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We report on bifurcation studies for the incompressible magnetohydrodynamic equations in three space dimensions with periodic boundary conditions and a temporally constant external forcing. Fourier reprsentations of velocity, pressure and magnetic field have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then special numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. In a part of the calculations, in order to reduce the number of modes to be retained, the concept of approximate inertial manifolds has been applied. For varying (incereasing from zero) strength of the imposed forcing, or varying Reynolds number, respectively, time-asymptotic states, notably stable stationary solutions, have been traced. A primary non-magnetic steady state loses, in a Hopf bifurcation, stability to a periodic state with a non-vanishing magnetic field, showing the appearance of a generic dynamo effect. From now on the magnetic field is present for all values of the forcing. The Hopf bifurcation is followed by furhter, symmetry-breaking, bifurcations, leading finally to chaos. We pay particular attention to kinetic and magnetic helicities. The dynamo effect is observed only if the forcing is chosen such that a mean kinetic helicity is generated; otherwise the magnetic field diffuses away, and the time-asymptotic states are non-magnetic, in accordance with traditional kinematic dynamo theory.
We report on bifurcation studies for the incompressible Navier-Stokes equations in two space dimensions with periodic boundary conditions and an external forcing of the Kolmogorov type. Fourier representations of velocity and pressure have been used to approximate the original partial differential equations by a finite-dimensional system of ordinary differential equations, which then has been studied by means of bifurcation-analysis techniques. A special route into chaos observed for increasing Reynolds number or strength of the imposed forcing is described. It includes several steady states, traveling waves, modulated traveling waves, periodic and torus solutions, as well as a period-doubling cascade for a torus solution. Lyapunov exponents and Kaplan-Yorke dimensions have been calculated to characterize the chaotic branch. While studying the dynamics of the system in Fourier space, we also have transformed solutions to real space and examined the relation between the different bifurcations in Fourier space and toplogical changes of the streamline portrait. In particular, the time-dependent solutions, such as, e.g., traveling waves, torus, and chaotic solutions, have been characterized by the associated fluid-particle motion (Lagrangian dynamics).
The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.
Inhalt: Begriffsklärung -Ökologisches Marketing -Dialog -Chancen -Umweltmanagement Verankerung einer Dialogorientierung im Normativen Umweltmanagement: Das dialogische Verantwortungskonzept Dialogchancen im Strategischen Umweltmanagement -Anspruchsgruppenmanagement -Risiko- und Krisenmanagement -Konflikt- und Konsensusmanagement -Issue-Management Dialogische Verfahren und Techniken der ökologischen Kommunikationspolitik
Aus der Einleitung: In der industrialisierten Volkswirtschaft ist die Energiewirtschaft einer der bedeutendsten Sektoren. Die Elektrizitätswirtschaft als Zweig der Energiewirtschaft umfaßt die gesamte Erzeugung, Fortleitung und Abgabe elektrischer Energie. Die Elektrizitätsversorgung ist - neben den nationalen, historischen, politischen und rechtlichen Besonderheiten - durch maßgebliche physikalische Charakteristiken in zweierlei Hinsicht geprägt: Die nur durch hohen wirtschaftlichen Aufwand gekennzeichnete Speicherbarkeit sowie die ausschließliche Leitungsgebundenheit der Transportwege stellen die primären Determinanten der Elektrizitätsversorgung dar. Die faktisch nicht vorhandene Speicherbarkeit verlangt nach einem, dem Nachfrageverhalten synchronen Angebotsverhalten. Die Leitungsgebundenheit bedingt zum einen kapitalintensive Investitionen, zum anderen eine langfristige Planung hinsichtlich der prognostizierten Nachfrageveränderungen, um eine sichere Versorgung mit elektrischer Energie zu gewährleisten. Die Versorgungssicherheit ist neben den physikalischen Gegebenheiten ein determinierendes primäres Ziel in der Elektrizitätswirtschaft.
Part of the intorduction: The task of writing a reliable and convincing paper on this topic is a very uneasy one because it is threefold: one has to know at least a bit about the agricultural sector, biology (or more precisely ecology), and about the sometimes beneficial but often distorting consequences of human activities. And all that has to be judged from the perspective of an economist who is aware of the steadily increasing uncertainties which are closely connected with post-modem sciences. Especially with regard to global, but also regional environmental issues, neither the conventional applied sciences nor the traditional professional consultancy deliver promising results. Today scientists have to tackle problems which are created by political necessities overwhelmingly caused by short-term human behavior, due in part to a serious lack of information on the longterm behavioral consequences. In these issues, typically, information stacks are high, scientific facts uncertain, individual as well as collective values disputed, and political decisions very urgent. "In general, the post-normal situation is one where the traditional opposition of 'hard'facts and 'soft' values is inverted. Here we find decisions that are 'hard' in every sense, for which the scientific inputs are irremediably 'soft'" (FUNTOWICZ/RAVETZ, 1991, p. 138).
The bifurcation behaviour of the 3D magnetohydrodynamic equations has been studied for external forcings of varying degree of helicity. With increasing strength of the forcing a primary non-magnetic steady state loses stability to a magnetic periodic state if the helicity exceeds a threshold value and to different non-magnetic states otherwise.
Inhalt: Polnische Staatsverschuldung vor 1990 - Auslandsverschuldung - Inlandsverschuldung Die Entwicklung der Staatsverschuldung in der Transformationsphase - Entwicklung der Auslandsverschuldung in den Jahren 1990 - 1994 - Entwicklung der Inlandsverschuldung in den Jahren 1990 - 1994 Szenarien für die Entwicklung des Schuldendienstes - Die Gesamtverschuldungsprognose in Inlandswährung - Szenarien für die Staatseinnahmenentwicklung - Gegenüberstellung der Staatseinnahmen und des Gesamtschuldendienstes - Entwicklung des Auslandsschuldendienstes in Auslandswährung Zur Realitätsnähe der Szenarien
Inhalt: Wettbewerb der Regionen Marketing-Konzept für Regionen -Die Region als Produkt und Unternehmung -Regionales Management -Phasen zur Entwicklung eines Regionen-Marketing-Konzepts Eine empirische Studie zur Region Brandenburg -Theorien zur Standortwahl privater Unternehmen -Design und Ergebnisse der empirischen Studie: Standorteignung und Standortanforderungen, Unternehmenstypologie nach marketingrelevanten Kriterien, Imageanalyse, Resümee