Wolfram Neutsch

The minimal 5-representation of Lyons' sporadic group

The Lyons simple group was first constructed by Sims [5] as a permutation group on 8835156 points. This representation is, because of its size, not very useful for calculating in the group. In this paper we obtain a representation of the Lyons group of dimension 111 over Fs. After finding three generators, the group G2(5) is identified as a subgroup, and then the matrices are proved to generate the Lyons group by checking the relations Sims used in his original construction.

The interstellar wind as a cause for longitudinal solar wind asymmetries

Abstract We show here that the relative motion of the solar system with respect to the ambient interstellar plasma enforces a clearly pronounced upwind/downwind momentum flow asymmetry in the shocked solar wind. With the help of an analytic description of this subsonic flow regime taken from Parker (1963, Interplanetary Dynamical Processes . Interscience, New York) we were able to quantitatively determine the expected momentum flow asymmetries and the forces exerted on closed surfaces from which such a flow is originating. Assuming that the up/down asymmetry can be forwarded from the subsonic to the supersonic solar wind through the heliospheric shock by that wind component behaving subsonically everywhere, i.e. electrons, we arrive at corresponding asymmetric outer boundary conditions which the adapted supersonic solar wind solutions have to match. We shall prove in this paper that via the subsonic solar wind electrons, the solar wind expansion actually realized can be strongly influenced by the asymmetric outside LISM momentum flow conditions. Though this situation cannot be consistently treated with existing solar wind models, we nevertheless want to give an idea of its consequences. With the help of a conventional two fluid solar wind model we produce such solutions here that in a quantitative form show longitudinal solar wind asymmetries even in the region between the coronal basis and the Earths orbit. In order to confirm the existence of such asymmetries we propose to monitor the solar wind momentum flow along the orbit of the Earth. We also calculate the braking rate of the solar system connected with such a momentum flow.

The influence of interstellar medium on subsonic stellar motions

It is not a trivial problem to imagine how a spherical high-pressure balloon with supersonic gas jets leaving from pores densely distributed on its surface can be influenced by an ambient gas flow. The relative motion of such a balloon can be controlled by a corresponding rearrangement of the gas outflow into an aspherical configuration. A similar problem is connected with stars driving a supersonic stellar wind and moving relative to the interstellar medium. As we shall show, the adapted circumstellar flow leads to an upwind-downwind pressure asymmetry balancing the momentum loss that is braking such stars. The opposite process — i.e., acceleration — may occur if luminous stars are closely associated and their wind systems interfere with each other. This should lead to a mutual repulsion.

Expanding envelopes of binary stars

HD 152270 is a binary system containing an O5 star and a Wolf-Rayet companion of spectral type WC 6–7. The prominent spectral features are emission lines of ionized helium and carbon which are generated in an expanding shell surrounding both stars. One of these-theCiii line at λ5696 Å-is of great interest because it is optically thin and not severely blended. We developed two simple descriptions for the envelope. It is the aim of this paper to discuss the validity of one of them, called the ‘cone model’. The other one, the ‘two-centre’ approximation, will be studied in a forthcoming article (Neutsch and Schmidt, 1985). The cone model is compared with a more physical one which is based on a Monte-Carlo simulation of the stellar wind flow and is believed to be a much better approximation to reality. Furthermore, we are able to test the assumptions of the cone model by quantitatively reducing spectral observations of HD 152270.

Simple integrals for solving of Kepler's equation

In this paper we derive integral representations for the solution of Keplers equations for elliptic and hyperbolic orbits. The integrands consist merely of rational expressions of the integration variable and its exponential.

Lattice integration on the 7-sphere

Abstract Recently, the 7-sphere S7 has been the subject of increased interest for mathematicians and theoretical physicists. In this paper we present integration algorithms of several different orders up to 19 which require no more than a few thousand points. In this respect, our formulae are highly superior to standard methods, e.g., Gaussian integration or the use of spherical t-designs.

Area-preserving Poincar mappings of the unit disk

The best way to investigate the long-time behaviour of dynamical systems is to introduce an appropriate Poincaré mapping P and study its iterates.Two cases of physical interest arise: Conservative and dissipative systems. While the latter has been considered by a great many authors, much less is known for the first one (according to Liouvilles theorem, here the mapping leaves a certain measure in phase space invariant). In this paper, we concentrate our attention on compact phase spaces (or, rather, surfaces of section). This assumption is mathematically useful and physically reasonable.We consider the simplest possible (2-dimensional) systems whehre the phase space is the compact unit disk D in ℝ2. A family of simple area-preserving mappings from D onto itselves will be given and discussed in detail.It is shown that general characteristics of the dynamics are quite similar to those of e.g. the Hénon-Heiles system, while other features, as the structure of invariant curves, are different.