Unpinning of scroll waves under the influence of a thermal gradient

Programmable, Spatiotemporal Control of Colloidal Motion Waves via Structured Light

Traveling waves in a reaction-diffusion system are essential for long-range communication in living organisms and inspire biomimetic materials of similar capabilities. One recent example is the traveling motion waves among photochemically oscillating, silver (Ag)-containing colloids. Being able to manipulate these colloidal waves holds the key for potential applications. Here, we have discovered that these motion waves can be confined by light patterns and that the chemical clocks of silver particles are moved forward by reducing local light intensity. Using these discoveries as design principles, we have applied structured light technology for the precise and programmable control of colloidal motion waves, including their origins, propagation directions, paths, shapes, annihilation, frequency, and speeds. We have also used the controlled propagation of colloidal waves to guide chemical messages along a predefined path to activate a population of micromotors located far from the signal. Our demonstrated capabilities in manipulating colloidal waves in space and time offer physical insights on their operation and expand their usefulness in the fundamental study of reaction-diffusion processes. Moreover, our findings inspire biomimetic strategies for the directional transport of mass, energy, and information at micro- or even nanoscales.

Influence of temperature on Turing pattern formation

The Turing instability is one of the most commonly studied mechanisms leading to pattern formation in reaction–diffusion systems, yet there are still many open questions on the applicability of the Turing mechanism. Although experiments on pattern formation using chemical systems have shown that temperature differences play a role in pattern formation, there is far less theoretical work concerning the interplay between temperature and spatial instabilities. We consider a thermodynamically extended reaction–diffusion system, consisting of a pair of reaction–diffusion equations coupled to an energy equation for temperature, and use this to obtain a natural extension of the Turing instability accounting for temperature. We show that thermal contributions can restrict or enlarge the set of unstable modes possible under the instability, and in some cases may be used to completely shift the set of unstable modes, strongly modifying emergent Turing patterns. Spatial heterogeneity plays a role under several experimentally feasible configurations, and we give particular consideration to scenarios involving thermal gradients, thermodynamics of chemicals transported within a flow, and thermodiffusion. Control of Turing patterns is also an area of active interest, and we also demonstrate how patterns can be modified using time-dependent control of the boundary temperature.

Emergent spatiotemporal instabilities in reactive spatially extended systems by thermodiffusion

Thermodiffusion or thermophoresis or Soret effect, i.e., mass-transport induced by thermal gradient, has immense application in segregation of species in two or multicomponent gaseous, liquid, or colloidal mixtures. Here, we show that an external thermal gradient can be effectively utilized in creation and modification of patterns in spatially extended systems. We consider Brusselator and chlorine-dioxide iodine malonic acid (CDIMA) reaction-diffusion systems, which follow activator-inhibitor kinetics subjected to an external thermal gradient. We find that the conspicuous interaction of emergent thermodiffusive flux with reaction kinetics and diffusion can lead to various spatiotemporal instabilities in these two models. Specifically, our result reveals formation of Turing-like spatial patterns even for equal diffusivities of the activator and inhibitor components in the Brusselator model under the influence of differential thermodiffusion, whereas formation of such stationary patterns in the CDIMA system from a homogenous stable steady state, which is also stable under differential diffusion, requires the same sign and magnitude of Soret coefficients. However, with equal diffusivities of the components of the CDIMA system and without starch in the medium, our result identifies formation of drifting spiral waves which finally disappears at longer times under the influence of thermodiffusion. We also show formation of propagating patterns of spotlike or stripelike heterogeneity in both the model systems under appropriate conditions. Our study provides a route to pattern formation beyond Turing space and reveals remarkable influence of thermodiffusion to modify the pattern types just by employing an external thermal gradient which also opens up the possibility to set up new related experiments.

Resonance of scroll rings with periodic external fields in excitable media

By direct numerical simulations of a chemical reaction-diffusion system coupled to a periodic external AC electric field with frequency equal to double frequency of the scroll wave rotation, we find that scroll rings resonate with the electric field and exhibit various dynamical behaviors, for example, their reversals, collapses, or growths, depending both on the initial phase of AC electric fields and on the initial phase of scroll rings. A kinematical model characterizing the drift velocity of the scroll rings along their radial directions as well as that of the scroll rings along their symmetry axes is proposed, which can effectively account for the numerical observations and predict the behaviors of the scroll rings. Besides, the existence of the equilibrium state of a scroll ring under the AC electric fields is predicted by the kinematical model and the predictions agree well with the simulations.

