Related papers: A Selection Criterion for Patterns in Reaction-Dif…

It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…

Reaction prediction, a critical task in synthetic chemistry, is to predict the outcome of a reaction based on given reactants. Generative models like Transformer have typically been employed to predict the reaction product. However, these…

We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…

Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…

Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively…

Spontaneous pattern formation is a fundamental scientific problem that has received much attention since the seminal theoretical work of Turing on reaction-diffusion systems. In molecular biophysics, this phenomena often takes place under…

Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…

Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localised patterns via the homoclinic snaking mechanism. This phenomenon is shown to occur naturally when balancing…

Reaction-Diffusion (RD) systems provide a computational framework that governs many pattern formation processes in nature. Current RD system design practices boil down to trial-and-error parameter search. We propose a differentiable…

We investigate Turing pattern formation in a stochastic reaction-diffusion model defined on $N$ lattice sites, where each lattice site is associated with a reaction vessel of volume $\Omega$. We focus on a regime where spatial discreteness…

Pattern dynamics on curved surfaces are found everywhere in nature. The geometry of surfaces have been shown to influence dynamics and play a functional role, yet a comprehensive understanding is still elusive. Here, we report for the first…

The discovery of inorganic crystal structures with targeted properties is a significant challenge in materials science. Generative models, especially state-of-the-art diffusion models, offer the promise of modeling complex data…

Excitable media are prevalent models for describing physical, chemical, and biological systems which support wave propagation. In this letter, we show that the time evolution of the medium state at the wave fronts can be determined by…

This paper illustrates a further application of topological data analysis to the study of self-organising models for chemical and biological systems. In particular, we investigate whether topological summaries can capture the parameter…

Cooperative behaviors arising from bacterial cell-to-cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic…

This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…

Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component reaction-diffusion system with one of its…

Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…

Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities…

We consider a reaction-diffusion system including discontinuous hysteretic relay operators in reaction terms. This system is motivated by an epigenetic model that describes the evolution of a population of organisms which can switch their…