Influence of the Earth's ring current strength on Størmer's allowed and forbidden regions of charged particle motion

Størmer's particles' trapping regions for a planet with an intrinsic dipolar magnetic field are considered, taking into account the ring current which arises due to the trapped particles' drift for the case of the Earth. The influence of the ring current on the particle trapping regions' topology is investigated. It is shown that a critical strength of the ring current exists under which further expansion of the trapping region is no longer possible. Before reaching this limit, the dipole field, although deformed, retains two separated Størmer regions. After transition of critical magnitude, the trapping region opens up, and charged particles, which form the ring current, get the opportunity to leave it, thus decreasing the ring current strength. Numerical calculations have been performed for protons with typical energies of the Earth's radiation belt and ring current. For the Earth's case, the Dst index for the critical ring current strength is calculated.

Influence of the Earth's ring current strength on the Størmer's allowed and forbidden regions of charged particles motion

Størmer's particles' trapping regions for a planet with an intrinsic dipolar magnetic field are considered, taking into account the ring current which arises due to the trapped particles drift for the case of Earth. The influence of the ring current on the particles' trapping regions topology is investigated. It is shown that a critical strength of the ring current exists, under which further expansion of the trapping region is no longer possible. Before reaching this limit, the dipole field, although deformed, retains two separated Størmer regions. After transition of critical magnitude, the trapping region opens up and charged particles, which form the ring current, get the opportunity to leave it (go to infinity or come to the trapping region from infinity), thus decreasing the ring current strength. Numerical calculations have been performed for protons with typical energies of Earth's radiation belt and ring current. For the Earth case, the Dst index for the critical ring current strength is calculated.

Three-dimensional coating and rimming flow: a ring of fluid on a rotating horizontal cylinder

The steady three-dimensional flow of a thin, slowly varying ring of Newtonian fluid on either the outside or the inside of a uniformly rotating large horizontal cylinder is investigated. Specifically, we study ‘full-ring’ solutions, corresponding to a ring of continuous, finite and non-zero thickness that extends all of the way around the cylinder. In particular, it is found that there is a critical solution corresponding to either a critical load above which no full-ring solution exists (if the rotation speed is prescribed) or a critical rotation speed below which no full-ring solution exists (if the load is prescribed). We describe the behaviour of the critical solution and, in particular, show that the critical flux, the critical load, the critical semi-width and the critical ring profile are all increasing functions of the rotation speed. In the limit of small rotation speed, the critical flux is small and the critical ring is narrow and thin, leading to a small critical load. In the limit of large rotation speed, the critical flux is large and the critical ring is wide on the upper half of the cylinder and thick on the lower half of the cylinder, leading to a large critical load. We also describe the behaviour of the non-critical full-ring solution and, in particular, show that the semi-width and the ring profile are increasing functions of the load but, in general, non-monotonic functions of the rotation speed. In the limit of large rotation speed, the ring approaches a limiting non-uniform shape, whereas in the limit of small load, the ring is narrow and thin with a uniform parabolic profile. Finally, we show that, while for most values of the rotation speed and the load the azimuthal velocity is in the same direction as the rotation of the cylinder, there is a region of parameter space close to the critical solution for sufficiently small rotation speed in which backflow occurs in a small region on the upward-moving side of the cylinder.

NUMERICAL INVESTIGATION OF FIVE-DIMENSIONAL GRAVITATIONAL COLLAPSES

We introduce our numerical studies of gravitational collapses in five-dimensional (5D) space-time, with a purpose of studying the cosmic censorship hypothesis and the hoop conjecture. The first model is the collapse of spindle matter which was performed by Shapiro and Teukolsky (1991) who announced an appearance of a naked singularity in 4D. Comparing with 4D cases, we found that 5D collapses proceed more rapidly, the final configurations tend to be spherical, and apparent horizon (AH) forms in wider parameter ranges. We also observed positive evidence for formation of a naked singularity in highly spindle cases as well. The second model is the formation of black-ring in 5D. Our code does not include angular momentum, but the model would be helpful for basic understandings. We constructed an initial data sequence with ring-shaped matter, and observed the topology of AHs, if formed. We found a critical ring radius for ring-shaped AH, and it suggests a dynamical transition of AH topology from ring-shaped to spherical. We demonstrate such an example in time evolution.

Planetary ring dynamics

The dynamics of planetary rings are reviewed in the light of data derived from the recent spacecraft missions to the outer planets. It is shown that although the ring systems of Jupiter, Saturn, Uranus and Neptune display a great diversity of phenomena and dynamical structures, they have many features and problems in common. The role of small satellites in determining ring structure is reviewed, with particular emphasis on the ring system of Saturn. There is mounting evidence that some of the smaller satellites may have densities as low as 0.6 g cm -3 . Because Saturn has examples of most of the types of rings seen elsewhere in the Solar System, the forthcoming Cassini mission has particular importance for ring dynamicists. A summary is presented of the critical ring observations that can only be made by a spacecraft orbiting Saturn for an extended period.

The Mappilla Rebellion, 1921: Peasant Revolt in Malabar

In any society the dominant groups are the ones with the most to hide about the way society works. Very often therefore truthful analyses are bound to have a critical ring, to seem like exposures rather than objective statements, … For all students of human society, sympathy with the victims of historical processes and skepticism about the victors' claims provide essential safeguards against being taken in by the dominant mythology. A scholar who tries to be objective needs these feelings as part of his ordinary working equipment.