Confined Scroll Rings

  • Jan Frederik TotzEmail author
Part of the Springer Theses book series (Springer Theses)


Among self-organized spatio-temporal patterns rotating spiral-shaped waves are very common. This suggests, that their emergence must depend on general rules, that transcend microscopic details. As depicted in Fig. 2.1, an initially planar wave front can break up due to interaction with inhomogeneities in an active medium. The resulting wave features an open end far from any boundaries. Still, the excitation (fire) will spread from the current excited region to any surroundings that are not in their refractory, unexcitable (burnt) state. This means that the main front will continue forward, but at the wave tip the excitation can spread upwards in addition. While the tip continues on its pirouette-like motion, it becomes the source of excitation waves, that are periodically emitted into the medium. In this sense, the tip is the localized organizing center [1] of the delocalized spiral wave, that has a wavelength \(\lambda \) and rotation period T. Note that the oscillations at each location outside the spiral core are entrained to the rotation period of the spiral wave. Here, the non-equilibrium character manifests itself in the influx of external energy, that is required to return oscillators to their rest state (unburnt) so a neighboring excitation can restart the oscillation cycle.


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Authors and Affiliations

  1. 1.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany

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