Igal Berenstein

Université Libre de Bruxelles | ULB

Convective dynamics developing below growing sea ice are studied experimentally by freezing salt water from above in a quasi-two-dimensional Hele-Shaw cell. Observations of the convective processes are made with Schlieren and direct imaging systems, allowing visualization both under and within the growing ice. Buoyancy-driven flows are seen to deve...

Spatiotemporal chaos in the form of defect-mediated turbulence is known for oscillators coupled by diffusion. Here we explore the same conditions that produce defect turbulence, in an array of oscillators that are coupled through the activator to a regular oscillator. We find that for very small coupling the oscillators behave independent of each o...

In this paper, we investigate pattern formation in a model of a reaction confined in a microemulsion, in a regime where both Turing and wave instability occur. In one-dimensional systems, the pattern corresponds to spatiotemporal intermittency where the behavior of the systems alternates in both time and space between stationary Turing patterns and...

In this Comment, we review the results of pattern formation in a reaction-diffusion-advection system following the kinetics of the Gray-Scott model. A recent paper by Das [Phys. Rev. E 92, 052914 (2015)] shows that spatiotemporal chaos of the intermittency type can disappear as the advective flow is increased. This study, however, refers to a singl...

In this paper, we show experimentally that inside a microfluidic device, where the reactants are segregated, the reaction rate of an autocatalytic clock reaction is accelerated in comparison to the case where all the reactants are well mixed. We also find that, when mixing is enhanced inside the microfluidic device by introducing obstacles into the...

Pattern formation is studied numerically for a reactive microemulsion when two parts of the system with different droplet fractions are initially put into contact. We analyze the resulting dynamics when the volume droplet fraction readjusts by diffusion. When both parts initially sustain Turing patterns, the whole system readjusts its wavelength to...

In this paper, we study the emergence of spatiotemporal chaos from mixed-mode oscillations, by using an extended Oregonator model. We show that bursting dynamics consisting of fast/slow mixed mode oscillations along a single attractor can lead to spatiotemporal chaotic dynamics, although the spatially homogeneous solution is itself non-chaotic. Thi...

Standing wave-like patterns are obtained in the Gray-Scott model when the dynamics that correspond to defect-mediated turbulence for equal diffusivities interact with a Turing instability. The Turing instability can be caused by either differential or cross-diffusion. We compare results with the Oregonator model, for which standing wave-like patter...

In this paper, we show that the Gray-Scott model is able to produce defect-mediated turbulence. This regime emerges from the limit cycle, close or far from the Hopf bifurcation, but always right before the Andronov homoclinic bifurcation of the homogeneous system. After this bifurcation, as the control parameter is further changed, the system start...

This paper studies the spatiotemporal dynamics of a reaction-diffusion-advection system corresponding to an extension of the Oregonator model, which includes two inhibitors instead of one. We show that when the reaction-diffusion, two-dimensional problem displays stationary patterns the addition of a plug flow can induce the emergence of new types...

We explore the effect of cross-diffusion on pattern formation in the two-variable Oregonator model of the Belousov-Zhabotinsky reaction. For high negative cross-diffusion of the activator (the activator being attracted towards regions of increased inhibitor concentration) we find, depending on the values of the parameters, Turing patterns, standing...

Systems with the same local dynamics but different types of diffusive instabilities may show the same type of patterns. In this paper, we show that under the influence of advective flow the scenario of patterns that is formed at different velocities change; therefore, we propose the use of advective flow as a tool to uncover the underlying instabil...

We studied transitions between spatiotemporal patterns that can be induced in a spatially extended nonlinear chemical system by a unidirectional flow in combination with constant inflow concentrations. Three different scenarios were investigated. (i) Under conditions where the system exhibited two stable fixed points, the propagation direction of t...

In this paper, we show by means of numerical simulations how new patterns can emerge in a system with wave instability when a unidirectional advective flow (plug flow) is added to the system. First, we introduce a three variable model with one activator and two inhibitors with similar kinetics to those of the Oregonator model of the Belousov-Zhabot...

We show that quasi-standing wave patterns appear in the two-variable Oregonator model of the Belousov-Zhabotinsky reaction when a cross-diffusion term is added, no wave instability is required in this case. These standing waves have a frequency that is half the frequency of bulk oscillations displayed in the absence of diffusive coupling. The stand...

We report spatiotemporal chaos in the Oregonator model of the Belousov-Zhabotinsky reaction. Spatiotemporal chaos spontaneously develops in a regime, where the underlying local dynamics show stable limit cycle oscillations (diffusion-induced turbulence). We show that spatiotemporal chaos can be suppressed by a unidirectional flow in the system. Wit...

