Localized stationary and traveling reaction-diffusion patterns in a two-layer<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi><mml:mspace width="0.16em" /><mml:mo>+</mml:mo><mml:mspace width="0.16em" /><mml:mrow><mml:mi>B</mml:mi><mml:mspace width="0.16em" /><mml:mo>→</mml:mo></mml:mrow></mml:math>oscillator system

Budroni, Marcello A.; Wit, A. De

doi:10.1103/physreve.93.062207

Cited by 10 publications

(18 citation statements)

References 47 publications

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“…The Brusselator model has been used previously to obtain localized oscillations and Turing patterns within gradients of concentration of reactants. 18,19,22,[31][32][33][34][35] Here, speci cally, the initial concentrations of the various reactant species in the con guration described in Fig. 1 is…”

Section: Chemohydrodynamic Modelmentioning

confidence: 99%

“…Equations (18)- (22) are solved numerically using Fourier pseudospectral techniques. 38 In this technique, the variables A, B, Y, X, and are transformed into Fourier space as…”

Section: B Numerical Approachmentioning

confidence: 99%

“…[16][17][18] Localized oscillations 19 or stationary Turing patterns 20,21 can be obtained in autocatalytic reactions around A + B → oscillator fronts when putting in contact two zones containing separate reactants A and B of an oscillatory reaction. 17,18,22,23 From the theoretical point of view, it has been shown that localized oscillations and Turing structures can interact with buoyancy-driven ows when the reactants A and B of the oscillatory Brusselator model are initially separated, meet by di usion, and produce the intermediate X and Y species locally, which changes the density. 18 Experimentally, interplay between the oscillating Belousov-Zhabotinsky (BZ) reaction and buoyancy-driven motions has been analyzed when two subsets of the reactants are put in contact along a horizontal line in the gravity eld.…”

Section: Introductionmentioning

confidence: 99%

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Reaction-driven oscillating viscous fingering

Rana

Wit

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Localized oscillations can develop thanks to the interplay of reaction and di usion processes when two reactants A and B of an oscillating reaction are placed in contact, meet by di usion, and react. We study numerically the properties of such an A + B → oscillator con guration using the Brusselator model. The in uence of a hydrodynamic viscous ngering instability on localized concentration oscillations is next analyzed when the oscillating chemical reaction changes the viscosity of the solutions involved. Nonlinear simulations of the related reaction-di usion-convection equations with the uid viscosity varying with the concentration of an intermediate oscillatory species show an active coupling between the oscillatory kinetics and the viscously driven instability. The periodic oscillations in the concentration of the intermediate species induce localized changes in the viscosity, which in turn can a ect the ngering instability. We show that the oscillating kinetics can also trigger viscous ngering in an initially viscously stable displacement, while localized changes in the viscosity pro le can induce oscillations in an initially nonoscillating reactive system.

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Section: Chemohydrodynamic Modelmentioning

confidence: 99%

“…Equations (18)- (22) are solved numerically using Fourier pseudospectral techniques. 38 In this technique, the variables A, B, Y, X, and are transformed into Fourier space as…”

Section: B Numerical Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reaction-driven oscillating viscous fingering

Rana

Wit

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In these, numerical simulations often promote understanding the effects of the applied initial and boundary conditions. 15 , 16 However, periodic forcing and coupling of reaction–diffusion systems are still at the forefront of research. Frequency-locking, standing-wave patterns, and tongue-shaped regions of resonance have been reported in a light-sensitive form of the BZ reaction–diffusion system.…”

Section: Introductionmentioning

confidence: 99%

Reaction–Diffusion Dynamics of pH Oscillators in Oscillatory Forced Open Spatial Reactors

et al. 2021

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Studying the effect of coupling and forcing of oscillators is a significant area of interest within nonlinear dynamics and has provided evidence of many interesting phenomena, such as synchronization, beating, oscillatory death, and phase resetting. Many studies have also reported along this line in reaction–diffusion systems, which are preferably explored experimentally by using open reactors. These reactors consist of one or two homogeneous (well-stirred) tanks, which provide the boundary conditions for a spatially distributed part. The spatiotemporal dynamics of this configuration in the presence of temporal oscillations in the homogeneous part has not been systematically investigated. This paper aims to explore numerically the effect of time-periodic boundary conditions on the dynamics of open reactors provided by autonomous and forced oscillations in the well-stirred part. A simple model of pH oscillators can produce various phenomena under these conditions, for example, superposition and modulation of spatiotemporal oscillations and forced bursting. The autonomous oscillatory boundary conditions can be generated by the same kinetic instabilities that result in spatiotemporal oscillations in the spatially distributed part. The forced oscillations are induced by sinusoidal modulation on the inflow concentration of the activator in the tank. The simulations confirmed that this type of forcing is more effective when the modulation period is longer than the residence time of the well-stirred part. The use of time-periodic boundary conditions may open a new perspective in the control and design of spatiotemporal phenomena in open one-side-fed and two-side-fed reactors.

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“…The properties of such kind of fronts have been analysed in details during the past decades. Recently, the group of Anne De Wit have investigated theoretically and experimentally the dynamics of an A + B → oscillator front, where the initial reactants of an oscillatory reaction are separated in space at the beginning [6][7][8]. Their theoretical results show diverse spatially localized dynamics, including the formation of localized waves and Turing patterns.…”

Section: Introductionmentioning

confidence: 99%

Front dynamics of pH oscillators with initially separated reactants

Dúzs

Szalai

2017

Reac Kinet Mech Cat

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The spatiotemporal dynamics of the Landolt-type pH oscillators are studied both numerically and experimentally with initially separated reagents in space. This configuration results in an A + B → oscillator front type system with localized patterns. The generic Rábai model of the pH-oscillators predicts the formation of an asymmetric acidic domain at the interface of the two zones loaded by different sets of chemicals. This asymmetry is rather caused by the initial conditions than the difference in the diffusivities of the components. As the influence of the negative feedback process increases, this acidic zone becomes to be localized around the interface. At some point the acidic zone bifurcates, a less acidic zone separates and starts to move forward the oxidant rich zone. In a limited domain of parameters, spatiotemporal oscillations are found due to the instability of the main acidic zone. The appropriate conditions for the development of this periodic behaviour is characterized by simulations. The numerically predicted phenomena are supported by experiments performed with the bromate-sulfite-ferrocyanide and with the hydrogen peroxide-sulfite-ferrocyanide systems, except the oscillatory phenomena.

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Localized stationary and traveling reaction-diffusion patterns in a two-layerA+B→oscillator system

Cited by 10 publications

References 47 publications

Reaction-driven oscillating viscous fingering

Reaction-driven oscillating viscous fingering

Reaction–Diffusion Dynamics of pH Oscillators in Oscillatory Forced Open Spatial Reactors

Front dynamics of pH oscillators with initially separated reactants

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