Emergent spatiotemporal instabilities in reactive spatially extended systems by thermodiffusion

Radially evolving spiral wave patterns in the Gierer-Meinhardt reaction-diffusion system

Spiral wave formation in spatially extended systems is a fascinating phenomenon that has garnered significant attention in reaction-diffusion systems. In this study, we explore the emergence of spiral wave-like patterns in the Gierer-Meinhardt reaction-diffusion model. By employing a multiple-time scale perturbation technique, we derive amplitude equations that reveal the conditions for spiral wave formation. Notably, our analysis shows that the amplitude of these spiral waves varies with the radial distance, introducing a distinctive feature to this pattern. Our theoretical predictions are further substantiated by numerical simulations, which confirm the emergence of spiral wave structures and validate the distinct radial dependence of their amplitude.

Unravelling diverse spatiotemporal orders in chlorine dioxide-iodine-malonic acid reaction-diffusion system through circularly polarized electric field and photo-illumination

Designing and predicting self-organized pattern formation in out-of-equilibrium chemical and biochemical reactions holds fundamental significance. External perturbations like light and electric fields exert a crucial influence on reaction-diffusion systems involving ionic species. While the separate impacts of light and electric fields have been extensively studied, comprehending their combined effects on spatiotemporal dynamics is paramount for designing versatile spatial orders. Here, we theoretically investigate the spatiotemporal dynamics of chlorine dioxide-iodine-malonic acid reaction-diffusion system under photo-illumination and circularly polarized electric field (CPEF). By applying CPEF at varying intensities and frequencies, we observe the predominant emergence of oscillating hexagonal spot-like patterns from homogeneous stable steady states. Furthermore, our study unveils a spectrum of intriguing spatiotemporal instabilities, encompassing stripe-like patterns, oscillating dumbbell-shaped patterns, spot-like instabilities with square-based symmetry, and irregular chaotic patterns. However, when we introduce periodic photo-illumination to the hexagonal spot-like instabilities induced by CPEF in homogeneous steady states, we observe periodic size fluctuations. Additionally, the stripe-like instabilities undergo alternating transitions between hexagonal spots and stripes. Notably, within the Turing region, the interplay between these two external influences leads to the emergence of distinct superlattice patterns characterized by hexagonal-and square-based symmetry. These patterns include parallel lines of spots, target-like formations, black-eye patterns, and other captivating structures. Remarkably, the simple perturbation of the system through the application of these two external fields offers a versatile tool for generating a wide range of pattern-forming instabilities, thereby opening up exciting possibilities for future experimental validation.

Phase transition of three-dimensional finite-sized charged dust clusters in a plasma environment

The dynamics of a harmonically trapped three-dimensional Yukawa ball of charged dust particles immersed in plasma is investigated as function of external magnetic field and Coulomb coupling parameter using molecular dynamics simulation. It is shown that the harmonically trapped dust particles organize themselves into nested spherical shells. The particles start rotating in a coherent order as the magnetic field reaches a critical value corresponding to the coupling parameter of the system of dust particles. The magnetically controlled charged dust cluster of finite size undergoes a first-order phase transition from disordered to ordered phase. At sufficiently high coupling and strong magnetic field, the vibrational mode of this finite-sized charged dust cluster freezes, and the system retains only rotational motion.

Deciphering electric field induced spatial pattern formation in the photosensitive chlorine-dioxide iodine malonic acid reaction and the Brusselator reaction-diffusion systems

Reaction-diffusion systems involving ionic species are susceptible to an externally applied electric field. Depending on the charges on the ionic species and the intensity of the applied electric field, diverse spatiotemporal patterns can emerge. We here considered two prototypical reaction-diffusion systems that follow activator-inhibitor kinetics: the photosensitive chlorine dioxide-iodine-malonic acid (CDIMA) reaction and the Brusselator model. By theoretical investigation and numerical simulations, we unravel how and to what extent an externally applied electric field can induce and modify the dynamics of these two systems. Our results show that both the uni- and bi-directional electric fields may induce Turing-like stationary patterns from a homogeneous uniform state resulting in horizontal, vertical, or bent stripe-like inhomogeneity in the photosensitive CDIMA system. In contrast, in the Brusselator model, for the activator and the inhibitor species having the same positive or negative charges, the externally applied electric field cannot develop any spatiotemporal instability when the diffusion coefficients are identical. However, various spatiotemporal patterns emerge for the same opposite charges of the interacting species, including moving spots and stripe-like structures, and a phenomenon of wave-splitting is observed. Moreover, the same sign and different magnitudes of the ionic charges can give rise to Turing-like stationary patterns from a homogeneous, stable, steady state depending upon the intensity of the applied electric field in the case of the Brusselator model. Our findings open the possibilities for future experiments to verify the predictions of electric field-induced various spatiotemporal instabilities in experimental reaction-diffusion systems.

Thermodiffusion-induced traveling and shock waves in a colloidal solution

The formation of chemical waves in a nonlinear spatially extended system is one of the most fascinating far-from-equilibrium phenomena. An externally imposed thermal gradient in a liquid mixture may induce a concentration gradient generating a thermodynamic cross-flow, which is known as thermal diffusion or the Ludwig-Soret effect. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fraction in space and time. Here, we show that under an externally imposed constant thermal gradient, a traveling wave can emerge in a solution of self-propelled neutral colloid. An exact analytic solution of the spatially extended system is presented in one dimension for a constant thermal gradient to show the time development of a traveling wave. We analyze the effect of a small finite relaxation time of flux, which takes care of the finite inertia of the dispersing colloidal species. While the wave speed remains unaffected, the wave shape is significantly modified by the presence of the finite relaxation time of flux. Our result demonstrates that the traveling wave may reduce to a shock wave provided the product of the square of the wave speed and the relaxation time exactly balances the mass diffusion coefficient. This condition can be achieved by suitably adjusting the velocity of the emergent traveling wave by tuning the value of the constant thermal gradient and maintaining the appropriate boundary condition.

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.