Related papers: Pattern selection in reaction diffusion systems
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
Linear diffusion processes serve as canonical continuous-time models for dynamic decision-making under uncertainty. These systems evolve according to drift matrices that specify the instantaneous rates of change in the expected system…
Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales where the cascade is eventually arrested by dissipation. In this article, we show how to harness these…
In this paper, we introduce a novel approach to study reaction-diffusion systems -- dynamic transition theory approach developed in Ma and Wang 2015. This approach generalizes Turing's classical result (linear stability analysis) on pattern…
Biological systems excel at building spatial structures on scales ranging from nanometers to kilometers and exhibit temporal patterning from milliseconds to years. One approach that nature has taken to accomplish this relies on the…
We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second…
We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…
Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model…
The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…
As proposed by Alan Turing in 1952 as a ubiquitous mechanism for nonequilibrium pattern formation, diffusional effects may destabilize uniform distributions of reacting chemical species and lead to both spatially and temporally…
Although the pattern formation on polymer gels has been considered as a result of the mechanical instability due to the volume phase transition, we found a macroscopic surface pattern formation not caused by the mechanical instability. It…
Active matter systems display a fascinating range of dynamical states, including stationary patterns and turbulent phases. While the former can be tackled with methods from the field of pattern formation, the spatio-temporal disorder of the…
In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show…
Dissipative structures are generally observed when a system relaxes from a far from equilibrium state. To address the reverse question given by the title, we investigate the relaxation process in a closed chemical reaction-diffusion system…