Winfree spirals

At time zero (top) the circular wave is subject to a plane parallel electric (ohmic) field. The part of the circle propagating towards the negative electrode is annihilated beyond a critical field strength and a crescent wave is observed to propagate (bottom). Note the free ends which are stabilized by the applied field and which become Winfree spirals when the field is turned off. (See Ref. 13 for details.)... 

A. Winfree. Spiral waves of chemical activity. Science, 175 634-636, 1972. 

A classical example of reaction-diffusion processes is the Belousov-Zhabotinsky reaction that forms moving Winfree spirals in a two-dimensional reactor. In this reaction the many sequential reaction steps comprise a very complex system, yet the spirals can be simulated with a very simple three-state cellular automaton. This model accounts for the morphology given certain initial conditions but it does not... 

Winfree A T 1972 Spiral waves of chemical activity Science 175 634-6... 

Spiral waves also arise in the oxidation of carbon-monoxide on platinum surfaces [10]. In 1972 they have been discovered by Winfree [79] in the photosensitive Belousov-Zhabotinsky (BZ) reaction, see for recent investigations for example [83, 84, 87]. Both reactions are studied in the SFB 555. The classical BZ reaction is a catalytic oxidation of malonic acid, using bromate in an acidic environment. Experimentally it exhibits well reproducible drift, meander and chaotic motions of the spiral wave and its tip. 

Since with increasing arc length the front curvature goes rapidly to zero, it is not necessary to use this rather complicated approach to determine the front shape far away from the rotation center. A. Winfree was the first who suggested to approximate the spiral front by an Archimedean spiral [2]... 

The spiral or concentric waves observed for the spatial distribution of cAMP (fig. 5.6) present a striking analogy with similar wavelike phenomena found in oscillatory chemical systems, of which the Belousov-Zhabotinsky reaction (fig. 5.7) provides the best-known example (Winfree, 1972a). 

Winfree, A.T. 1991b. Varieties of spiral wave behavior An experimentalist s approach to the theory of excitable media. Chaos 1 303-34 and (Erratum) 2 273 (1992). 

Winfree has (1974a) presented an interesting model of excitable kinetics, f(x), and computed spiral wave solutions to Eq. (10) in two spatial dimensions. He borrows the kinetics from the theory of action potentials in nerve membranes (FitzHugh, 1961 McKean, 1970)... 

Winfree, A. T. (1972). "Spiral wayes of chemical activity." Science 175, 634-636. 

Arthur Winfree, a biologist with an interest in spatial and temporal patterns, had attended the Prague conference and had decided to pursue the study of pattern formation in the BZ reaction. In 1972, the cover of Science magazine featured Winfree s photo of spiral wave patterns in the BZ reaction (Winfree, 1972). Figure 1.7 shows such patterns. Field and Noyes immediately saw how to understand the development of such patterns with the aid of the FKN mechanism, and they published an explanation the same year (Field and Noyes, 1972). 

Figure 6.10 Meander patterns in the Keener-Tyson Oregonator model. Below the solid line, spiral waves fail to propagate. (Reprinted with permission from Jahnke, W. Winfree, A. T. 1991. A Survey of the Spiral-Wave Behaviors in the Oregonator Model, /nt. J. Bifurc. Chaos /, 445-466. cC 1991 World Scientific Publishing.)...

Winfree, A. 1972. Spiral Waves of Chemical Activity, Science 175, 634-635. 

Winfree, A. T. 1991. Varieties of Spiral Wave Behavior An Experimentalist s Approach to the Theory of Excitable Media, Chaos 1, 303-334. 

Winfree, A. T. (1972) Spiral waves of chemical activity. Science 175, 634 Winfree, A. T. (1974a) Rotating chemical reactions. Sci. Am. 230, 82... 

The survey of spiral-wave behavior in the Oregonator model by Jahnke and Winfree [41] revealed a number of trajectories with high rotation symmetry in a region of the s, f) plane marked with the name meander by the authors. In this region the path of the spiral tip forms closed floral patterns for specific choices of the parameters (e, / ). The center of these regular patterns have... 

Fig. 1. Scroll wave filaments (dashed curves) move slowly through space as the scroll rotates, (a) An elongated spiral becomes symmetric, and (b) an elongated ring becomes circular and then disappears (after Winfree [10]). (c) A scroll ring shrinks and disappears, and (d) a figure-eight ring splits into two circular rings which then shrink and disappear (after Welsh [17]).

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