Two- and three-dimensional standing waves in a reaction-diffusion system

Abstract

We observe standing waves of chemical concentration in thin layers [quasi-two-dimensional (2D)] and capillaries [three-dimensional (3D)] containing the aqueous Belousov-Zhabotinsky reaction in a reverse microemulsion stabilized by the ionic surfactant sodium bis-2-ethylhexyl sulfosuccinate (AOT) and with cyclo-octane as the continuous phase. The 3D structures are oscillatory lamellae or square-packed cylinders at high and low volume fractions, respectively, of aqueous droplets. These patterns correspond to oscillatory labyrinthine stripes and square-packed spots in the 2D configuration. Computer simulations, as well as observations in E. coli, give qualitative agreement with the observed patterns and suggest that, in contrast to Turing patterns, the structures are sensitive to the size and shape of the system.

Birth and Death of Invading Standing Waves in the BZ‐AOT Reaction‐diffusion System

“…In our experiments, the BZ‐AOT experimental medium is a far‐from‐equilibrium dynamical system within a batch reactor, and so over time the system must approach and ultimately reach equilibrium. Previous experiments in the BZ‐AOT system have shown that standing waves can transition to traveling waves ,. The wavelength of the pattern was halved in the transition observed by Kaminaga et al ., and transitions to spirals and packet waves were reported by Bánsági et al .…”

“…Turing patterns, bulk oscillations and waves have been observed in the Belousov‐Zhabotinsky (BZ) reaction incorporated into an AOT (dioctyl sodium sulfosuccinate) reverse microemulsion. Multiple types of waves have been observed in this system, including standing waves ,. Localized domains of standing waves have also been reported .…”

“…The wavelength of the pattern was halved in the transition observed by Kaminaga et al ., and transitions to spirals and packet waves were reported by Bánsági et al . While there have been numerical investigations of standing waves,, and modulated standing wave behavior, in chemical reaction‐diffusion systems, the transitions studied have not, to our knowledge, included spiral formation. Peña and Bestehorn used the following three‐variable model to observe the interaction between Hopf and wave instabilities, generating modulated standing waves and different types of spirals, depending on the proximity to the codimension‐2 point of the instabilities.…”

Dissipative Bz Patterns in Systems of Coupled Nano- And Microdroplets

“…We have utilized tomographic techniques to study three-dimensional Turing patterns and 3D standing waves in the BZ-AOT system. 32,33 Examples of such 3D patterns are shown in Figs. 3 and 4.…”

Size matters for nonlinear (protein) wave patterns

“…They are, e.g., often composed of several coupled nonlinear equations and/ or include higher order nonlinearities (see e.g. [3,21,22,[44][45][46][47][48][49]). Moreover, traveling waves can occur far from the onset of pattern formation.…”