Collective behavior of particle-like chemical waves

Stabilized waves in weakly excitable media propagate with constant velocity and can be directionally controlled with applied excitability gradients. Multiple waves with directional control governed by pairwise interaction potentials form cohesive groups. Processional modes arise in collections of waves with random initial conditions, in which spontaneous alignment plays an essential role. Rotational modes occur with special initial conditions, and highly complex orbits are exhibited in larger groups. The ordered behavior is associated with waves following paths of minimum potential.     

Irregular wakes in reaction-diffusion waves

Reaction-diffusion equations have proved to be highly successful models for a wide range of biological and chemical systems, but chaotic solutions have been very rarely documented. We present a new mechanism for generating apparently chaotic spatiotemporal irregularity in such systems, by analysing in detail the bifurcation structure of a particular set of reaction-diffusion equations on an infinite one-dimensional domain, with particular initial conditions. We show that possible solutions include travelling fronts which leave behind either regular or irregular spatiotemporal oscillations. Using a combination of analytical and numerical analysis, we show that the irregular behaviour arises from the instability of oscillations induced by the passage of the front. Finally, we discuss the generality of this mechanism as a way in which spatiotemporal irregularities can arise naturally in reaction-diffusion systems.     

Packet waves in a reaction-diffusion system

The finite-wavelength instability gives rise to a new type of wave in reaction-diffusion systems: packet waves, which propagate only within a wave packet, are found in experiments on the Belousov-Zhabotinsky reaction dispersed in water-in-oil AOT microemulsion (BZ-AOT) as well as in model simulations. Inwardly moving packet waves with negative curvature occur in experiments and in a model of the BZ-AOT system when the dispersion d omega(k)/dk is negative at the characteristic wave number k(0). This result sheds light on the origin of anti-spirals.     

Dash waves in a reaction-diffusion system

Patterns in reaction-diffusion systems generally consist of smooth traveling waves or of stationary, discontinuous Turing structures. Hybrid patterns that blend the properties of waves and Turing structures have not previously been observed. We report observation of dash waves, which consist of wave segments regularly separated by gaps, moving coherently in the Belousov-Zhabotinsky system dispersed in water-in-oil microemulsion. Dash waves emerge from the interaction between excitable and pseudo-Turing-unstable steady states. We are able to generate dash waves in simulations with simple models.     

Theory of spike spiral waves in a reaction-diffusion system

We discovered a type of spiral wave solutions in reaction-diffusion systems--spike spiral wave, which significantly differs from the spiral waves observed in the models of FitzHugh-Nagumo type. We present an asymptotic theory of these waves in the Gray-Scott model [Chem. Sci. Eng. 38, 29 (1983)]. We derive the kinematic relations describing the shape of this spiral, and find the dependence of its main parameters on the control parameters. The theory does not rely on the specific features of the Gray-Scott model and thus is expected to be applicable to a broad range of reaction-diffusion systems.     

Inward propagating chemical waves in a single-phase reaction-diffusion system

We report our experimental and theoretical studies of inwardly propagating chemical waves (antiwaves) in a single-phase reaction-diffusion (RD) system. The experiment was conducted in an open spatial reactor using chlorite-iodide-malonic acid reaction. When the system was set to near Hopf bifurcation point, antiwaves appeared spontaneously, as predicted using both the reaction-diffusion (RD) equation and the complex Ginzburg-Landau equation (CGLE). Antiwaves change to ordinary waves when the system was moved away from the Hopf onset, which still agreed with RD simulations but could not be predicted by CGLE. We thus witnessed a new type of antiwave-wave exchange. Our analysis showed that this exchange occurred when the CGLE broke down as the system was far from the Hopf onset.     

Doppler instability of antispiral waves in discrete oscillatory reaction-diffusion media

This paper investigates antispiral wave breakup phenomena in coupled two-dimensional FitzHugh-Nagumo cells with self-sustained oscillation via Hopf bifurcation.When the coupling strength of the active variable decreases to a critical value,wave breakup phenomenon first occurs in the antispiral core region where waves collide with each other and spontaneously break into spatiotemporal turbulence.Measurements reveal for the first time that this breakup phenomenon is due to the mechanism of antispiral Doppler instability.     

Chemical waves as a result of instability in reaction-diffusion systems

Many-component reaction-diffusion systems are shown to be able to undergo the instability, leading to the spontaneous formation of waves. In the one-dimensional case the general equations, governing the dynamics in the neighbourhood of the wave-type instability point, are derived. The investigation of all steady state solutions of these equations shows that depending on the magnitude of only one essential parameter stable are either a uniform running wave and “leading center” regime or a uniform standing wave. All other solutions are unstable.     

