Pinned Scroll Rings in an Excitable System

Jiménez, Zulma A.; Marts, Bradley; Steinbock, Oliver

doi:10.1103/physrevlett.102.244101

Cited by 43 publications

(41 citation statements)

References 23 publications

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“…Our results reveal the formation of vortex structures in which neighboring filament branches are stationary despite strong curvature. The experimental preparation of these states relies on recent advances that allow the pinning of scroll waves to inert and impermeable heterogeneities [22][23][24]. A comparison with curvature-flow simulations yields quantitative information on the distance-dependence of filament interaction.…”

mentioning

confidence: 99%

Stationary Vortex Loops Induced by Filament Interaction and Local Pinning in a Chemical Reaction-Diffusion System

Jiménez

Steinbock

2012

Phys. Rev. Lett.

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Scroll rings are three-dimensional excitation waves rotating around one-dimensional filament loops. In experiments with the Belousov-Zhabotinsky reaction we show that the collapse of these loops can be stopped by local pinning to only two unexcitable heterogeneities. The resulting vortices rotate around stationary but curved filaments. The absence of filament motion can be explained by repulsive interaction that counteracts the expected curvature-induced motion. The shape and key dependencies of the stationary filaments are well described by a curvature-flow model with additive interaction velocities that rapidly decrease with filament distance.

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confidence: 99%

Stationary Vortex Loops Induced by Filament Interaction and Local Pinning in a Chemical Reaction-Diffusion System

Jiménez

Steinbock

2012

Phys. Rev. Lett.

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“…Using (14), the parameter plane of D 1 as a function of k for b = 1 were plotted in Fig. 1, which is divided into two regions.…”

Section: Dependence Of Output Signal Amplitude On Multiplicative Noismentioning

confidence: 99%

Effect of Correlated Dichotomous Noises on Stochastic Resonance in a Linear System

Nie

Shu

et al. 2012

J Stat Phys

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A linear system driven by correlated asymmetric dichotomous noises and periodic signal was investigated in the overdamped case. The exact expressions of output signal amplitude and signal-to-noise ratio (SNR) of the system were derived. By means of numerical calculations, we found that: (i) At some fixed multiplicative noise intensities, the output signal amplitude with frequency exhibits the structure of a weak peak, even no peak as the dichotomous noise is asymmetric; (ii) In the case of asymmetric dichotomous noise, the signal frequency can cause non-monotonous behavior of the output signal amplitude with respect to multiplicative noise intensity; (iii) The curve of SNR with frequency has a weak peak and a trough in the case of symmetric dichotomous noise, but no peak with asymmetric; (iv) Whether the multiplicative noise is symmetric or asymmetric, the noise can enhance response of the system; (v) The SNR increases with the correlation strength between the two noises decreasing. In addition, the plane of multiplicative noise intensity versus noise symmetric parameter was plotted.

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“…Examples include investigations of scroll waves pinned to inert obstacles such as tori, double tori, spheres, and cylinders [25,[28][29][30]. These experiments have revealed that pinning qualitatively alters the evolution of the filament and often results in lifetime enhancement or complete stabilization of vortices that, in the absence of pinning sites, would rapidly shrink and annihilate.…”

Section: Introductionmentioning

confidence: 99%

Analysis of anchor-size effects on pinned scroll waves and measurement of filament rigidity

et al. 2014

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Inert, spherical heterogeneities can pin three-dimensional scroll waves in the excitable Belousov-Zhabotinsky reaction. Three pinning sites cause initially circular rotation backbones to approach equilateral triangles. The resulting stationary shapes show convex deviations that increase with decreasing anchor radii. This dependence is interpreted as a transition between filament termination at large surfaces and true, local pinning of a continuous curve. The shapes of the filament segments are described by a hyperbolic cosine function which is predicted by kinematic theory that considers filament tension and rigidity. The latter value is measured as (1.0 ± 0.7) × 10 −6 cm 4 /s.

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Pinned Scroll Rings in an Excitable System

Cited by 43 publications

References 23 publications

Stationary Vortex Loops Induced by Filament Interaction and Local Pinning in a Chemical Reaction-Diffusion System

Stationary Vortex Loops Induced by Filament Interaction and Local Pinning in a Chemical Reaction-Diffusion System

Effect of Correlated Dichotomous Noises on Stochastic Resonance in a Linear System

Analysis of anchor-size effects on pinned scroll waves and measurement of filament rigidity

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