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.     

Sunspot nests

For the period August 1959–December 1964 the Greenwich Photoheliographic Results were searched for sunspot nests. Such a nest is a sequence of sunspot groups that appear within a small area on the solar surface and that last for several months. The search procedure is described and data for 41 probable sunspot nests are given. At least three quarters of these nests appear to be real, and not chance clusters.The nests are the same type of activity sequences as the Fleckenherde discovered by Becker (1955) and the complexes of activity pointed out by Gaizauskas et al. (1983). The complexes of activity as defined by Bumba and Howard (1965) are different patterns, however; the relation between complexes and the nests is shown.Some properties of the nests are: (i) many nests appear as double structures; (ii) single nests and components of double nests are quite compact: the effective areas are comparable to those of medium-large sunspot groups; (iii) each nest rotates at its own steady rate about the Sun; (iv) the intrinsic scatter in the rotation rates is much larger than the trend in the differential rotation; (v) displacements in latitude are less than a few meters per second; (vi) many nests live for 6 to 15 Carrington rotation periods, the minimum lifetime is not yet determined; (vii) the fraction of the sunspot groups that are members of nests is large (at least 30%).     

Further considerations on contracting solar nebula

Prentice (1978a) in his modern Laplacian theory of the origin of the solar system has established the scenario of the formation of the solar system on the basis of the usual laws of conservation of mass and angular momentum and the concept of supersonic turbulent convection that he has developed. In this, he finds the ratio of the orbital radii of successively disposed gaseous rings to be a constant - 1.69. This serves to provide a physical understanding of the Titius-Bode law of planetary distances. In an attempt to understand the law in an alternative way, Rawal (1984) starts with the concept of Roche limit. He assumes that during the collapse of the solar nebula, the halts at various radii are brought about by the supersonic turbulent convection developed by Prentice and arrives at the relation: R _p= Ra^p, where R _pare the radii of the solar nebula at various halts during the collapse, R the radius of the present Sun and a = 1.442. a is referred here as the Roche constant. In this context, it is shown here that Kepler's third law of planetary system assumes the form: T _p = T ₀(a^3/2)^p, where T _p are the orbital periods at the radii R _p, T ₀ - 0.1216d - 3 h, and a the Roche constant. We are inclined to interpret T ₀' to be the rotation period of the Sun at the time of its formation when it attained the present radius. It is also shown that the oribital periods T _pcorresponding to the radii R _psubmit themselves to the Laplace's resonance relation.     

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.     

Static properties of galaxies in the Shapley-centaurus cluster

The data of Paper I (Doddet al., 1986), representing a catalogue of parameters measured for bright galaxies in field 444 of the Southern Sky Survey, are examined in a search for non-random effects. A global trend of bimodal alignment of galaxies in this field is found. This effect is present even for galaxies of large apparent ellipticity (e0.5) and is interpreted as revealing a real physical phenomenon on the large scale in this field. Analysis of nearest neighbouring pairs of galaxies reveals evidence also for small-scale interactions. The difference in apparent ellipticities between close pairs is larger than would be expected if the galaxies were randomly distributed. Nearest neighbouring galaxies also show a strong preference to be aligned with their major axes parallel. The results are discussed with regard to theories for galaxy formation.     

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.     

The production of light elements in unconventional cosmologies with VMOs

The abundances of light elements (deuterium, helium and lithium) are calculated in unconventional cosmologies in which these elements are produced by interaction of fast -particles ejected by massive pregalactic stars with a purely hydrogenous cosmological substrate. The number density and energetics of such stars needed for suitable production of light elements are estimated. It is shown that the models always lead to overproduction of lithium. The intensity of ultraviolet, X-ray, and -ray emission caused by explosions of pregalactic massive stars is calculated. The distortions of cosmic background radiation by Compton losses of electrons heated by explosive stars are also calculated.     

Comparison of analytical and numerical calculations of the first class periodic orbits

The analytic construction of the direct periodic orbits in the circular 3-body problem is given in explicit form to the linear terms in . It is shown to be in good agreement with the numerically found orbits for large values of .