Phototaxis of Spiral Waves

Markus, Mario; Nagy-Ungvárai, Zs.; Hess, Benno

doi:10.1126/science.257.5067.225

Cited by 81 publications

(44 citation statements)

References 23 publications

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“…Temporal resonance [6], drift of vortices due to parameter gradients [7,8] or external fields [9], and anchoring on localized defects [10] are among the most studied effects.…”

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confidence: 99%

Brownian Motion of Spiral Waves Driven by Spatiotemporal Structured Noise

et al. 2000

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Spiral chemical waves subjected to a spatiotemporal random excitability are experimentally and numerically investigated in relation to the light-sensitive Belousov-Zhabotinsky reaction. Brownian motion is identified and characterized by an effective diffusion coefficient which shows a rather complex dependence on the time and length scales of the noise relative to those of the spiral. A kinematically based model is proposed whose results are in good qualitative agreement with experiments and numerics. PACS numbers: 82.40.Bj, 05.45.Jn, 47.54. + r Spirals are generic structures in extended nonequilibrium systems. They are characteristic of many reactiondiffusion systems [1], the most paradigmatic experimental example being the Belousov-Zhabotinsky (BZ) reaction [2], and they have been observed in systems as complex as the heart muscle associated to cardiac fibrillation [3,4]. Spiral patterns appear also as elementary solutions of the complex Ginzburg-Landau (CGL) equation [5].Beyond the standard description of spiral waves, their response to spatial and/or temporal forcing has been largely analyzed. Temporal resonance [6], drift of vortices due to parameter gradients [7,8] or external fields [9], and anchoring on localized defects [10] are among the most studied effects.On the other hand, the influence of random heterogeneities on extended excitable systems has recently attracted much attention. Noise as an initiator of new spatial structures [11][12][13], or sustaining wave propagation in subexcitable media [14][15][16], is a subject of much theoretical and experimental interest. Complementarily, the role of superimposed disorder on preexisting spatiotemporal patterns has been examined, in relation to propagating pulses [17], to the dynamics of CGL spirals [18] and 3D structures [19].In this paper, we study the effect of a spatiotemporal structured noise on the motion of a spiral wave for the photosensitive BZ reaction. In the absence of randomness, the spiral tip rotates quasirigidly around its core, with no net translational mobility. When the noise is switched on, Brownian diffusion of the spiral is observed, characterized by a nonmonotonous dependence on the parameters of the noise. These observations are confirmed numerically using a two-variable Oregonator model. The analysis is completed by proposing a simple theoretical model based on a kinematic approach [20], capturing the basic features observed in experiments.Experiments were carried out in a Petri dish of 9 cm diameter. The catalyst, ruthenium bipyridil, is immobilized in a thin, 1 mm thick, film of silica gel, prepared as in [21].A solution of catalyst-free BZ reaction (initial concentrations 0.18M KBr, 0.33M malonic acid, 0.39M NaBrO 3 , and 0.50M H 2 SO 4 ) was poured onto the gel. The temperature was kept constant at 25 6 1 ± C. Spatiotemporal noise is introduced by projecting on to the Petri dish the desired patterned illumination, controlling the excitability of the system, by means of a video projector (SONY CPJ-D500). Experiments were capt...

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“…Temporal resonance [6], drift of vortices due to parameter gradients [7,8] or external fields [9], and anchoring on localized defects [10] are among the most studied effects.…”

mentioning

confidence: 99%

Brownian Motion of Spiral Waves Driven by Spatiotemporal Structured Noise

et al. 2000

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“…The travelling and spiral waves here show a similar behaviour to waves in prebiotic evolution 6 , in host-parasitoid systems 7 , as well as in excitable media (see Refs 4,[8][9][10] and references therein) such as chemical reactions, heart muscle and epidemics. In the latter, the black, dashed and white regions shown in Fig 3b, correspond to excited, refractory (or immune) and excitable (or resting) states, respectively.…”

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confidence: 69%

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Markus¹,

Schulz²,

Goles³

2002

ScienceAsia

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We present an evolutionary model that marks an encounter of two seemingly unrelated disciplines: population dynamics and number theory. Assuming mutations and selection of predators and prey, we show that prey cycles with non-prime lengths are unstable, while cycles with prime lenghts are stable. Allowing arbitrarily long cycles, this model is a number-theoretical tool for the calculation of large prime numbers. An extension of this purely temporal process to an evolutionary game on a spatial array leads to homogeneity, or to travelling or spiral waves having a predominance of prime prey cycle lengths. These results may be related to the appearance of cicadas (genus Magicicadae) every 13 or 17 years.

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“…Quite recently, it was found that light induces oscillations in the H 2 O 2-Fe(CN) 6 4-system in a continuously stirred tank reactor (CSTR). 8,9 As far as Ru(II)-catalyzed BZ systems are concerned, light works both as an inhibitor and promotor of temporal 4,[10][11][12][13][14][15][16] and spatial [17][18][19][20][21][22] oscillations. The work dealing with the influence of light on the Ru(II)-catalyzed BZ systems can be divided into two groups.…”

Section: Introductionmentioning

confidence: 99%

Influence of Visible Light and Malonic Acid Derivatives on the Autocatalytic Oxidation of Ru(II) by Bromate Ions

2002

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The influence of visible light on the autocatalytic oxidation of Ru(II) by bromate ions has been investigated. The inflection time (IT) was measured in darkness, at constant illumination, or as a function of the length of a perturbing light pulse. Measurements were performed without organic substrate, as well as in the presence of the malonic acid derivatives HOOC-CHR-COOH (RMA), with R being H, methyl-, ethyl-, n-butyl-, or the benzyl-group. The presence of RMA influences the length of the inflection time in darkness and for light-perturbed conditions. In the presence of benzylmalonic acid (BzMA), small amplitude oscillations are observed in darkness at the end of the autocatalytic oxidation of Ru(II). The most pregnant effects of RMA are observed by malonic acid (MA). At constant illumination, the inflection time is found to increase with increasing MA concentration and small-amplitude oscillations can even be observed in the preexponential phase of the Ru(II) oxidation. Model calculations based on a modified Noyes-Field-Thompson mechanism are in accordance with experimental observations. The calculations suggest that the small-amplitude oscillations observed in the BzMA and MA systems are due to second-order organic radical recombination.

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Phototaxis of Spiral Waves

Cited by 81 publications

References 23 publications

Brownian Motion of Spiral Waves Driven by Spatiotemporal Structured Noise

Brownian Motion of Spiral Waves Driven by Spatiotemporal Structured Noise

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Influence of Visible Light and Malonic Acid Derivatives on the Autocatalytic Oxidation of Ru(II) by Bromate Ions

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