Wavelength selection is an important feature in pattern forming systems. There are two distinct instabilities that arise when a mismatching wavelength is imposed on a pattern forming system, the Eckhaus instability (when the imposed wavelength is smaller than the preferred wavelength) and the zigzag instability (when the imposed wavelength is large...

Breathing spiral waves are observed in the oscillatory chlorine dioxide-iodine-malonic acid reaction-diffusion system. The breathing develops within established patterns of multiple spiral waves after the concentration of polyvinyl alcohol in the feeding chamber of a continuously fed, unstirred reactor is increased. The breathing period is determin...

The addition of polyethylene glycol to the Belousov-Zhabotinsky reaction increases the frequency of oscillations, which in an extended system causes a transition from traveling to standing waves. A further increase in frequency causes another transition to bulk oscillations. The standing waves are composed of two domains, which oscillate out of pha...

In the Belousov-Zhabotinsky (BZ) reaction carried out in a reverse microemulsion with Aerosol OT as surfactant, the existence of two different sizes of droplets containing the BZ reactants leads to the emergence of segmented (dashed) waves. This bimodal distribution of sizes is stabilized by adding small amounts of the homopolymer poly(ethylene oxi...

Several reaction-diffusion systems that exhibit temporal periodicity when well mixed also display spatio-temporal pattern formation in a spatially distributed, unstirred configuration. These patterns can be travelling (e.g. spirals, concentric circles, plane waves) or stationary in space (Turing structures, standing waves). The behaviour of coupled...

We perform experiments on the chlorine dioxide-iodine-malonic acid (CDIMA) reaction forced with light with a pattern of moving stripes in which the spatiotemporal behavior is the oscillating movement of stripes (waving). This behavior is seen for different relative wavelengths between stationary and moving patterns. Different velocities of forcing...

We observe traveling waves emitted from Turing spots in the chlorine dioxide-iodine-malonic acid reaction. The newborn waves are continuous, but they break into segments as they propagate, and the propagation of these segments ultimately gives rise to spatiotemporal chaos. We model the wave-breaking process and the motion of the chaotic segments. W...

We study the mechanism of development of superlattice Turing structures from photochemically generated hexagonal patterns of spots with wavelengths several times larger than the characteristic wavelength of the Turing patterns that spontaneously develop in the nonilluminated system. Comparison of the experiment with numerical simulations shows that...

O papel das metil cetonas em reações oscilantes do tipo Belousov-Zhabotinsky (BZ) é eliminar bromo molecular através de um processo de enolização, mas sua importância na dinâmica da reação depende do composto orgânico usado como substrato. Este trabalho mostra que em uma mistura binária de metil cetonas , cada cetona age independentemente mas com e...

Turing patterns in the chlorine dioxide-iodine-malonic acid reaction are studied in a system consisting of two coupled gel layers. Patterns with two wavelengths are observed. Changing the strength of the interlayer coupling causes a transition between a superposition of Turing patterns and a superlattice pattern. The effects of the reactant concent...

Families of complex superlattice structures, consisting of combinations of basic hexagonal or square patterns, are found in a photosensitive reaction-diffusion system. The structures are induced by simple illumination patterns whose wavelengths are appropriately related to that of the system's intrinsic Turing pattern. Computer simulations agree wi...

We study the influence of the intensity of light and the wavelength of an imposed parallel striped mask on the development of striped Turing patterns. Depending on the ratio R = λF/λP of the wavelength of the mask to the wavelength of the natural pattern and on the amplitude of forcing, stripes develop parallel or perpendicular to the orientation o...

Spontaneously evolving Turing structures in the chlorine dioxide-iodine-malonic acid reaction-diffusion system typically exhibit many defects that break the symmetry of the pattern. Periodic spatial forcing interacts with the Turing structures and modifies the pattern symmetry and wavelength. We investigate the role of the amplitude and wavelength...

When a methyl ketone is added to the Belousov−Zhabotinskii (BZ) reaction, an increase of the induction period and in the number of oscillations is observed. This behavior can be explained by the competition of malonic acid and the methyl ketone for molecular bromine. We studied the effect of four methyl ketones in the BZ reaction and found a direct...

Contrary to what has been thought, systems classified as bromine-hydrolysis-controlled (BHC) show an induction period. In studies on the effect of a family of ketones upon this type of oscillators, it was found that an induction period appears in an interval of concentrations of the ketone, or in an interval of the value of the enolization constant...

"UMI:3164720." Thesis (Ph.D.)--Brandeis University, 2005. Includes bibliographical references (p. 96-105) Photocopy. s