Cylindrical oscillations of force-free electromagnetic fields

This paper is devoted to Force-Free Electromagnetic Oscillations in a constant magnetic field. A correction is made in the derivation of the basic equation. The paper confirms the predicted spectrum of frequencies, namely _n = _o (n + 1)^1/2;n = 0, 1, 2, .... In addition it is suggested that hybrid frequency _n = ( _n ² + _H ² )^1/2 should be found in observational data.     

A high-resolution bragg spectrometer for the observation of the hot interstellar medium X-ray emission

We present a high-resolution Bragg spectrometer designed for the observation of the soft X-ray cosmic diffuse background. The instrument concept is derived from the de Broglie geometry for the study of extended sources. It consists in a mosaïc of spherical TlAP crystals associated with position sensitive detectors located on the focussing surface. The spectral resolution and its variation with the field of view is estimated by Monte-Carlo simulations for different X-ray energies chosen among the most intense lines emitted by an astrophysical plasma in the temperature range 1–4×10⁶K. The estimated sensitivity and the simulations of actual space observations show that the instrument is capable to separate the strongest lines emitted by the most abundant ions (OVII,OVIII, FeXVII, NeIX, etc.) and to map the whole sky during a six month mission.     

Variations in the HCN/HNC abundance ratio in the Orion molecular cloud

We have used observations of the rare isotopes of HCN and HNC to determine the relative abundance of these two chemical isomers along the central ridge of the Orion molecular cloud. The abundance ratio [HCN]/[HNC] decreases by more than an order of magnitude from the relatively warm plateau and hot core sources toward the KL nebula to the colder, more quiescent clouds to the north and south. Even in the cooler regions, however, the ratio is an order of magnitude larger than that found in previous investigations of cold dark clouds. We determine the kinetic temperature in the regions we have studied from new observations of methylacetylene (CH3CCH), together with other recent estimates of the gas temperature near KL. The results suggest that the warmer portions of the cloud are dominated by different chemical pathways than those in the general interstellar cloud material.     

A note on the total mass of comets in the solar system

The assumption that the very low albedo determined for Halley's comet is typical of all short period comets, taken together with the assumption that the average sizes of long and short period comets are approximately equal, leads to an increase in the total mass of comets in the solar system by almost two orders of magnitude. If gravitational ejection from the Uranus - Neptune zone during the later phases of planet formation is indeed responsible for the classical Oort cloud between 10⁴–10¹⁵ AU, then the mass of comets in this transplanetary region during cosmogonie times has to exceed the combined masses of Uranus and Neptune by over an order of magnitude. Furthermore, if the recent arguments for as many as 10¹⁴ comets in an inner Oort cloud between ~40– 10⁴AU are valid, then the total mass of comets in the solar system approaches 2% of a solar mass.     

Experiences numeriques sur des billards C1 formes de quatre arcs de cercles

The paper deals with some properties of the dynamical system with two degrees of freedom defined by the motion of a particle in a certain type of billiard. These properties are studied by means of numerical experiments. Most results are represented in the now classical surface of section. One parameter families of billiards with a C¹ boundary constructed with four arcs of circles are defined; we use the property that the four meeting points of such billiards lie on the same circle. These billiards may be convex or non convex. They generalize the ‘oval’ billiard with two axes of symmetry studied by Benettin and Strelcyn. We call them generalized billiards. We find the following results:

1. The periodic orbit along the small diameter of a billiard is stable or unstable in the linear approximation according to the position of the center of each relevant are with respect to the opposite one. This orbit is always stable if the billiard is symmetric with respect to its large diameter.
2. When the center of an arc lies on the opposite arc two different transition patterns from order to chaos are observed for the same billiard. If the billiard is of the Benettin and Strelcyn type three distinct nested chaotic seas are seen two of which are separated by a pseudo-invariant curve generated by a so called cancellation orbit.
3. The total area of non chaotic regions is greater for symmetric billiards.
4. Peanut shaped billiards always look ergodic. It can happen also that strictly convex asymmetric billiards look ergodic. This is important since no strictly convex billiard is known for which ergodicity has been proven. The conjecture is proposed that a generalized billiard with neither 2-periodic nor 4-periodic stable orbit in the linear approximation is ergodic.
5. Transverse invariant curves such as the one found by Hénon and Wisdom seem common for billiards with two axes of symmetry but probably do not exist for asymmetric billiards.

