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671.
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:
- 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.
- 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.
- The total area of non chaotic regions is greater for symmetric billiards.
- 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.
- 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.
672.
R. A. Howland 《Celestial Mechanics and Dynamical Astronomy》1986,39(4):329-340
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. 相似文献
673.
Marie K. McCabe Zdeněk F. Švestka Russell A. Howard Bernard V. Jackson Neil R. Sheeley Jr. 《Solar physics》1986,103(2):399-408
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. 相似文献
674.
Some attempts of polarimetric sounding of Comet Halley will be undertaken from the flyby probes. In order to facilitate the final planning and the future interpretation of these experiments we have done a thorough analysis of practically all available polarimetric observations. An emphasis is made on interpretation attempts and their discussion. The results of the phase dependence of polarization investigations are presented covering a wide range of phase angles . The chief peculiarities of this dependence are: maximum polarization at = 90, diminishing through zero at 20, negative values up to several per cent and a final growth to zero at zero . A division into gaseous and dusty comets on polarimetric basis is revealed. The wavelength dependence of polarization is discussed. The numerous results of detailed polarimetry are compared to the negative results of attempts to detect the elliptical polarization. New observational problems arising from the evidence given by the negative polarization at small phase angles and by the opposition effect recently discovered are discussed. 相似文献
675.
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. 相似文献
676.
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. 相似文献
677.
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. 相似文献
678.
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. 相似文献
679.
Vladimir A. Osherovich Erast B. Gliner Israel Tzur Michael L. Kuhn 《Solar physics》1985,97(2):251-266
A nonpolytropic model of a polar coronal hole at 2 R
R 5 R
is constructed. Our main assumptions are: (1) the magnetic structure of the Sun can be described by a combination of dipole-like and radial fields; (2) in the magnetically dominated region [(v
2/2) < (B
2/8)] the influence of the outflow on the magnetic structure is negligible. The magnetic and thermodynamic structures are obtained by solving the force balance equation for plasma with the observationally derived electron density. Profiles of velocities in the acceleration regime are presented and the influence of the outflow on the thermodynamic structure of the solar corona above the polar region is discussed.This paper is the first part of a joint project of the Space Environment Laboratory, the Joint Institute for Laboratory Astrophysics, and the High Altitude Observatory, NCAR. The second paper by Munro and Tzur is in preparation.Work done while at the Space Environment Laboratory, NOAA, ERL, Boulder, CO 80303, U.S.A.1982–83 Visiting Fellow at the Joint Institute for Laboratory Astrophysics, National Bureau of Standards and University of Colorado.The National Center for Atmospheric Research is sponsored by the National Science Foundation.Visitor at NCAR. 相似文献
680.
Profiles of the O i 7773 triplet obtained at a spatial resolution 0.5 are analyzed using spectral line inversion techniques. Inferences are made about departures from LTE, convective velocity fields, and solar temperature fluctuations. 相似文献