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

Turing patterns modulation by chemical gradient in isothermal and non-isothermal conditions

Chemical gradients imposed through boundary conditions induce spatial symmetry breaking of Turing patterns in small systems.

Thermodynamic and morphological characterization of Turing patterns in non-isothermal reaction-diffusion systems

The effect of temperature on the bifurcation diagram and Turing instability domain under non isothermal conditions is studied in the reversible Gray-Scott model. After adding the energy balance to the cubic autocatalytic model, the thermostat temperature and heat transfer coefficient are used as control parameters in the Turing pattern formation. The patterns obtained in the domain of the thermal parameter are characterized by quantifying the overall entropy generation rate and two topological indices; Shannon entropy and Minkowski functionals. The results show that it is possible to induce transitions between Turing patterns of different morphologies by regulating the temperature, and that these transitions take place at a lower entropy generation value compared to other parameters, such as kinetic constants and reactant fluxes. Finally, a correlation between entropy generation and topological indices shows that a difference between direct and inverse patterns is mainly morphological and not energetic.

Pattern-fluid interpretation of chemical turbulence

The spontaneous formation of heterogeneous patterns is a hallmark of many nonlinear systems, from biological tissue to evolutionary population dynamics. The standard model for pattern formation in general, and for Turing patterns in chemical reaction-diffusion systems in particular, are deterministic nonlinear partial differential equations where an unstable homogeneous solution gives way to a stable heterogeneous pattern. However, these models fail to fully explain the experimental observation of turbulent patterns with spatio-temporal disorder in chemical systems. Here we introduce a pattern-fluid model as a general concept where turbulence is interpreted as a weakly interacting ensemble obtained by random superposition of stationary solutions to the underlying reaction-diffusion system. The transition from turbulent to stationary patterns is then interpreted as a condensation phenomenon, where the nonlinearity forces one single mode to dominate the ensemble. This model leads to better reproduction of the experimental concentration profiles for the "stationary phases" and reproduces the turbulent chemical patterns observed by Q. Ouyang and H. L. Swinney [Chaos 1, 411 (1991)].

Accelerated dynamics in active media: from Turing patterns to sparkling waves

We report the destabilization of stationary Turing patterns and the subsequent emergence of fast spatiotemporal dynamics due to reactant consumption. The localized hexagonal Turing spots switch from a stationary regime to a dynamics state by exhibiting spatial oscillations with two characteristic wavelengths and one representative temporal period. These oscillatory Turing spots are not temporally stable and evolve into traveling spiral tips that, in addition to the unexpected birth of spots, rapidly transform into target patterns and originate multiple collisions and wave breakups due to their proximity, degenerating into a chaotic scenario.

Influence of oscillatory centrifugal forces on the mechanism of Turing pattern formation

Constantly acting centrifugal forces on Turing pattern forming systems have been observed to induce orientation and wavelength changes on Turing structures. Here, we will consider a periodic modulation of such centrifugal forces and their effects on pattern formation. Depending on the oscillation period the system exhibits a wide variety of stationary (stripes, H(0), etc.) or nonstationary patterns (black eyes, etc.), as well as transitions and instabilities such as Eckhaus, zigzag, etc. In this paper, a detailed description of the different patterns and patterning mechanisms will be described and understood within the previous context. The system considered is the Belousov-Zhabotinsky reaction encapsulated in AOT micelles modeled by the adapted version of the Oregonator model.