Igal Berenstein

Long-lasting dashed waves in a reactive microemulsion

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 oxide) (PEO). Addition of PEO lengthens the period during which these patterns are observed, so that dashed waves can persist for 12-14 h, in contrast to the 2-3 h found in earlier studies without added polymer.

Coupled and forced patterns in reaction-diffusion systems

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 and forced temporal oscillators has been well studied, but much less is known about the phenomenology of forced and coupled patterns. We present experimental results focusing primarily on coupled patterns in two chemical systems, the chlorine dioxide–iodine–malonic acid reaction and the Belousov–Zhabotinsky reaction. The observed behaviour can be simulated with simple chemically plausible models.

Coexistence of Eckhaus instability in forced zigzag Turing patterns

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 larger than the preferred wavelength). These two perhaps contradicting instabilities coexist in an experiment in which Turing patterns are forced with slowly moving stripes with a wavelength that is about 1.5 the wavelength of the Turing patterns. We also show that these two instabilities coupled together can lead to the reorientation of patterns under traveling stripe forcing.

Transition from traveling to standing waves as a function of frequency in a reaction-diffusion system

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 phase with a small delay between them, the delay being smaller as the frequency of oscillations is increased.