Parametric resonance of a vortex in an active medium

Muñuzuri, Alberto P.; Gómez‐Gesteira, M.; Pérez‐Muñuzuri, V.; Krinsky, V. I.; Pérez‐Villar, V.

doi:10.1103/physreve.50.4258

Cited by 60 publications

(43 citation statements)

References 17 publications

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“…One observes that the simulation results agree well with the theoretical prediction from Eq. (13). Similarly, the graph in Fig.…”

Section: Quantitative Results Using Response Functionsmentioning

confidence: 90%

“…For instance, they occur in the classical Belousov-Zhabotinsky (BZ) reaction, [2][3][4] on platinum surfaces during the process of catalytic oxidation of carbon monoxide, 5 in the liquid crystal, 6 during aggregation of Dictyostelium discoideum amoebae, 7 in the chicken retina, 8 and in cardiac tissue where they are thought to lead to life-threatening cardiac arrhythmias. 9 To date, much attention has been paid to spiral dynamics as they respond to various external fields such as dc and ac electric fields, [10][11][12][13][14][15] periodic forcing, [16][17][18][19][20] mechanical deformation, [21][22][23] and heterogeneity. [24][25][26][27][28][29] As reactiondiffusion (RD) systems exhibit mirror symmetry, CCW and CW spiral waves are physically identical and the response of spiral waves with opposite chirality to achiral fields is identical up to mirror symmetry.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Phase-locked scroll waves defy turbulence induced by negative filament tension

Gao

Zheng

et al. 2016

Phys. Rev. E

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Responses of an immobilized-catalyst Belousov-Zabotinsky reaction system to electric fields J. Chem. Phys. 109, 7462 (1998) Chirality is one of the most fundamental properties of many physical, chemical, and biological systems. However, the mechanisms underlying the onset and control of chiral symmetry are largely understudied. We investigate possibility of chirality control in a chemical excitable system (the Belousov-Zhabotinsky reaction) by application of a chiral (rotating) electric field using the Oregonator model. We find that unlike previous findings, we can achieve the chirality control not only in the field rotation direction, but also opposite to it, depending on the field rotation frequency. To unravel the mechanism, we further develop a comprehensive theory of frequency synchronization based on the response function approach. We find that this problem can be described by the Adler equation and show phase-locking phenomena, known as the Arnold tongue. Our theoretical predictions are in good quantitative agreement with the numerical simulations and provide a solid basis for chirality control in excitable media.

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“…One observes that the simulation results agree well with the theoretical prediction from Eq. (13). Similarly, the graph in Fig.…”

Section: Quantitative Results Using Response Functionsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Phase-locked scroll waves defy turbulence induced by negative filament tension

Gao

Zheng

et al. 2016

Phys. Rev. E

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“…27 Depending on the excitability, different behaviors were found. For low excitability (Figure 2a), as soon as (Figure 2c), high rotational flow regions close to the fingers favor the break of the target waves symmetry and the nucleation of small spirals at the interface.…”

Section: Low Values Of [Bromentioning

confidence: 99%

Self-Organized Traveling Chemo-Hydrodynamic Fingers Triggered by a Chemical Oscillator

Escala

Budroni

Landeira

et al. 2014

J. Phys. Chem. Lett.

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Pulsatile chemo-hydrodynamic patterns due to a coupling between an oscillating chemical reaction and buoyancy-driven hydrodynamic flows can develop when two solutions of separate reactants of the Belousov−Zhabotinsky reaction are put in contact in the gravity field and conditions for chemical oscillations are met in the contact zone. In regular oscillatory conditions, localized periodic changes in the concentration of intermediate species induce pulsatile density gradients, which, in turn, generate traveling convective fingers breaking the transverse symmetry. These patterns are the self-organized result of a genuine coupling between chemical and hydrodynamic modes. SECTION: Liquids; Chemical and Dynamical Processes in SolutionO ut-of-equilibrium, breaking of symmetries and related spatiotemporal patterns have been much studied in hydrodynamic and reaction−diffusion (RD) systems. 1−3 At the intersection between these two fields, chemo-hydrodynamics focuses on analyzing patterns and instabilities that result from a nonlinear coupling of hydrodynamic and RD processes. 4 Related problems range from fingering instabilities of reactive interfaces 5,6 or traveling chemical fronts 4 to the spatiotemporal dynamics of chemicals advected in complex flow fields. 7,8 The reaction−diffusion−convection (RDC) interplay impacts numerous applications areas as diverse as combustion, 9 polymer processing, 10 extraction techniques 5,11 and CO 2 sequestration. 12 When chemicals are passively slaved to the flow, the convective motions develop independently of the presence of reactive processes. On the other hand, in presence of active chemistry, the reactions modify a physical property of the fluid like its density, viscosity, or surface tension for instance. Concentration gradients in RD processes can then trigger unfavorable mobility gradients, which in turn can yield convection. As an example, even when starting from an initially stable density stratification of a less dense reactive solution on top of a denser one in the gravity field, chemical processes can trigger buoyancy-driven convection. This occurs when the reaction produces either a denser product locally or when differential diffusion phenomena implying the various chemicals 6,13−16 or heat and mass 17 come into play. The hydrodynamic patterns are then typically convective fingers growing vertically. Simple A+B→ C reactions have been shown to be able to break the up−down symmetry of such convective fingers. 13 More complex reactions prone to produce spatiotemporal RD structures can induce other synergetic combinations of chemical and hydrodynamic modes. Typical examples of such intrinsic chemo-hydrodynamic scenarios include reaction-driven convection around a traveling chemical front stably stratified from both solutal and thermal perspectives 4,17,18 and buoyancy or Marangoni-induced convective cells following chemical waves in excitable and oscillatory systems. 19−23 In such cases, the chemical kinetics drives the source of the convective flows, and the velo...

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“…It is based on the fact that once the rotating spiral center is driven to a boundary (e.g., heart's surface), spiral waves are no longer sustained and they will vanish eventually. Because of its fundamental and potential practical importance, many studies have been carried out to understand or manipulate the motion of the spiral tips under various situations such as external ex-citation waves [24], periodic illumination [25,26], a parameter gradient [27] as well as dc and ac electric fields [28,29]. It is [30] pointed out that when forced frequency is equal to the natural frequency of spiral waves, a global periodically forced spiral exhibits a drift along a straight line.…”

Section: Introductionmentioning

confidence: 99%

Motion of spiral waves induced by local pacing

Chen

Wei

et al. 2008

Open Physics

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Abstract:The motion of spiral waves in excitable media driven by a weak pacing around the spiral tip is investigated numerically as well as theoretically. We presented a Bifurcations diagram containing four types of the spiral motion induced by different frequencies of pacing: rigidly rotating, inward-petal meandering, resonant drift, and outward-petal meandering spiral. Simulation shows that the spiral resonantly drifts when the frequency of pacing is close to that of the spiral rotation. We also find that the speed and direction of the drift can be efficiently controlled by means of the strength and phase of the local pacing, which is consistent with analytical results based on the framework of the weak deformation approximation.

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Parametric resonance of a vortex in an active medium

Cited by 60 publications

References 17 publications

Phase-locked scroll waves defy turbulence induced by negative filament tension

Phase-locked scroll waves defy turbulence induced by negative filament tension

Self-Organized Traveling Chemo-Hydrodynamic Fingers Triggered by a Chemical Oscillator

Motion of spiral waves induced by local pacing

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