Related papers: Fluctuation-driven Turing patterns
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…
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 investigate Turing pattern formation in a stochastic and spatially discretized version of a reaction diffusion advection (RDA) equation, which was previously introduced to model synaptogenesis in \textit{C. elegans}. The model describes…
Enhancement of the predictive power and robustness of nonlinear population dynamics models allows ecologists to make more reliable forecasts about species' long term survival. However, the limited availability of detailed ecological data,…
We extend the mechanism for noise-induced phase transitions proposed by Ibanes et al. [Phys. Rev. Lett. 87, 020601-1 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this…
This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
Generative modeling has recently undergone remarkable advancements, primarily propelled by the transformative implications of Diffusion Probabilistic Models (DPMs). The impressive capability of these models, however, often entails…
For decades, procedural worlds have been built on procedural noise functions such as Perlin noise, which are fast and infinite, yet fundamentally limited in realism and large-scale coherence. Conversely, diffusion models offer unprecedented…
Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into…
Traveling waves are ubiquitous in nature and control the speed of many important dynamical processes, including chemical reactions, epidemic outbreaks, and biological evolution. Despite their fundamental role in complex systems, traveling…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
Procedural noise is a fundamental component of computer graphics pipelines, offering a flexible way to generate textures that exhibit "natural" random variation. Many different types of noise exist, each produced by a separate algorithm. In…
Friction is ubiquitous in daily life, from nanoscale machines to large engineering components. By probing the intricate interplay between system parameters and frictional behavior, scientists seek to unveil the underlying mechanisms that…
A Fluctuation Theorem (FT), both Classical and Quantum, describes the large-deviations in the approach to equilibrium of an isolated quasi-integrable system. Two characteristics make it unusual: (i) it concerns the internal dynamics of an…
Diffusion models rely on a high-dimensional latent space of initial noise seeds, yet it remains unclear whether this space contains sufficient structure to predict properties of the generated samples, such as their classes. In this work, we…
Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The related pattern formation models normally comprise a system of…
Machine learning is becoming increasingly important for nonlinear system identification, including dynamical systems with spatially distributed outputs. However, classical identification and forecasting approaches become markedly less…
We set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium, nonequilibrium thermodynamic potentials…
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion…