Advances in radiative transfer

This review describes advances in radiative transfer theory since about 1985. We stress fundamental aspects and emphasize modern methods for the numerical solution of the transfer equation for spatially multidimensional problems, for both unpolarized and polarized radiation. We restrict the discussion to two-level atoms with noninverted populations for given temperature, density and velocity fields. Unfortunately this article was originally published with typesetter's errors: The correct publication date was 25 February 2006, not 3 January 2006. The content was not in the final form. The publishers wish to apologize for this mistake. The online version of the original version can be found at /10.1007/s00159-005-0025-8.     

A model for galactic centres

A rotating Supermassive Magnetized Disk is proposed as a model for all the violent phenomena occurring in the nuclei of galaxies, in the form of quasars, Lacertids, radio galaxies, Seyferts, exploding galaxies, etc. The cold disk feeds a fast-rotating supermassive core (some 10³ Schwarzschild radii in extent), which emits (1) an unsteady thermal wind of filamentary geometry, (2) Low-Frequency magnetic Waves, and (3) relativistic electrons and positrons. The latter reach high -factors by phase-riding the LFWs, emit synchro-Compton radiation on crossing scattered waves (from -ray energies down to radio frequencies), and are eventually focused into two antipodal relativistic beams by their frozen-in toroidal magnetic field. Torsional oscillations between the core and disk give rise to a pulsed injection, and a breathing double-onion shape of the LFW windzone can explain the superluminal jetlike appearance. A big nuclear explosion ends each duty cycle, but many smaller explosions prevent the settling core from collapsing. In this model, the helium production of galactic centres is comparable to the observed cosmic helium.     

Numerical simulations of granular dynamics II: Particle dynamics in a shaken granular material

Surfaces of planets and small bodies of our Solar System are often covered by a layer of granular material that can range from a fine regolith to a gravel-like structure of varying depths. Therefore, the dynamics of granular materials are involved in many events occurring during planetary and small-body evolution thus contributing to their geological properties.We demonstrate that the new adaptation of the parallel N-body hard-sphere code pkdgrav has the capability to model accurately the key features of the collective motion of bidisperse granular materials in a dense regime as a result of shaking. As a stringent test of the numerical code we investigate the complex collective ordering and motion of granular material by direct comparison with laboratory experiments. We demonstrate that, as experimentally observed, the scale of the collective motion increases with increasing small-particle additive concentration.We then extend our investigations to assess how self-gravity and external gravity affect collective motion. In our reduced-gravity simulations both the gravitational conditions and the frequency of the vibrations roughly match the conditions on asteroids subjected to seismic shaking, though real regolith is likely to be much more heterogeneous and less ordered than in our idealised simulations. We also show that collective motion can occur in a granular material under a wide range of inter-particle gravity conditions and in the absence of an external gravitational field. These investigations demonstrate the great interest of being able to simulate conditions that are to relevant planetary science yet unreachable by Earth-based laboratory experiments.     

Numerical simulation of coronal heating by resonant absorption of Alfvén waves

The heating of coronal loops by resonant absorption of Alfvén waves is studied in compressible, resistive magnetohydrodynamics. The loops are approximated by straight cylindrical, axisymmetric plasma columns and the incident waves which excite the coronal loops are modelled by a periodic external driver. The stationary state of this system is determined with a numerical code based on the finite element method. Since the power spectrum of the incident waves is not well known, the intrinsic dissipation is computed. The intrinsic dissipation spectrum is independent of the external driver and reflects the intrinsic ability of the coronal loops to extract energy from incident waves by the mechanism of resonant absorption.The numerical results show that resonant absorption is very efficient for typical parameter values occurring in the loops of the solar corona. A considerable part of the energy supplied by the external driver, is actually dissipated Ohmically and converted into heat. The heating of the plasma is localized in a narrow resonant layer with a width proportional to ^1/3. The energy dissipation rate is almost independent of the resistivity for the relevant values of this parameter. The efficiency of the heating mechanism and the localization of the heating strongly depend on the frequency of the external driver. Resonant absorption is extremely efficient when the plasma is excited with a frequency near the frequency of a so-called collective mode.     

The dependence on system parameters of strange-mode instabilities in accretion discs

A systematic study of the dependence on disc parameters and input physics, such as opacity and the treatment of convection, of strange-mode instabilities in thin accretion discs, which have been discovered recently, is presented. The instabilities are found to exist for a wide range of parameters, are partly very robust, and their growth rates can reach the dynamical range. Even discs on galactic scales around massive black holes are affected by them. Two groups of instabilities can be distinguished, the first of which is related to the radiation-pressure-dominated part of the disc, and the second to helium/hydrogen ionization. By application of the NAR approximation, both of them can be shown to be of mechanical origin, and the classical κ -mechanism can be excluded as the instability mechanism. A heuristic model for strange-mode instabilities proposed in the context of stellar strange-mode instabilities in luminous stars seems to be applicable to the group associated with dominant radiation pressure.     

How does landfill leachate affect the chemical processes in a lake system downgradient from a landfill site?

A field study on the geochemical properties of a chemically-stressed limnic environment was performed in Lake Silbersee, which receives leachate water of high inorganic loading from an upgradient landfill site. The highly concentrated sulfate ion in groundwater, when entering the pore water system of the lake, gives rise to an intensive microbial sulfate reduction. A diagenetic approach was used to explain the existence of a marine-like aqueous system within a geologically slightly acidic aquifer, consisting of a well-buffered lake water and an alkalinity producing, excess sulphide containing sediment pore water system.     

