Elastic excitable medium

Muñuzuri, A. P.; Innocenti, Claudia; Flesselles, J.-M.; Gilli, J. M.; Agladze, Konstantin; Krinsky, V. I.

doi:10.1103/physreve.50.r667

Cited by 55 publications

(42 citation statements)

References 15 publications

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“…On the other hand, Munuzuri et al [20] designed an appropriate elastic excitable medium by incorporating the BZ reaction into a polyacrylamide-silica gel and experimentally studied the influence of periodic mechanical contraction of excitable media on the behavior of rotating spiral waves. Recently, we derived, directly from origin reaction-diffusion equations, a formula of drifting velocity using weak-deformation approximation and explained the drift of spiral waves under resonant frequency [21].…”

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The effect of mechanical deformation on spiral turbulence

Zhang

Sheng

et al. 2006

Europhys. Lett.

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Abstract. -The behavior of spiral turbulence in mechanically deformed excitable media is investigated. Numerical simulations show that when the forcing frequency is chosen around the characteristic frequency of the system, complicated spiral turbulence may be quenched within a shorter evolution time, compared to the case free of mechanical deformation. It is shown that the observed phenomenon occurs due to enhancing the drift of spiral tips induced by mechanical deformation.A wide range of self-organized phenomena exists in spatially distributed systems. One of the most paradigmatic examples of spatiotemporal self-organized structures is a class of spiral waves, which have been observed in a variety of physical [1], chemical [2][3][4][5] and biological systems [6][7][8][9]. The attractiveness of investigating the dynamics of spiral waves is not only because they own a special structure, i.e., the core regarded as a phase-singular in mathematical language, but more important they contribute to the underlying class of cardiac disease also, such as tachycardia and fibrillation [6][7][8][9]. It is thus that, from a practical point of view, controlling the behaviors of spiral waves, particularly eliminating spiral waves and spiral turbulence, is extremely important and meaningful. Up to now, various methods to control two-, and even three-dimensional spiral waves and turbulence have been put forward [10][11][12][13][14][15][16][17][18][19].On the other hand, Munuzuri et al. [20] designed an appropriate elastic excitable medium by incorporating the BZ reaction into a polyacrylamide-silica gel and experimentally studied the influence of periodic mechanical contraction of excitable media on the behavior of rotating spiral waves. Recently, we derived, directly from origin reaction-diffusion equations, a formula of drifting velocity using weak-deformation approximation and explained the drift of spiral waves under resonant frequency [21]. Besides, spiral breakup due to mechanical deformation was studied in our recent work [22]. To our knowledge, however, the influences of mechanical

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“…(2) are identical with the model of mechanical deformation in ref. [20]: the contraction of the medium is modeled by varying the size of the grid in the x-direction in the numerical simulation of eqs. (1).…”

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The effect of mechanical deformation on spiral turbulence

Zhang

Sheng

et al. 2006

Europhys. Lett.

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“…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.…”

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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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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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“…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 reaction-diffusion (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%

Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field

Cai

Zhang

et al. 2014

The Journal of Chemical Physics

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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 BZ 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

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Elastic excitable medium

Cited by 55 publications

References 15 publications

The effect of mechanical deformation on spiral turbulence

The effect of mechanical deformation on spiral turbulence

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

Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field

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