Related papers: Stochastic Turing pattern formation in a model wit…

We introduce a class of stochastic advection problems amenable to analysis of turbulent transport. The statistics of the flow field are represented as a continuous time Markov process, a choice that captures the intuitive notion of…

We adopt a stochastic approach to study the charge transport in transistors. In this approach, the hole and electron densities are ruled by diffusion-reaction stochastic partial differential equations satisfying local detailed balance…

We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin…

We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…

Diffusion models generate structure by progressively transforming noise into data, yet the mechanisms underlying this transition remain poorly understood. In this work, we show that pattern formation in trained diffusion models can be…

We describe an R package developed by the research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von Ossietzky University of Oldenburg, which extracts the (stochastic) evolution equation underlying a set of data or…

The generation of non-separable, physically motivated covariance functions is a theme of ongoing research interest, given that only a few classes of such functions are available. We construct a non-separable space-time covariance function…

Diffusive motion is a fundamental transport mechanism in physical and biological systems, governing dynamics across a wide range of scales -- from molecular transport to animal foraging. In many complex systems, however, diffusion deviates…

We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…

We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In…

Deep linear networks (DLNs) are used as an analytically tractable model of the training dynamics of deep neural networks. While gradient descent in DLNs is known to exhibit saddle-to-saddle dynamics, the impact of stochastic gradient…

Modelling the evolution of a system using stochastic dynamics typically implies a greater subjective uncertainty in the adopted system coordinates as time progresses, and stochastic entropy production has been developed as a measure of this…

Stochastic perturbations of transport type are a common and widely accepted way of representing turbulent effects in fluid dynamics models. In many known examples, it even leads to improved solution theory, a phenomenon known as…

The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…

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…

Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…

We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…

A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining…

We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the…

We propose a stochastic volatility model for time series of curves. It is motivated by dynamics of intraday price curves that exhibit both between days dependence and intraday price evolution. The curves are suitably normalized to…