On the distribution of rainfall over the Sultanate of Oman

Rainfall distribution over the Sultanate of Oman is analysed. Data from seven recently installed weather stations as well as supporting data from scattered sources were used. Distribution maps were drawn. NW and NE winter wind meet resulting in troughs and rainfall on the Mountains and Coastal Strips. Summer monsoon wind dominates the S. Central areas of overlap receive light showers from both summer monsoons and winter local troughs. Heavier amounts of rainfall are generally associated with high altitude.     

Crystal structure refinement of hendricksite,A Zn- and Mn-rich trioctahedral potassium mica: A contribution to the crystal chemistry of zinc-bearing minerals

Summary The crystal structure of hendricksite, a trioctahedral mica of biotite type, characterized by high Zn²⁺ and Mn²⁺ contents has been refined by least square methods. The structural formula is: (K_0.89Na_0.10Ba_0.04)(Mg_1.57Zn_0.54Mn _0.40 ²⁺ Fe _0.25 ²⁺ Al_0.07Ti_0.07Cr_0.01)(Si_2.92Al_1.08)O₁₀ (OH)₂. The space group isC2/m and the cell parameters are:a=5.340(2) Å,b=9.524(2) Å,c=10.235(3) Å, =100.07(2)^o, the cell volume isV=497.98 ų. The final unweightedR=0.072. Average cation-anion distances in polyhedra are: T–O=1.659 Å, M(1)–O=2.093 Å, M(2)–O=2.088 Å, A–O_long=3.316 Å and A–O_short=3.004 Å; A is the alkaline cation. The rotation angle of tetrahedra is =6.7°. The analysis of electron densities, of the dimensions and distorsions of polyhedra shows that Zn²⁺ is exclusively in octahedral sites; there is no order between six-fold coordinated cations. A comparison between the structural features of hendricksite and those of the two main end-members of biotites, phlogopite and annite, is presented.The effect of the strong covalence of Zn–O bonds is particularly visible on the dimensions and orientations of the thermal ellipsoids of octahedral sites M(1) and M(2) which contain zinc. In all the published structures of trioctahedral micas, the ellipsoids of cationic sites are uniaxial positive, elongated parallel toc ^*. In hendricksite, this is observed only for the two zinc-free sites (T and A; in the octahedra M(1) and M(2), which contain zinc, the ellipsoids are approximately uniaxial negative, flattened parallel toa, which is a unique situation.Zinc which habitually favours the tetrahedral coordinations with oxygen, enters the octahedra only, i.e. the chemically anisotropic sites, in hendricksite. The strong polarizability of Zn²⁺ is proposed to explain this behaviour.An examination of the behaviour of Zn²⁺ in other compounds shows that this situation is general, zinc favours chemically anisotropic sites and specially those adjacent to OH or H₂O.

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Affinement de la structure cristalline de la hendricksite, mica trioctaédrique potassique riche en Zn et Mn; une contribution à la connaissance cristallochimique des minéraux zincifères

Résumé On a affiné par moindres carrés la structure de la hendricksite, mica trioctaédrique de type biotite, caractérisé par une teneur élevée en Zn²⁺ et Mn²⁺. La formule structurale de ce mica est: (K_0m89Na_0,10Ba_0,04)(Mg_1,57Zn_0,54Mn _0,40 ²⁺ Fe _0,25 ²⁺ Al_0,07Ti_0,07Cr_0,01)(Si_2,92Al_1,08)O₁₀(OH)₂. Le groupe spatial estC2/m et les paramètres de la maille:a=5,340(2) Å,b=9,254(2) Å,c=10,235(3) Å, =100,07(2)°; le volume de la maille estV=497,98 ų. Le résidu final non-pondéré estR=0,072. Les distances cation-anion moyennes dans les polyèdres sont les suivantes: T–O=1,659 Å, M(1)–O=2,093 Å, M(2)–O=2,088 Å, A–O_long=3,316 Å et A–O_court=3,004 Å où A désigne le cation alcalin. L'angle de rotation tétraédrique, =6,7°, est très semblable à celui de la phlogopite. L'analyse des densités électroniques, des dimensions et distorsions des polyèdres montre que Zn²⁺ est exclusivement en coordinance octaédrique et qu'il n'y a pas d'ordre entre les cations hexacoordonnés. On présente une comparaison des caractères structuraux de la hendricksite avec ceux des deux principaux pôles des biotites, la phlogopite et l'annite.L'effet de la forte covalence de la liaison Zn–O est particulièrement visible sur les dimensions et orientations des ellipsoides d'agitation thermique des deux sites octaédriques, sites zincifères. Dans toutes les structures de micas trioctaédriques publiées, les ellipsoides des sites cationiques sont uniaxes positifs, allongés parallèlement àc ^*, ce qui s' observe effectivement dans les deux sites non-zincifères (T et A) de la hendricksite, par contre, dans les octaèdres M(1) et M(2), qui contiennent le zinc, les ellipsoides sont approximativement uniaxes négatifs, applatis parallèlement àa, ce qui est une situation unique.Le zinc, qui se fixe généralement en sites tétraédriques dans les structures de type oxyde, occupe les sites octaédriques, c'est-à-dire les sites chimiquement anisotropes dans la hendricksite. La forte polarisabilité de Zn²⁺ est proposée pour expliquer ce comportement.Un examen du comportement de Zn²⁺ dans d'autres phases montre que cette situation est tout à fait générale, le zinc privilégiant les sites chimiquement anisotropes et en particulier ceux adjacents à OH où H₂O.