Chemical-wave dynamics in a vertically oscillating fluid layer

Neuromorphic Engineering in Wetware: Discriminating Acoustic Frequencies through Their Effects on Chemical Waves

Some features of the human nervous system can be mimicked not only through software or hardware but also through liquid solutions of chemical systems maintained under out-of-equilibrium conditions. We describe the possibility of exploiting a thin layer of the Belousov-Zhabotinsky (BZ) reaction as a surrogate for the cochlea for sensing acoustic frequencies. Experiments and simulations demonstrate that, as in the human ear where the cochlea transduces the mechanical energy of the acoustic frequencies into the electrochemical energy of neural action potentials and the basilar membrane originates topographic representations of sounds, our bioinspired chemoacoustic system, based on the BZ reaction, gives rise to spatiotemporal patterns as the representation of distinct acoustic bands through transduction of mechanical energy into chemical energy. Acoustic frequencies in the range 10-2000 Hz are partitioned into seven distinct bands based on three attributes of the emerging spatiotemporal patterns: (1) the types and frequencies of the chemical waves, (2) their velocities, and (3) the Faraday waves' wavelengths.

Flow-induced transitions in bistable systems

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 trigger fronts could be reversed, so that domains of the less stable fixed point invaded the system. (ii) For bistability between a stable fixed point and a limit cycle we observed that above a critical flow velocity, the unstable focus at the center of the limit cycle could be stabilized. Increasing the flow speed further, a regime of damped flow-distributed oscillations was found and, depending on the boundary values at the inflow, finally the stable fixed point dominated. Similarly, also in the case of spatiotemporal chaos (iii), the unstable steady state could be stabilized and was replaced by the stable fixed point with increasing flow velocity. We finally outline a linear stability analysis that can explain part of our findings.

Motion of rotating pairs in a hexagonal superlattice pattern within dielectric barrier discharge

Stochastic rotation of rotating pairs in a hexagonal superlattice pattern is observed in a dielectric barrier discharge system. It is found that the pairs rotate with orientation and diameter randomly changing by observing a series of frames recorded by a high speed video camera. Frames recorded by a high speed framing camera with an exposure time corresponding to current pulse phases in one half cycle of the applied voltage show that one rotating spot, six small spots, and another rotating spot in one cell discharge successively. Based on this discharging sequence, forces exerted on a rotating spot are analyzed at different discharging stages in a half voltage cycle. A resultant force on a rotating spot with both magnitude and direction varied leads to the stochastic rotation.

Pattern formation in a reaction-diffusion-advection system with wave instability

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-Zhabotinsky reaction. For this model, we explore the type of patterns that can be obtained without advection, and then explore the effect of different velocities of the advective flow for different patterns. We observe standing waves, and with flow there is a transition from out of phase oscillations between neighboring units to in-phase oscillations with a doubling in frequency. Also mixed and clustered states are generated at higher velocities of the advective flow. There is also a regime of "waving Turing patterns" (quasi-stationary structures that come close and separate periodically), where low advective flow is able to stabilize the stationary Turing pattern. At higher velocities, superposition and interaction of patterns are observed. For both types of patterns, at high velocities of the advective field, the known flow distributed oscillations are observed.

Characterizing topological transitions in a Turing-pattern-forming reaction-diffusion system

Turing structures appear naturally and they are demonstrated under different spatial configurations such as stripes and spots as well as mixed states. The traditional tool to characterize these patterns is the Fourier transformation, which accounts for the spatial wavelength, but it fails to discriminate among different spatial configurations or mixed states. In this paper, we propose a parameter that clearly differentiates the different spatial configurations. As an application, we considered the transitions induced by an external forcing in a reaction-diffusion system although the results are straightforwardly extended to different problems with similar topologies. The method was also successfully tested on a temporally evolving pattern.

Double cascade turbulence and Richardson dispersion in a horizontal fluid flow induced by Faraday waves

We report the experimental observation of Richardson dispersion and a double cascade in a thin horizontal fluid flow induced by Faraday waves. The energy spectra and the mean spectral energy flux obtained from particle image velocimetry data suggest an inverse energy cascade with Kolmogorov type scaling E(k) ∝ k(γ), γ ≈ -5/3 and an E(k) ∝ k(γ), γ ≈ -3 enstrophy cascade. Particle transport is studied analyzing absolute and relative dispersion as well as the finite size Lyapunov exponent (FSLE) via the direct tracking of real particles and numerical advection of virtual particles. Richardson dispersion with <ΔR(2)(t)> ∝ t(3) is observed and is also reflected in the slopes of the FSLE (Λ ∝ ΔR(-2/3)) for virtual and real particles.

Manipulation of diffusion coefficients via periodic vertical forcing controls the mechanism of Turing pattern formation

We study, theoretically and experimentally, the dynamical response of macroscopic Turing patterns to a mechanical periodic forcing which implies a sinusoidal modulation of gravity. Theoretical predictions indicate that the extra energy, due to the forcing, modifies the diffusion coefficient at a microscopic level, producing changes in the Turing domain and in the pattern characteristics, in particular its wavelength. To check the theoretical analysis, we perform numerical simulations with standard models. Experiments were also performed in the closed Belousov-Zhabotinsky reaction confined in AOT microemulsion (BZ-AOT system). Experiments as well as numerical and theoretical results show good agreement.

Propagation of a chemical wave front in a quasi-two-dimensional superdiffusive flow

Pattern formation in reaction-diffusion systems is an important self-organizing mechanism in nature. Dynamics of systems with normal diffusion do not always reflect the processes that take place in real systems when diffusion is enhanced by a fluid flow. In such reaction-diffusion-advection systems diffusion might be anomalous for certain time and length scales. We experimentally study the propagation of a chemical wave occurring in a Belousov-Zhabotinsky reaction subjected to a quasi-two-dimensional chaotic flow created by the Faraday experiment. We present a novel analysis technique for the local expansion of the active wave front and find evidence of its superdiffusivity. In agreement with these findings the variance σ(2)(t)∝t(γ) of the reactive wave grows supralinear in time with an exponent γ>2. We study the characteristics of the underlying flow with microparticles. By statistical analysis of particle trajectories we derive flight time and jump length distributions and find evidence that tracer-particles undergo complex trajectories related to Lévy statistics. The propagation of active and passive media in the flow is compared.