Derivation of frequency-dependentX- andY-functions for a non-coherent scattering problem

The equation of transfer for the case of non-coherent scattering (Hummer, 1968; Ivanov, 1973; McCormick and Siewert, 1970) has been considered. The correspondingX- andY-functions have been derived by a combination of eigenfunction method developed by Case, and from the principle of invariance as developed by Chandrasekhar (1960).     

A stepwise method for determining the number of component distributions in a mixture

This paper considers the problem of estimatingm, the number of components in a finite mixture of distributions from a parametric family. A step-up procedure using the bootstrap method is proposed. Some properties of the procedure are illustrated with simulation studies. An example of the method, applied to orientation of beach clasts, is given.     

Three-dimensional linear solution for wave propagation with slopingbottom

This paper presents a three-dimensional analytic linear wave solution for surface gravity wave propagation over a sloping bottom that is valid for small, but realistic, slopes. The sloping-bottom linear model is compared to published laboratory data and to predictions of two-dimensional, constant-bottom nonlinear theories. The model is shown to describe the measured wave-height growth in the wave transformation region up to a limiting local Ursell number U_r of 0.35-1.0, depending on the wave type, although, as a linear model, it does not predict the harmonics observed in that range. For U_r<0.35, the harmonics can generally be neglected and the sloping-bottom linear theory agrees closely with both the published wave-height data and third-order Stokes nonlinear theory. As a three-dimensional linear model, superposition can be invoked to synthesize and relate wave structure in the transformation region to complex incident ocean spectra with both wind wave and swell components that arrive with a range of incidence angles. As such, the sloping-bottom linear model presented here should be a convenient useful tool for ocean modeling through a significant portion of the wave transformation region     

Ambipolar diffusion in the solar atmosphere

The process of non-linear ambipolar diffusion in the region overlying the solar surface can be an effective mechanism for producing sharp magnetic structures and current sheets. These may be the sites responsible for the occurrence of connectivity of magnetic field lines, and the subsequent explosive input of energy for heating of some of the features in the atmosphere of the Sun..     

Circumstellar Silicate Mineralogy

This paper reviews spectra obtained with the SWS on board of ISO of dust shells around O-rich objects. These spectra reveal the presence of many new emission features between 10 and 45 μm. These bands are generally much narrower than the well-known 10 and 20 μm silicates features. The strength of these features relative to the underlying broad continuum varies from source to source (≅ 5-50%). The 10 μm region shows evidence for the presence of Al2O3 grains. At longer wavelength, the spectra are dominated by features due to crystalline olivine and pyroxene. The exact peak position of these features shows that the emitting grains consist of the Mg-rich end-members of these minerals with an Fe-content of < 10%. The underlying continuum is attributed to amorphous silicate grains. These observations of aluminum-rich and magnesium-rich compounds compare well with the thermodynamic condensation sequence of minerals expected for O-rich outflows. The observations also imply that freeze out (ie., kinetics) of this condensation sequence at different temperatures is an important characteristic of dust formation in these objects. It is suggested that the absence of Fe-rich silicates is a natural consequence of the low temperature at which gaseous Fe reacts with Mg-rich silicates in these outflows, resulting in amorphous grains with little characterizing spectral detail. This revised version was published online in August 2006 with corrections to the Cover Date.     

Exposure history of the Torino meteorite

Abstract— We determined He, Ne, Ar, ¹⁰Be, ²⁶Al, ³⁶Cl, and ¹⁴C concentrations, as well as cosmic-ray track densities and halogen concentrations in different specimens of the H6 chondrite Torino, in order to constrain its exposure history to cosmic radiation. The Torino meteoroid had a radius of ～20 cm and travelled in interplanetary space for 2.5–10 Ma. Earlier, Torino was part of a larger body. The smallest possible precursor had a radius of 55 cm and a journey through space longer than ～65 Ma. If the first-stage exposure took place in a body with a radius of >3 m or in the parent asteroid, then it lasted nearly 300 Ma. The example of Torino shows that it is easy to underestimate first-stage exposure ages when constructing two-stage histories.     

Evolution of 2:1 layered silicates in low-grade metamorphosed Liassic shales of Central Switzerland

White mica from the Liassic black shales and slates in Central Switzerland was analysed by transmission electron microscopy (TEM) and electron microprobe to determine its textural and compositional evolution during very low-grade prograde metamorphism. Samples were studied from the diagenetic zone, anchizone and epizone (T ≈100°–450 °C). Phyllosilicate minerals analysed include illite/smectite (I/S), phengite, muscovite, brammallite, paragonite, margarite and glauconite. Textural evolution primarily is towards larger, more defect-free grains with compositions that approach those of their respective end-members. The smectite-to-illite transformation reduced the amounts of the exchange components SiK_?1Al_?1, MgSiAl_?2, and Fe³⁺Al_?1. These trends continue to a lesser degree in the anchizone and epizone. Correlations between the proportion of smectite in I/S and the composition of I/S indicate that smectite layers may contain a high layer charge. Illite in I/S bears a compositional resemblance to macrocrystalline phengite in some samples, but is different in others. Paragonite first appears in the upper diagenetic zone or lower anchizone as an interlayer-deficient brammallite, and it may be mixed with muscovite on the nanometre scale. Owing to the small calculated structure factor for paragonite-muscovite superstructures, conventional X-ray powder diffraction cannot distinguish between mixed-layer structures and a homogeneous compositionally intermediate solid solutions. However, indirect TEM evidence shows that irregularly shaped domains of Na- and K-rich mica exist below 10 nm. Subsequent coarsening of domains at higher grades produced discrete paragonite grains at the margins of muscovite crystals or in laths parallel to the basal plane of the host muscovite. Margarite appears in the epizone and follows a textural evolution similar to paragonite in that mixtures of margarite, paragonite, and muscovite may initially occur on the nanometre scale. However, no evidence of interlayer-poor margarite has been found.