On the uncertainty of the transmission function of the optically thick AGB dust shells

The uncertainty of the spectral transmission function due to the nonsphericity of cosmic dust particles is analysed for optically thick C-rich and O-rich dust shells. The transmission function directly prescribes the intensity of radiation that passes through a dust shell. It is shown that nonspherical particles affect the stellar spectra in a different way than a system of equally sized spherical particles. Discrepancies in the stellar spectra for both morphological models (spheres and irregular targets) grow with optical thickness of the dust shell and the spectral behaviour of the optical thickness depends on the particle size distribution function. In particular, two most frequently used distrubutions, a power law and Dirac’s delta function, are considered in the presented numerical runs. Light transmission through C-rich dust shells is strongly influenced by absorption which dominates in case of carbonaceous particles. Irregularly shaped carbonaceous particles reduce the intensity of stellar spectra more efficiently than spherical particles of the same composition (the difference is about 10–30%). MgO particles which may be present in O-rich dust shells are almost pure scatterers, thus the ratio of transmission functions for irregularly shaped particles and spherical ones show specific resonant features (especially at wavelengths below 0.4 μm).     

Efficient Methods to Simulate Planar Free Surface in the 3D 4th-Order Staggered-Grid Finite-Difference Schemes

We numerically tested accuracy of two formulations of Levander's (1988) stress-imaging technique for simulating a planar free surface in the 4^th-order staggered-grid finite-difference schemes. We have found that both formulations (one with normal stress-tensor components at the surface, the other with shear stress-tensor components at the surface) require at least 10 grid spacings per minimum wavelength ( _min÷h = 10) if Rayleigh waves are to be propagated without significant grid dispersion in the range of epicentral distances up to 15 _dom ^S.Because interior 4^th-order staggered-grid schemes usually do not require more than 6 grid spacings per minimum wavelength, in the considered range of epicentral distances, it was desirable to find alternative techniques to simulate a planar free surface, which would not require denser spatial sampling than _min÷h = 6. Therefore, we have developed and tested new techniques: 1. Combination of the stress imaging (with the shear stress-tensor components at the surface) with Rodrigues' (1993) vertically refined grid near the free surface. 2. Application of the adjusted finite-difference approximations to the z-derivatives at the grid points at and below the surface that uses no virtual values above the surface and no stress imaging. The normal stress-tensor components are at the surface in one formulation, while the shear stress-tensor components are at the surface in the other formulation.The three developed formulations give for the spatial sampling _min÷h = 6 results very close to those obtained by the discrete-wavenumber method. Because, however, the technique with the vertically refined grid near the free surface requires 3 times smaller time step (due to the refined grid), the technique with adjusted finite-difference approximations is the most accurate and efficient technique from the examined formulations in the homogeneous halfspace.     

Factors controlling the morphology and volume (V)–length (L) relations of permanent gullies in the northern Ethiopian Highlands

Small‐scale aerial photographs and high‐resolution satellite images, available for Ethiopia since the second half of the twentieth century as for most countries, allow only the length of gullies to be determined. Understanding the development of gully volumes therefore requires that empirical relations between gully volume (V) and length (L) are established in the field. So far, such V–L relations have been proposed for a limited number of gullies/environments and were especially developed for ephemeral gullies. In this study, V–L relations were established for permanent gullies in northern Ethiopia, having a total length of 152 km. In order to take the regional variability in environmental characteristics into account, factors that control gully cross‐sectional morphology were studied from 811 cross‐sections. This indicated that the lithology and the presence of check dams or low‐active channels were the most important controls of gully cross‐sectional shape and size. Cross‐sectional size could be fairly well predicted by their drainage area. The V–L relation for the complete dataset was V = 0 · 562 L ^1·381 (n = 33, r² = 0 · 94, with 34 · 9% of the network having check dams and/or being low‐active). Producing such relations for the different lithologies and percentages of the gully network having check dams and/or being low‐active allows historical gully development from historical remote sensing data to be assessed. In addition, gully volume was also related to its catchments area (A) and catchment slope gradient (S_c). This study demonstrates that V–L and V–A × S_c relations can be very suitable for planners to assess gully volume, but that the establishment of such relations is necessarily region‐specific. Copyright © 2013 John Wiley & Sons, Ltd.     

Immiscible separation of metalliferous Fe/ Ti-oxide melts from fractionating alkali basalt: P-T-f O2 conditions and two-liquid elemental partitioning

Globules of iron-dominated (59–69 wt% FeO_tot) and titanium-dominated (43.5 wt% TiO₂) oxide melts have been detected in igneous xenoliths from Pliocene-to-Pleistocene alkali basalts of the Western Carpathians. Fluid inclusion and mineral composition data indicate immiscible separation of the high-iron-oxide melt (HIM) at magmatic temperatures. The HIM separation occurred during clinopyroxene (augite) accumulation in an alkali trachybasalt and continued during crystallization of amphibole (kaersutite) and K-feldspar (anorthoclase), the latter coexisting with trachyte and alkalic rhyolite residual melts. Some HIM was also expelled from sub-alkalic rhyolite (70–77% SiO₂), coexisting with An_27–45 plagioclase and quartz in granitic (tonalite-trondhjemite) xenoliths. Oxygen fugacities during HIM separation range from −1.4 to +0.6 log units around the QFM buffer. A close genetic relationship between HIM-hosted xenoliths and mantle-derived basaltic magma is documented by mineral ¹⁸O values ranging from 4.9 to 5.9‰ V-SMOW. δD values of gabbroic kaersutite between −61 and −86‰ V-SMOW are in agreement with a presumed primary magmatic water source. Most trace elements, except Li, Rb and Cs, have preferentially partitioned into the HIM. The HIM/Si-melt partition coefficients for transition elements (Sc, V, Cr, Co, Ni) and base metals (Zn, Cu, Mo) are between 2–160, resulting in extreme enrichment in the HIM. La and Ce also concentrate in the silicic melt, whereas Tb-Tm in the HIM. Hence, the immiscible separation causes REE fractionation and produces residual silicic melt enriched in LREE and depleted in HREE. The weak fractionation among Tb-Tm and Yb, Lu can be attributed to recurrent extraction of the HIM from the magmatic system, while flat HREE chondrite-normalized patterns are interpreted to indicate no or little loss of the HIM. Received: 30 September 1997 / Accepted: 23 March 1998     

Nongravitational forces and meteoroid streams

The action of the solar electromagnetic radiation on the moving interplanetary dust particles in its more complete form than the special case known as the Poynting-Robertson effect is theoretically discussed in application to meteoroid stream of comet Encke.Normal and transversal components of the perturbing nongravitational force are used due to the action of the solar electromagnetic radiation. It is shown that the normal component of the force is negligible. However, transversal component is very important: it can probably completely explain all the observed meteoroid streams situated along the orbit of comet Encke (and, possibly, some asteroids) as the product of the comet Encke alone. Much shorter time is required for producing such a meteoroid stream than is a general conception.If the idea about the significance of the transversal component of the nongravitational force (may be, not produced by electromagnetic radiation) is correct, it may have important consequences for our understanding of ageing of comets, global evolution of the cometary (and, partially, asteroidal) system, and, of course, for a long-term evolution of small interplanetary particles.