Time-dependent scattering and transmission function in an anisotropic two-layered atmosphere

In this paper we consider the time-dependent diffuse reflection and transmission problems for a homogeneous anisotropically-scattering atmosphere of finite optical depth and solve it by the principle of invariance. Also we consider the time-dependent diffuse reflection and transmission of parallel rays by a slab consisting of two anisotropic homogeneous layers, whose scattering and transmission properties are known. It is shown how to express the time-dependent reflected and transmitted intensities in terms of their components. In a manner similar to that given by Tsujita (1968), we assumed that the upward-directed intensities of radiation at the boundary of the two layers are expressed by the sum of products of some auxiliary functions depending on only one argument. Then, after some analytical manipulations, three groups of systems of simultaneous integral equations governing the auxiliary functions are obtained.     

Solution of the equation of transfer for coherent scattering in an exponential atmosphere by the method of discrete ordinates

A solution of the transfer equation for coherent scattering in stellar atmosphere with Planck's function as a nonlinear function of optical depth, viz., $$B_v (T) = b_0 + b_1 {\text{ }}e^{ - \beta \tau } $$ is obtained by the method of discrete ordinates originally due to Chandrasekhar.     

Ionospheric plasma measurements from the accelerator rocket Maimik

Results from an ionoipheric founding rocket of the “mother-daugther” type, equipped with an 8 keV electron accelerator, is reported. The emphasis is on the results obtained from the three plasma probes which monitored both the electron- and the ion-population. It is shown that no significant increase of the electron density was observed during the beam injections. However, the electron temperature varied rapidly during these pulses. The influence of the vehicle charging on the measurements is also discussed.     

Kelvin-Helmholtz instability of two viscous superposed rotating and conducting fluids

Kelvin-Helmholtz instability of the interface separating two viscous rotating-conducting fluids has been studied in the presence of finite ion-Larmor radius (FLR) effects. Emloying the normal mode technique, the solutions have been obtained when the fluids are assumed to be permeated by a uniform horizontal magnetic field. For the case of two highly viscous fluids, the dispersion relation has been derived and solved numerically. It is found that the streaming velocity has a stabilizing influence on the potentially unstable arrangement of the fluids. The viscosity and FLR effects are also found to have a stabilizing influence while the Coriolis forces have a destabilizing influence on the system.     

A predator–prey model for moon-triggered clumping in Saturn’s rings

UVIS occultation data show clumping in Saturn’s F ring and at the B ring outer edge, indicating aggregation and disaggregation at these locations that are perturbed by Prometheus and by Mimas. The inferred timescales range from hours to months. Occultation profiles of the edge show wide variability, indicating perturbations by local mass aggregations. Structure near the B ring edge is seen in power spectral analysis at scales 200–2000 m. Similar structure is also seen at the strongest density waves, with significance increasing with resonance strength. For the B ring outer edge, the strongest structure is seen at longitudes 90° and 270° relative to Mimas. This indicates a direct relation between the moon and the ring clumping. We propose that the collective behavior of the ring particles resembles a predator–prey system: the mean aggregate size is the prey, which feeds the velocity dispersion; conversely, increasing dispersion breaks up the aggregates. Moons may trigger clumping by streamline crowding, which reduces the relative velocity, leading to more aggregation and more clumping. Disaggregation may follow from disruptive collisions or tidal shedding as the clumps stir the relative velocity. For realistic values of the parameters this yields a limit cycle behavior, as for the ecology of foxes and hares or the “boom-bust” economic cycle. Solving for the long-term behavior of this forced system gives a periodic response at the perturbing frequency, with a phase lag roughly consistent with the UVIS occultation measurements. We conclude that the agitation by the moons in the F ring and at the B ring outer edge drives aggregation and disaggregation in the forcing frame. This agitation of the ring material may also allow fortuitous formation of solid objects from the temporary clumps, via stochastic processes like compaction, adhesion, sintering or reorganization that drives the denser parts of the aggregate to the center or ejects the lighter elements. Any of these more persistent objects would then orbit at the Kepler rate. We would also expect the formation of clumps and some more permanent objects at the other perturbed regions in the rings… including satellite resonances, shepherded ring edges, and near embedded objects like Pan and Daphnis (where the aggregation/disaggregation cycles are forced similar to Prometheus forcing of the F ring).