is also of special interest in deriving upper-atmosphere mean winds from the changes in inclination of decaying satellite orbits since the satellite may pass through a strong resonance.     

The effect of finite ionosphere conductivities on axisymmetric toroidal Alfvén wave resonances

Previously developed solutions for pure toroidal mode Alfvén waves with finite ionosphere conductivities are modified to apply both inside and outside the plasmapause.Detailed diagrams are provided to illustrate the effect of realistic ionosphere conductances on the wave-forms. As well as graphs of wave-period, these include: (a) half-wave solutions showing the effect of dipole field distortion and consequent enhancement of ionosphere electric fields; (b) half-wave solutions with low damping that are symmetric and asymmetric about the equatorial plane; (c) highly-damped half-wave and quarter-wave solutions with wave admittance at the ionosphere nearly equal to the ionosphere conductance; (d) a quarter-wave solution with low damping that has a “near-node” of electric field at one ionosphere and an antinode of electric field at the other.     

Response of hematological and biochemical parameters to heavy metal exposure: Implications in environmental monitoring

The use of selected hematological and biochemical parameters as indicators of metal exposure in aquatic organisms was evaluated. The hematological and biochemical parameters examined include glucose, hematocrit and aminotransferase levels in golden shiners exposed to cadmium. Cadmium exposure produced significant alterations in the levels of glucose, aspartate aminotransferase and alanine aminotransferase; however, hematocrit was not altered by exposure to cadmium. In addition, the comparative activity of Na/K adenosine triphosphatase (ATPase) was evaluated in the fathead minnow, golden shiner and bluegill sunfish. Basal Na/K ATPase activity was lowest in golden shiner (1·01 μmol Pi/mg protein/h) and highest in bluegill sunfish (1·45 μmol Pi/mg protein/h). While a stimulation of Na/K ATPase activity was observed at an exposure concentration of 1 μg Cd/liter in the fathead minnow and bluegill sunfish, inhibition of enzymatic activity was observed at higher exposure concentrations (10 and 100 μg Cd/liter). Gill Na/K ATPase activity in golden shiner was not significantly influenced by cadmium exposure. The observed insensitivity of ATPase in shiner may, in part, be related to higher background and accumulated concentrations of cadmium in gill tissue.     

Deformation conditions, kinematics, and displacement history of shallow crustal ductile shearing in the Norumbega fault system in the Northern Appalachians, eastern Maine

The Norumbega fault system in the Northern Appalachians in eastern Maine experienced complex post-Acadian ductile and brittle deformation from middle through late Paleozoic times. Well-preserved epizonal ductile shear zones in Fredericton belt metasedimentary rocks and granitic batholiths that intrude them provide valuable information on the nature, geometry, and evolution of orogen-parallel strike-slip Norumbega faulting. Metasedimentary rocks were ductilely sheared into phyllonite schistose mylonite, whereas granite into mylonite within the ductile shear zones. Ductile shearing took place at conditions of the lower greenschist facies with peak temperatures on the order of 300–350° based on comparison of plastic quartz and brittle feldspar microstructures, confirming a shallow crustal environment during faulting.Ductile shear strain was partitioned into two major shear zones in easternmost Maine—the Waite and Kellyland zones—but these zones converge toward the southwest. Megascopic, mesoscopic, and microscopic kinematic indicators confirm that fault motion in both zones was dominantly dextral strike-slip. Detailed mapping, especially in the plutonic rocks, reveals a complex ductile deformation history in the area where the Waite and Kellyland zones converge. Shear strain is broadly distributed in the rocks between Kellyland and Waite zones, and increases toward their junction. Multiple dextral high-strain zones oblique to both zones resemble megascopic synthetic c′ shear bands. Together with the Kellyland and Waite master shear zones, these define a megascopic S–C′ structure system produced in a regional-scale dextral strike-slip shear duplex that developed in the transition zone between the deeper (south-central Maine) and shallower (eastern Maine) segments of the Norumbega fault system.Granite plutons caught within the strike-slip shear duplex were intensely sheared and progressively smeared into long and narrow slivers identified by this study. The western lobe of the Deblois pluton and the Lucerne pluton have been recognized as the sources, respectively of the Third Lake Ridge and Morrison Ridge granite slivers. Restoration of both granite slivers to their presumed original positions yields approximately 25 km of dextral strike-slip displacement along only the Kellyland and synthetic ductile shear zones.     

