Turing patterns on rotating spiral growing domains

We investigate the emergence of Turing patterns in a system growing as a rotating spiral in two dimensions, utilizing the photosensitivity of the chlorine dioxide-iodine-malonic acid (CDIMA) reaction to control the growth process. We observe the formation of single and multiple (double and triple) stationary spiral patterns as well as transitional patterns. From numerical simulations of the Lengyel-Epstein model with an additional term to account for the effects of illumination on the reaction, we analyze the relationship between the final morphologies and the radial and angular growth velocities, identify conditions conducive to the formation of transitional structures, examine the importance of the size of the initial nucleation site in determining the spiral's multiplicity, and evaluate the stability and robustness of these Turing patterns. Our results indicate how inclusion of rotational degrees of freedom in the growth process may lead to the formation of a diverse new class of patterns in chemical and biological systems.

Entropy Production in Reaction-Diffusion Systems Confined in Narrow Channels

This work analyzes the effect of wall geometry when a reaction-diffusion system is confined to a narrow channel. In particular, we study the entropy production density in the reversible Gray-Scott system. Using an effective diffusion equation that considers modifications by the channel characteristics, we find that the entropy density changes its value but not its qualitative behavior, which helps explore the structure-formation space.

Morphogenesis in Synthetic Chemical Cells

We present an efficient model for describing morphogenesis and the emergence of spatiotemporal structures in synthetic chemical cells. This work is motivated by an experimental setup used for testing Turing's theory of morphogenesis. The model developed is based on the general theory of chemically active droplets, which combines the classical theory of phase separation with reaction-diffusion systems. Through the 2D calculations, we find the six spatiotemporal structures predicted by Turing in 1952 and experimentally observed, in a 1D array of droplets. Moreover, under Turing instability, with a determined chemical wavelength, the system undergoes morphogenesis. This theoretical approach provides a useful tool for understanding the physical differentiation through the direct calculation of the osmotic pressure in each cell as the chemical reaction occurs.

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.