Scroll Wave Filaments Terminate in the Back of Traveling Fronts

Three-dimensional spiral waves in an excitable reaction system: initiation and dynamics of scroll rings and scroll ring pairs

We report experimental results on spiral and scroll waves in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. The propagating concentration waves are detected by two-dimensional photometry and optical tomography. Wave pulses can disappear in front-to-front and front-to-back collisions. This anomaly causes the nucleation of vortices from collisions of three nonrotating waves. In three-dimensional systems, these vortices are scroll rings that rotate around initially circular filaments. Depending on reactant concentrations, the filaments shrink or expand indicating positive and negative filament tensions, respectively. Shrinkage results in vortex annihilation. Expansion is accompanied by filament buckling and bending, which is interpreted as developing Winfree turbulence. We also describe the initiation of scroll ring pairs in four-wave collisions. The two filaments are stacked on top of each other and their motion suggests filament repulsion.

Chemical oscillations and waves in the catalyzed bromate-pyrocatechol reaction

Long time series of temporal oscillations and wave formation are observed in the catalyzed bromate-pyrocatechol reaction conducted in a batch reactor, in which the induction time is insensitive to the presence of ferroin but is greatly shortened by Ce(III) or Mn(II). On the other hand, the number of oscillations is significantly increased by ferroin, while it is less sensitive to Ce(III) and Mn(II). The ferroin-catalyzed system also exhibits strong photosensitivity, in which illumination could quench the oscillatory behavior. A phase diagram illustrates that the oscillatory behavior of the studied system is more sensitive to the ratio of [pyrocatechol]/[bromate] than their absolute concentrations. Reactions conducted in a spatially extended medium show that the ferroin-catalyzed system supports a two-stage pattern formation with the wave activity surviving for up to 10 h.

Wave-pinned filaments of scroll waves

Scroll waves are three-dimensional excitation patterns that rotate around one-dimensional space curves. Typically these filaments are closed loops or end at the system boundary. However, in excitable media with anomalous dispersion, filaments can be pinned to the wake of traveling wave pulses. This pinning is studied in experiments with the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction and a three-variable reaction-diffusion model. We show that wave-pinned filaments are related to the coexistence of rotating and translating wave defects in two dimensions. Filament pinning causes a continuous expansion of the total filament length. It can be ended by annihilating the pinning pulse in a frontal wave collision. Following such an annihilation, the filament connects itself to the system boundary. Its postannihilation shape that is initially the exposed rim of the scroll wave unwinds continuously over numerous rotation periods.

Negative filament tension of scroll rings in an excitable system

Scroll rings are three-dimensional spiral waves of excitation that rotate around circular filaments. In a modified Belousov-Zhabotinsky reaction, these filaments expand, buckle, and build up gradients in rotation phase. The instability is caused by negative filament tension (-4.3x10;{-4}cm;{2}s) . Initial deformations are strongest in the direction normal to the filament's osculating plane, and their growth rates decrease rapidly with increasing wave number.