Confirmation of previous ground-based Cepheid P–L zero-points using Hipparcos trigonometric parallaxes

Comparisons show agreement at the 0.1-mag level between the calibration of the Cepheid period–luminosity (P–L) relation by Feast & Catchpole (FC) using the early release of Hipparcos data and four previous ground-based calibrations, three of which are either largely or totally independent of the distance to the Large Magellanic Cloud (LMC). Each of the comparisons has the sense that the FC calibration is brighter, but only at the level of ≲0.1 mag. In contrast, FC argue that their Hipparcos recalibration leads to a 0.2-mag revision in the distance to the LMC, and thereby to a 10 per cent decrease in the Hubble constant. We argue differently. The comparison of the Hipparcos recalibration with others should be made using only local Galactic Cepheids, not based on Cepheids in the LMC that require a set of precepts that are not germane to the direct Hipparcos recalibration. The comparison made here, using only Galactic Cepheids, gives a correction of ∼4 per cent or less to our value of H ₀ based on Type Ia supernovae, keeping all other factors and precepts the same.
  A second success of the Hipparcos mission is the calibration of the position of the main sequence in the Hertzsprung–Russell diagram as a function of metallicity using local subdwarfs. These data have been used by Reid and by Gratton et al. to obtain, similarly to FC, a brighter absolute magnitude of RR Lyrae stars by ∼0.3 mag from that often currently adopted. These new calibrations confirm the earlier brighter calibrations by Walker, by Sandage, and by Mazzitelli, D'Antona & Caloi, thereby reducing the ages of globular clusters by ∼30 per cent. This removes most of the cosmological time-scale problem if H ₀∼55 km s⁻¹ Mpc⁻¹. A similar conclusion, based on pulsation theory and MACHO data, has been reached by Alcock et al.     

Structural control of polyhedral compression in synthetic braunite, Mn2+Mn3+ 6O8SiO4

The compression of synthetic braunite, Mn²⁺Mn³⁺ ₆O₈SiO₄, was studied by high-pressure single-crystal X-ray diffraction carried out in a diamond-anvil cell. The equation of state at room temperature (third-order Birch-Murnaghan equation of state: V ₀=1661.15(8) ų, K _0,298=180.7±0.9 GPa, K′=6.5±0.3) was determined from unit-cell volume data to 9.18 GPa. Crystal structures were determined at 6 different pressures to 7.69 GPa. Compression of the structure (space group I4₁/acd) was found to be slightly anisotropic (a ₀=9.4262(4) Å, K _a =499±4 GPa, K _a ′=19.7±0.9; c ₀=18.6964(6) Å, K _c =657±6 GPa, K _c ′=15.7±1.4) which can be attributed to the fact that the Mn³⁺-O bonds, which are the most compressible bonds, are aligned closer to the (001) plane than to the c axis. The large bulk modulus is the result of the structural topology in which 2/3 and 1/2 of the edges of the Mn²⁺O₈ and Mn³⁺O₆ polyhedra share edges with other polyhedra. The Mn²⁺O₈ polyhedra were found to compress isotropically, whereas anisotropic compressional behaviour was observed for all three Mn³⁺O₆ octahedra. Although the polyhedral geometry of all three crystallographically independent Mn³⁺ sites shows the same type of uniaxially elongated distortion, the compression of the individual octahedral configurations was found to be strongly dependent upon both the geometry of the polyhedron itself and the types of, and the connectivity to, the neighbouring polyhedra. The differences in the configuration of the different oxygen atoms, and therefore the structural topology, is one of the major factors determining the type and degree of the pressure-induced distortion, while the Jahn-Teller effect plays a subordinate role.     

Minimum relative entropy and probabilistic inversion in groundwater hydrology

The similarity between maximum entropy (MaxEnt) and minimum relative entropy (MRE) allows recent advances in probabilistic inversion to obviate some of the shortcomings in the former method. The purpose of this paper is to review and extend the theory and practice of minimum relative entropy. In this regard, we illustrate important philosophies on inversion and the similarly and differences between maximum entropy, minimum relative entropy, classical smallest model (SVD) and Bayesian solutions for inverse problems. MaxEnt is applicable when we are determining a function that can be regarded as a probability distribution. The approach can be extended to the case of the general linear problem and is interpreted as the model which fits all the constraints and is the one model which has the greatest multiplicity or “spreadout” that can be realized in the greatest number of ways. The MRE solution to the inverse problem differs from the maximum entropy viewpoint as noted above. The relative entropy formulation provides the advantage of allowing for non-positive models, a prior bias in the estimated pdf and `hard' bounds if desired. We outline how MRE can be used as a measure of resolution in linear inversion and show that MRE provides us with a method to explore the limits of model space. The Bayesian methodology readily lends itself to the problem of updating prior probabilities based on uncertain field measurements, and whose truth follows from the theorems of total and compound probabilities. In the Bayesian approach information is complete and Bayes' theorem gives a unique posterior pdf. In comparing the results of the classical, MaxEnt, MRE and Bayesian approaches we notice that the approaches produce different results. In␣comparing MaxEnt with MRE for Jayne's die problem we see excellent comparisons between the results. We compare MaxEnt, smallest model and MRE approaches for the density distribution of an equivalent spherically-symmetric earth and for the contaminant plume-source problem. Theoretical comparisons between MRE and Bayesian solutions for the case of the linear model and Gaussian priors may show different results. The Bayesian expected-value solution approaches that of MRE and that of the smallest model as the prior distribution becomes uniform, but the Bayesian maximum aposteriori (MAP) solution may not exist for an underdetermined case with a uniform prior.     

