Helical deformation of the filament of a scroll wave

Abstract

In three-dimensional excitable systems scroll waves may lose their originally straight shape through different instabilities. In experiments, the formation of zigzag-shaped or helical filaments is often observed. Such a deformation may be due to either a twist-induced instability or a 3D meandering instability. We performed a systematic study using a Belousov-Zhabotinsky (BZ) system with a vertical gradient of excitability and determined the necessary twist for the onset of undulation in the filament. Thus, we demonstrate that in the case of a BZ system with a gradient parallel to the filament, the deformation of the filament is induced by a twist-induced instability.

Interaction of a Pair of Parallel Scroll Waves

“…Hence, the scroll wave twisted with time. 13,14 Once the twist exceeded the critical value, the filament became helical. 14 Pairs of scroll waves were found to behave similarly.…”

“…13,14 Once the twist exceeded the critical value, the filament became helical. 14 Pairs of scroll waves were found to behave similarly. This is shown in Figure 3 for a pair of co-rotating scroll waves in a BZ medium with a gradient of excitability parallel to the filaments.…”

“…The true dynamics in 3D remains hidden. However, the 3D dynamics of scroll waves and their filaments can be monitored in experimental model systems by optical tomography. , This technique requires transparent experimental model systems, such as the Belousov–Zhabotinsky (BZ) reaction, which allows for detailed experimental studies of scroll wave dynamics. − …”

Three-dimensional convection-driven fronts of the exothermic chlorite-tetrathionate reaction

“…When this reactive interface is driven by an exothermic reaction, multicomponent convection can evolve due to the interplay of thermal and solutal contri- where the various dynamics of the filaments in scroll waves represent behavior absent in two dimensions [2][3][4] , followed by studies of Turing patterns. 5,6 The introduction of the third dimension makes a difference even in the behavior of the simplest chemical pattern, a propagating reaction front defined by the narrow zone spatially separating the reactant and the autocatalytic product: a critical radius for local initiation exists for cubic autocatalysis only in three dimensions.…”

Twists of Opposite Handedness on a Scroll Wave

“…It causes an increase in proton concentration and, hence, in excitability of the BZ medium with the height of the reactor [27]. Furthermore, SDS suppresses or delays CO 2 bubble formation [27][28][29], enhancing the observation of 3D patterns by optical tomography [5,18,27,[30][31][32][33].…”