Schematic drawing of the experimental setup which allows wave detection by optical tomography and the controlled initiation of half-spherical waves using two silver wires. The viscous reaction system can be remixed using a magnetic stir bar. “M” denotes an electric motor which is used to rotate the sample cuvette for detection purposes.
Tomographic reconstruction of a scroll ring in the CHD-BZ reaction. (a) Single snapshot of the sample during its rotation around a vertical axis. (b) Sinogram obtained by combining absorption profiles at various observation angles but constant height . (c) Absorption in a horizontal slice obtained from the sinogram data using filtered back-projection. (d) Repetition of the reconstruction process at different heights yields the three-dimensional absorption field, which is shown as a fan of slices.
(a)–(d) Consecutive snapshots of merging waves in a thin layer of the CHD-BZ reaction. A pair of spiral waves nucleates from the second wave front emitted by the target pattern. Initial concentrations: , , and . Image area: . Time between frames: 27, 33, and . Reprinted from Ref. 31 . (e)–(h) Sequence of tomographically reconstructed wave patterns showing the nucleation of a scroll ring. Initial concentrations: and . Volume of boxes: . Time between frames: 38, 19, and .
Two consecutive reconstructions of a collapsing and rightward moving scroll ring in the CHD-BZ reaction. Initial concentrations: and . Volume of boxes: . The volume fraction of polyacrylamide solution is 26.3%. Time between frames: .
Image sequence showing the formation of a pair of counter-rotating scroll rings during the collision of four nonrotating, approximately half-spherical wave fronts. The filaments of the vortex pairs are two closely stacked circles. The black arrows in (c) mark small, chemically reduced regions that are connected three-dimensionally along a narrow ring. Initial concentrations: and . Image area: . Time between frames: 18, 17, 12, 9, and .
Negative filament tension in the CHD-BZ reaction inducing growth and buckling of initially circular vortex filaments. (a),(b) Two consecutive images of a scroll ring. Image size: . Time between frames: . (c),(d) Evolution a small scroll ring filament. Time between frames: . (d),(e) Evolution a larger scroll ring filament. Time between frames: . Initial concentrations: and .
Left column: Open circles are the measured distances of the filament from its best-fit circle at three consecutive times: (a) , (b) , and (c) . The polar angle is defined with respect to the circle’s center. The circles’ normal vector is fitted only for the initial filament and kept constant for all subsequent data sets. The solid curves are the sums of the corresponding first four Fourier modes. Right column: Plots (d)–(f) show the amplitudes of the first five Fourier modes as computed from the corresponding data in (a)–(c), respectively. Initial concentrations as stated in Fig. 6 .
Amplitude of the first three Fourier modes as a function of time as measured for the expansion of a typical scroll ring. The inset shows the temporal evolution of the Fourier phases for the first two modes. Circles, squares, and diamonds represent data for , 2, and 3, respectively. Initial concentrations as stated in Fig. 6 .
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