Related papers: Stochastic Turing pattern formation in a model wit…
Spontaneous pattern formation in homogeneous systems is ubiquitous in nature. Although Turing demonstrated that spatial patterns can emerge in reaction-diffusion (RD) systems when the homogeneous state becomes linearly unstable, it remains…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is…
Long after Turing's seminal Reaction-Diffusion (RD) model, the elegance of his fundamental equations alleviated much of the skepticism surrounding pattern formation. Though Turing model is a simplification and an idealization, it is one of…
Motivated by recent experiments and models of biological segmentation, we analyze the exicitation of pattern-forming instabilities of convectively unstable reaction-diffusion-advection (RDA) systems, occuring by means of constant or…
Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
We propose a stochastic model for intracellular transport processes associated with the activity of molecular motors. This out-of-equilibrium model, based on a generalized Langevin equation, considers a particle immersed in a viscoelastic…
We investigate the stochastic dynamics of an active particle moving at a constant speed under the influence of a fluctuating torque. In our model the angular velocity is generated by a constant torque and random fluctuations described as a…
Many biological activities are induced by cellular chemical reactions of diffusing reactants. The dynamics of such systems can be captured by stochastic reaction networks. A recent numerical study has shown that diffusion can significantly…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
Markedly increased computational power and data acquisition have led to growing interest in data-driven inverse dynamics problems. These seek to answer a fundamental question: What can we learn from time series measurements of a complex…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…
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…
In this work, we investigate the large-scale transport properties of a passive scalar advected by a turbulent fluid, modelled as a superposition of divergence-free vector fields, each weighted by an independent symmetric…
Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that…