Archaean quartz arenites in the Canadian Shield: examples from the Superior and Churchill Provinces

Units of remarkably pure Archaean quartz arenite occur in the northwestern part of the Superior Province and in the northern terrane of the Western Churchill Province (Rae Province) of the Canadian Shield. In the Superior Province, silica-cemented quartz arenites of Archaean age are well preserved in several greenstone belts. The example from the Keeyask Lake sedimentary assemblage displays tabular–planar and trough cross-beds, ripple marks, reactivation surfaces and pebble lag deposits. In spite of penetrative deformation and greenschist-grade metamorphism, primary textures are extremely well preserved, showing framework grains to be very well rounded and sorted. The succession of Keeyask Lake quartz-arenite beds is overlain by siltstones containing small-scale stratiform, domal and columnar stromatolites. A shallow-marine environment of deposition is inferred. Detrital heavy minerals include pyrite, magnetite, zircon, tourmaline, apatite, sphene and topaz. In the northern part of the Western Churchill Province (Rae Province), Archaean quartz arenites occur in northeasterly trending belts where intense structural deformation has in most places obscured or obliterated primary textures and structures. This has led to speculation that some of these units are metachert or recrystallized vein quartz, but local preservation of primary textures and structures provides clear evidence of epiclastic origin. In the example described herein, quartz arenites of the Woodburn Lake Group display sparse occurrences of trough and tabular–planar cross-beds, channels, ripple marks and pebble lag deposits. Probable environments of deposition for these quartz arenites include fluvial systems and shallow-marine shelf settings. The occurrence of unequivocal quartz-arenite clasts in beds of intercalated conglomerate provides direct evidence of at least two episodes of accumulation of almost pure quartz sand. Thin sections and polished slabs reveal frameworks of clastic quartz grains with little to no matrix (now mainly muscovite), and rare detrital grains of accessory heavy minerals, predominantly zircon and opaque iron oxides. Pyrite and other sulphides have been introduced along fractures, but some intergranular sulphide grains may be of detrital origin. The principal source for the quartz arenites in both areas must have been quartz-rich granitoid rocks. Conditions of intense chemical weathering are indicated. The widespread occurrence of extremely mature quartz arenites throughout Archaean terranes of the Canadian Shield, and in other shields of the world, are suggestive of crustal stability during early Earth history. The association of quartz arenites and ultramafic rocks, uncharacteristic of younger terranes, is now recognized in many Archaean greenstone belts of the Canadian Shield.     

Quaternary and extant euryhaline Lamprothamnium Groves (Charales) from Australia: Gyrogonite morphology and paleolimnological significance

Charophytes are very common in Australian modern and Quaternary waterbodies, and are quite commonly incorrectly reported as “Chara” sp. or Lamprothamnium papulosum (Wallroth) Groves. This paper is the first attempt at the identification of the widespread euryhaline genus Lamprothamnium in Australia, and its use as a paleoenvironmental indicator. Lamprothamnium is distributed worldwide in all continents, except north and central America. The Australian environment, characterized by increasing aridity during the last 500 ka, has an abundance of saline lakes. We sampled 30 modern lakes and identified extant Lamprothamnium macropogon (A. Braun) Ophel and Lamprothamnium succinctum (A. Braun in Ascherson) Wood. Fossil gyrogonites, from lacustrine sediments ∼65 ka old from Madigan Gulf, Lake Eyre, were identified as Lamprothamnium williamsii sp. nov. We applied statistical analysis (analysis of variance, ANOVA) to the morphometry of the gyrogonites from one fossil and three living Lamprothamnium populations. The ANOVA test suggests all the populations are different, including two separate populations of extant L. macropogon, interpreted in this case as the expression of ecophenotypic variability. Lamprothamnium is a useful paleoenvironmental indicator because it indicates a non-marine environment with varying salinity ranging from fresh (usually 2–3 g l⁻¹) to 70 g l⁻¹, and water bodies holding water for at least 70 consecutive days. Collectively, these parameters provide important information in the study of ephemeral habitats.