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Anmerkungen über das uneingelöste Rekonstruktionsproblem in Curriculumentwicklung und Fachdidaktik
(1995)
Flexibilisierung und Individualisierung der Arbeitszeit setzt sich immer mehr durch. Arbeitsmarktpolitische und individuelle Gründe sprechen jedenfalls dafür. Auch die Tarifpartner zeigen sich immer aufgeschlossener, obwohl der rechtliche Geltungsrahmen vielfach noch gar nicht klar abgesteckt ist. Die zahlreichen Praxisbeispiele machen Mut, auf dem begangenen Weg fortzufahren. In diesem Buch werden wertvolle Informationen geliefert, die sowohl aus individueller als auch aus betrieblicher Sicht den Entscheidungsprozeß für eine zunehmende Arbeitszeitindividualisierung und -flexibilisierung erleichtern.
Basismodelle des Unterrichts
(1995)
Excerpt: Hasidic Ashkenazi literature is known to scholars of Jewish religion as one of the most prolific sources of medieval Jewish magic or magical beliefs. This is all the more astonishing as the non esoteric writings of the Hasidey Ashkenaz represent a rather traditional Jewish piety as known to us from talmudic sources. Considering this duality of an almost traditional Jewish piety on the one hand and very distinct magic tenets on the other, we may ask whether the Hasidey Ashkenaz themselves perceived any difference between magic and religion. There are indeed a number of modern historians of religion who completely deny the validity of such a distinction, for in most historical religions magic and religion are in fact intertwined to a certain degree, thus permitting almost no differentiation between the two.
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).
Contents: I. Algorithms 1. Theoretical Backround 2. Numerical Procedures 3. Graph Representation of the Solutions 4. Applications and Example II. Users' Manual 5. About the Program 6. The Course of a Qualitative Analysis 7. The Model Module 8. Input description 9. Output Description 10. Example 11. Graphics