Bounded motion in a generalized two-body problem

In this paper we prove the existence of ring-type bounded motion in an isolated system consisting of a massive point particle and a homogeneous cube. We study the case of planar motion where the particle moves in a symmetry plane of the cube and we use a rotating frame of reference with its center at the mass center of the cube and its axes coinciding with the symmetry axes of the cube. We prove that, for negative values of the total energy and properly chosen values of the total angular momentum, the relative distance of the bodies has an upper and a lower bound-i.e., the regions of possible motion lie inside an annulus around the cube (motion inside a ring or an island).     

Convection flow over a uniform-flux vertical surface with variable viscosity

A regular perturbation analysis is presented for natural convection flow over an uniform flux vertical surface with temperature dependent viscosity. Numerical calculations are presented forP _r=6.7 which show that the first-order correction to the local temperature difference and to the local skin-fraction are negative whereas it is positive for the local Nusselt number. The effects of variable viscosity on the temperature, velocity profiles, the local temperature difference, the local Nusselt number and the local skin fraction are discussed.     

Muon flux at the geographical South Pole

The muon flux at the South Pole was measured for five zenith angles, 0°, 15°, 35°, 82.13° and 85.15° with a scintillator muon telescope incorporating ice Cherenkov tank detectors as the absorber. We compare the measurements with other data and with calculations.     

Origin and early evolution of the planetary system

It is shown by linear stability analysis that a preplanetary (presatellite) disk of dust and gas with Keplerian velocity field can become unstable due to the collective self-gravity of the disk. The radial distribution of rings, which may result from this instability, is derived. These rings later on can be the formation sites for planets around the Sun and for satellites around the planets. The derived orbits are shown to be in good agreement with that of the planets and the satellites (of Jupiter, Saturn, and Uranus). Predictions and conclusions seem to be possible for the existence of three yet unknown Uranian satellites, the origin of the early Moon and the possible radial extension of the planetary system.     

Thermal effects in the ultrarelativistic two-stream instability

The dispersion relation for longitudinal waves in a one-dimensional ultrarelativistic plasma is calculated. Analytical and numerical results for the growth rate and frequency of the two-stream instability are presented as a function of the energy spread in the denser stream when the dilute stream is cold. The case of energy spreads in both beams is investigated numerically: it is found that relatively small energy spreads in both streams can lead to suppression of the instability.