There are therefore several properties which differentiate symmetric billiards from asymmetric ones. We conclude by emphasizing that C¹ generalized billiards are indeed inadequate models for smooth mappings in general.     

Quadratic analytical solution of general systems through formal hamiltonization

A technique for the quadratic analytical solution of general nonlinearly perturbed periodic systems is presented. It relies on a device recognized as early as Birkhoff (1927), through which any system of ordinary differential equations can be cast in Hamiltonian form through the introduction of a set of auxiliary conjugate variables. The particular implementation applies the author's quadratic Hamiltonian approach, utilizing Lie transforms (so admitting of easy inversion), and featuring the ability to determine the frequencies of the system to twice the order of the solution at the last step. The method is exemplified through an analysis of the van der Pol equation to find the solution to second order, and frequencies to fourth, of the limit cycle of the system. Finally, the relationship of the approach to other perturbation techniques, particularly the vector/matrix Lie transform method, is discussed.     

Coronal mass ejection associated with the stationary post-flare arch of 21–22 May 1980

By using a combination of X-ray (HXIS), H (Haleakala), white-light corona (Solwind), and zodiacal light (Helios) images on 21–22 May, 1980 we demonstrate, and try to explain, the co-existence of a coronal mass ejection with a stationary post-flare coronal arch. The mass ejection was seen, both by Solwind and Helios, in prolongation of the path of a powerful spray, whereas the active region filament did not erupt. A tentative comparison is made with other occurrences of stationary, or quasi-stationary post-flare coronal arches.     

The skin friction in the unsteady free-convection flow past an accelerated plate

In this paper the unsteady laminar free-convection flow of a viscous incompressible fluid, past an accelerated infinite vertical porous plate subjected to a constant suction (or injection) in considered. Numerical results for the skin-friction on the plate are obtained for the class of accelerated motions whose velocity is of the formU ₀ t ⁿ wheret is time,U ₀ a constant, andn is a positive integer. The skin friction tends to zero with increasingt when the Grashof number Gr=², the Prandtl number =1,n=0, and >0 which corresponds to suction.On leave of absence from the Department of Mathematics, University of Dhaka, Bangladesh.On leave from absence from the Department of Mathematics, University of Dar-es-Salaam, Tanzania.     

Reference models of sunspot chromospheres

Recent observational and theoretical studies of the structure of umbral chromosphres have led us to propose new models of the region. We combine space and ground based determinations of the densitytemperature structure of the transition region with existing Caii H, K, and IR triplet spectral data to establish relatively high density, gradient models of the sunspot chromosphere.Avrett in 1981 presented theSunspot Sunspot Model which can be characterized as a physically extended, low density, plateau model. However, in a similar study, the authors (Beebeet al., 1982) pointed out that the relatively high transition region pressures derived from space observations indeed are required to reproduce high resolution Caii spectral features. Studies of the umbral chromosphere as a resonant cavity for slow-mode magneto-acoustic waves producing umbral oscillations (Zhugzhdaet al., 1984) also lead to atmospheres of relatively small physical thickness, thus higher densities.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

The sources of large-scale heliospheric disturbances

Observations on a grid of 900 radio sources have been used to map and to track large-scale structures in the solar wind at distances of 0.6–1.5 AU from the Sun. Most of the disturbances were shells of enhanced density followed by high-speed streams lasting for several days, although more stable corotating interaction regions were also observed. Ninety-six disturbances were mapped during August 1978–September 1979 and those of the erupting stream-type were usually accompanied by shocks and geomagnetic activity if they encountered the Earth. Back-projection to the Sun indicated sources that were always associated with coronal holes. Possible associations with solar flares and disappearing filaments occurred but on many occasions no flare or filament activity was evident anywhere on the disc within a suitable time interval. It is concluded that erupting streams are transients generated by coronal hole activity. Evidence is presented which further suggests that coronal mass ejections of the curved-front variety may be identified with these erupting streams.