Pattern-fluid interpretation of chemical turbulence

Abstract

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)].

Nonequilibrium phase transitions and pattern formation as consequences of second-order thermodynamic induction

“…Instead one may see an increase in fluctuations at all length scales, a result resembling hydrodynamic turbulence. Such an effect, termed chemical turbulence, has been observed in reaction-diffusion systems [28,38]. It may indeed be the case that in systems exhibiting chemical turbulence, the dispersion relation is very flat.…”

Exploring complex pattern formation with convolutional neural networks

“…Possibilities include Fourier transforms, 8 statistical methods, 23 and integral-geometric analysis. 9,10,24,25 The drawback of these methods is that they only work in special cases and cannot be generalized easily.…”

Cell Shape Analysis of Random Tessellations Based on Minkowski Tensors

“…In physical literature, they are commonly referred to as "Minkowski functionals" (The only difference to the mathematical literature is in the normalization.) These functionals and their tensor valuations extensions, the "Minkowski tensors" are efficient numerical tools, which have been successfully applied to a variety of biological [12,8] and physical systems [64,65,43] on all length scales from nuclear physics [95,96], over condensed and soft matter [30,39,104,88], to astronomy and cosmology [41,16,85,26,22,27] as well as to pattern analysis [63,11,58,87]. They allow for a versatile morphometric analysis of random spatial structures on very different length scales [43].…”