Controlling three-dimensional vortices using multiple and moving external fields

Spirals or scroll wave activities in cardiac tissues are the cause of lethal arrhythmias. The external control of these waves is thus of prime interest to scientists and physicians. In this article, we demonstrate the spatial control of scroll waves by using external electric fields and thermal gradients in experiments with the Belousov-Zhabotinsky reaction. We show that a scroll ring can be made to trace cyclic trajectories under a rotating electric field. Application of a thermal gradient in addition to the electric field deflects the motion and changes the nature of the trajectory. Our experimental results are analyzed and corroborated by numerical simulations based on an excitable reaction diffusion model.

A note on stress-driven anisotropic diffusion and its role in active deformable media

We introduce a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to employ diffusion tensors directly influenced by the coupling with mechanical stress. The proposed generalised reaction-diffusion-mechanics model reveals that initially isotropic and homogeneous diffusion tensors turn into inhomogeneous and anisotropic quantities due to the intrinsic structure of the nonlinear coupling. We study the physical properties leading to these effects, and investigate mathematical conditions for its occurrence. Together, the mathematical model and the numerical results obtained using a mixed-primal finite element method, clearly support relevant consequences of stress-driven diffusion into anisotropy patterns, drifting, and conduction velocity of the resulting excitation waves. Our findings also indicate the applicability of this novel approach in the description of mechano-electric feedback in actively deforming bio-materials such as the cardiac tissue.

Removal of pinned scroll waves in cardiac tissues by electric fields in a generic model of three-dimensional excitable media

Spirals or scroll waves pinned to heterogeneities in cardiac tissues may cause lethal arrhythmias. To unpin these life-threatening spiral waves, methods of wave emission from heterogeneities (WEH) induced by low-voltage pulsed DC electric fields (PDCEFs) and circularly polarized electric fields (CPEFs) have been used in two-dimensional (2D) cardiac tissues. Nevertheless, the unpinning of scroll waves in three-dimensional (3D) cardiac systems is much more difficult than that of spiral waves in 2D cardiac systems, and there are few reports on the removal of pinned scroll waves in 3D cardiac tissues by electric fields. In this article, we investigate in detail the removal of pinned scroll waves in a generic model of 3D excitable media using PDCEF, AC electric field (ACEF) and CPEF, respectively. We find that spherical waves can be induced from the heterogeneities by these electric fields in initially quiescent excitable media. However, only CPEF can induce spherical waves with frequencies higher than that of the pinned scroll wave. Such higher-frequency spherical waves induced by CPEF can be used to drive the pinned scroll wave out of the cardiac systems. We hope this remarkable ability of CPEF can provide a better alternative to terminate arrhythmias caused by pinned scroll waves.

Chemical waves in heterogeneous media

Formation of precipitation patterns and wave propagation in excitable media have attracted considerable scientific interest in the context of nonlinear chemical kinetics because of a new approach to micro and nanofabrication, in addition to some biological aspects. All precipitation patterns share common morphological characteristics, namely the formed patterns are stationary and no dynamical patterns can be observed in these classical precipitation systems (e.g., Liesegang phenomenon). However, it has been recently shown that in several circumstances dynamic patterns (chemical waves) can exist in purely inorganic precipitation systems similar to the well-known and studied (excitable) waves in Belousov-Zhabotinsky reaction. In this study, we show how to fine-tune the pattern characteristics in precipitation systems, such as the wavelength and the pattern morphology by changing the concentrations of the reagents, and we demonstrate chemical waves on a moving 3D spherical precipitation layer. We show that such precipitation waves have anomalous transport property, specifically superdiffusive nature, and it can be controlled by the initial concentration of the inner electrolyte. Moreover, we present several precipitation systems in which chemical wave propagation inside a moving precipitation layer can emerge. This observation points out the generality and robustness of similar behavior in diffusion-precipitation systems.