Collective behavior of electronic fireflies

A simple system composed of electronic oscillators capable of emitting and detecting light-pulses is studied. The oscillators are biologically inspired, there are designed for keeping a desired light intensity, W, in the system. From another perspective, the system behaves like modified integrate and fire type neurons that are pulse-coupled with inhibitory type interactions: the firing of one oscillator delays the firing of all the others. Experimental and computational studies reveal that although no direct driving force favoring synchronization is considered, for a given interval of W phase-locking appears. This weak synchronization is sometimes accompanied by complex dynamical patterns in the flashing sequence of the oscillators.     

Behavior of reaction-diffusion waves with fast activator diffusion near propagation threshold

Numerical simulation is performed to analyze behavior of reaction-diffusion waves in a medium whose parameters are near both the propagation threshold and diffusive (oscillatory) instability boundary. The wave decays in the subthreshold parameter region and propagates at a constant velocity in the parameter region well above the threshold. Just above the threshold, the wave velocity exhibits alternate intervals of chaotic and constant-amplitude oscillations. The transition from steady to chaotic propagation is a sequence of period-doubling bifurcations that occupies a narrow interval of the bifurcation parameter. In the subthreshold region, the wave decay time is a random function of the bifurcation parameter increasing on average toward the threshold.     

Oblique detonation waves stabilized in rectangular-cross-section bent tubes

Oblique detonation waves, which are generated by a fundamental detonation phenomenon occurring in bent tubes, may be applied to fuel combustion in high-efficiency engines such as a pulse detonation engine (PDE) and a rotating detonation engine (RDE). The present study has experimentally demonstrated that steady-state oblique detonation waves propagated stably through rectangular-cross-section bent tubes by visualizing these waves using a high-speed camera and the shadowgraph method. The oblique detonation waves were stabilized under the conditions of high initial pressure and a large curvature radius of the inside wall of the rectangular-cross-section bent tube. The geometrical shapes of the stabilized oblique detonation waves were calculated, and the results of the calculation were in good agreement with those of our experiment. Moreover, it was experimentally shown that the critical condition under which steady-state oblique detonation waves can stably propagate through the rectangular-cross-section bent tubes was the curvature radius of the inside wall of the rectangular-cross-section bent tube equivalent to 14–40 times the cell width.     

Collective behavior of thermally active colloids

Colloids with patchy metal coating under laser irradiation could act as local heat sources and generate temperature gradients that could induce self-propulsion and interactions between them. The collective behavior of a dilute solution of such thermally active particles is studied using a stochastic formulation. It is found that when the Soret coefficient is positive, the system could be described in a stationary state by the nonlinear Poisson-Boltzmann equation and could adopt density profiles with significant depletion in the middle region when confined. For colloids with a negative Soret coefficient, the system can be described as a dissipative equivalent of a gravitational system. It is shown that in this case the thermally active colloidal solution could undergo an instability at a critical laser intensity, which has similarities to a supernova explosion.     

Critical behavior of a two-species reaction-diffusion problem in 2D

In this work we study the critical behavior of a model that simulates the propagation of an epidemic process over a population. We simulate the model on two-dimensional finite lattices to determine the critical density of the diffusive population. A finite size scaling analysis is employed to determine the order parameter and correlation length critical exponents.     

Collective behavior in out-of-equilibrium colloidal suspensions

Colloidal suspensions, heterogeneous fluids containing solid microscopic particles, play an important role in our everyday life, from food and pharmaceutical industries to medicine and nanotechnology. Colloidal suspensions can be divided in two major classes: equilibrium, and active, i.e. maintained out of thermodynamic equilibrium by external electric or magnetic fields, light, chemical reactions, or hydrodynamic shear flow. While the properties of equilibrium colloidal suspensions are fairly well understood, out-of-equilibrium colloids pose a formidable challenge and the research is in its early exploratory stage. The possibility of dynamic self-assembly, a natural tendency of simple building blocks to organize into complex functional architectures, is one of the most remarkable properties of out-of-equilibrium colloids. Examples range from tunable, self-healing colloidal crystals and membranes to self-assembled microswimmers and robots. In contrast to their equilibrium counterparts, out-of-equilibrium colloidal suspensions may exhibit novel material properties, e.g. reduced viscosity, enhanced self-diffusivity, etc. This work reviews recent developments in the field of self-assembly and collective behavior of out-of-equilibrium colloids, with the focus on the fundamental physical mechanisms.