相关论文: Homogenisation of a Passive Scalar Transported by …

A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…

This paper concerns the diffusion-homogenization of transport equations when both the adimensionalized scale of the heterogeneities $\alpha$ and the adimensionalized mean-free path $\eps$ converge to 0. When $\alpha=\eps$, it is well known…

We propose a stochastic representation for a simple class of transport PDEs based on Ito representations. We detail an algorithm using an estimator stemming for the representation that, unlike regularization by noise estimators, is…

We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…

Quantum stochastic processes are widely used in describing open quantum systems and in the context of quantum foundations. Physically relevant quantum stochastic processes driven by multiplicative colored noise are generically non-Markovian…

The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative…

We study a stochastically driven, damped nonlinear oscillator whose frequency is modulated by a white or coloured noise. Using diagrammatic perturbation theory, we find that in the absence of nonlinearity, parametric modulation by a…

We prove that diffusion equations with a space-time stationary and ergodic, divergence-free drift homogenize in law to a deterministic stochastic partial differential equation with Stratonovich transport noise. In the absence of spatial…

In the last few years it was proved that scalar passive quantities subject to suitable stochastic transport noise, and more recently that also vector passive quantities subject to suitable stochastic transport and stretching noise, weakly…

Stochastic modelling necessitates an interpretation of noise. In this paper, we describe the loss of deterministically stable behaviour in a fundamental fluid mechanics problem, conditional to whether noise is introduced in the sense of…

Stabilization and sufficient conditions for mixing by stochastic transport are shown. More precisely, given a second order linear operator with possibly unstable eigenvalues on a smooth compact Riemannian manifold, it is shown that the…

We extend our recently introduced stochastic nonlocal traffic flow model to more general random perturbations, including Markovian noise derived from a discretized Jacobi-type stochastic differential equation. Invoking a deterministic…

We study approximations to a class of vector-valued equations of Burgers type driven by a multiplicative space-time white noise. A solution theory for this class of equations has been developed recently in [Hairer, Weber, Probab. Theory…

We investigate theoretically and numerically transport noise-induced diffusion in flows on the sphere. Previous analysis on the torus demonstrated that suitably chosen transport noise in the Euler equations leads to diffusive behavior…

We study the compressible Navier-Stokes system driven by physically relevant transport noise, where the noise influences both the continuity and momentum equations. Our approach is based on transforming the system into a partial…

Homogenization method is used to analyse the equivalent behavior of transient flow of a passive solute through highly heterogeneous porous media. The flow is governed by a coupled system which includes an elliptic equation and a linear…

This paper is concerned with stochastic systems whose state is a diffusion process governed by an Ito stochastic differential equation (SDE). In the framework of a nominal white-noise model, the SDE is driven by a standard Wiener process.…

This contribution investigates an original stochastic approach for the emergence of stop-and-go waves in traffic flow, a collective phenomenon with significant safety and environmental implications. Using a stable nonlinear car-following…

A stochastic free-boundary problem for the three-dimensional barotropic compressible Navier--Stokes equations is studied. The main feature of the model is that the free boundary is transported by a Stratonovich stochastic flow, so that the…

When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…