The Socially Situated Dynamics of Children’s Learning Processes in Classrooms:What Do We Learn from a Complex Dynamic Systems Approach?

This article concentrates on the question what kind of model-conceptual and statistical -can serve as a good working model for the study of learning and teaching processes qua processes. We claim that a good way of answering this question is to begin by observing a teaching and learning process as, where, and when it occurs. In addition, a conceptual model of intertwined learning-teaching processes is discussed, and dynamic modeling as an approach to theory formation about teaching-learning processes. The focus lies on the evolution term, the timescale of interaction processes, state space as a perspective on teacher-student interaction dynamics, and the principle of agency. Finally, an empirical approach to studying teaching-learning processes is illustrated by means of a case study, focusing on the use of cluster analyses techniques. In the Conclusion and Discussion section, further perspectives on theory building and empirical research are discussed

Self organized mode locking effect in superconductor / ferromagnet hybrids

The vortex dynamics in a low temperature superconductor deposited on top of a rectangular array of micrometer size permalloy triangles is investigated experimentally. The rectangular unit cell is such that neighboring triangles physically touch each other along one direction. This design stabilizes remanent states which differ from the magnetic vortex state typical of individual non-interacting triangles. Magnetic Force Microscopy images have revealed that the magnetic landscape of the template can be switched to an ordered configuration after magnetizing the sample with an in-plane field. The ordered phase exhibits a broad flux flow regime with relatively low critical current and a highly anisotropic response. This behavior is caused by the spontaneous formation of two separated rows of vortices and antivortices along each line of connected triangles. The existence of a clear flux flow regime even for zero external field supports this interpretation. The density of induced vortex-antivortex pairs is directly obtained using a high frequency measurement technique which allows us to resolve the discrete motion of vortices. Strikingly, the presence of vortex-antivortex rows gives rise to a self organized synchronized motion of vortices which manifests itself as field independent Shapiro steps in the current-voltage characteristics.Comment: 9 pages, 11 figure

Vortex rectification effects in films with periodic asymmetric pinning

We study the transport of vortices excited by an ac current in an Al film with an array of nanoengineered asymmetric antidots. The vortex response to the ac current is investigated by detailed measurements of the voltage output as a function of ac current amplitude, magnetic field and temperature. The measurements revealed pronounced voltage rectification effects which are mainly characterized by the two critical depinning forces of the asymmetric potential. The shape of the net dc voltage as a function of the excitation amplitude indicates that our vortex ratchet behaves in a way very different from standard overdamped models. Rather, as demonstrated by the observed output signal, the repinning force, necessary to stop vortex motion, is considerably smaller than the depinning force, resembling the behavior of the so-called inertia ratchets. Calculations based on an underdamped ratchet model provide a very good fit to the experimental data.Comment: 5 pages, 4 figure

Voltage rectification in two dimensional Josephson junction arrays

We study numerically the directed motion of vortices (antivortices) under an applied ac bias in two-dimensional Josephson junction arrays (JJA) with an asymmetrically modulated periodic vortex pinning potential. We find that the ratchet effect in large 2D JJA can be obtained using the RSJ model for the overdamped vortex dynamics. The rectification effect shows a strong dependence on vortex density as well as an inversion of the vortex flow direction with the ac amplitude, for a wide range of high magnetic field around f=1/2 (f being the vortex density). Our results are in good agreement with very recent experiments by D.E. Shalom and H. Pastoriza [Phys. Rev. Lett. 94, 177001, (2005)].Comment: 4 pages, 4 figures, Proceedings Vortex IV Conference, September 3-9, 2005, Crete, Greece. To appear in Physica