Related papers: Effective energy-enstrophy diffusion process and c…
We investigate the existence of invariant measures for self-stabilizing diffusions. These stochastic processes represent roughly the behavior of some Brownian particle moving in a double-well landscape and attracted by its own law. This…
Recent computer simulation results [Barrat {\em et al.}, Physica A 334 (2004) 513] for granular mixtures subject to stochastic driving have shown the validity of the Einstein relation $\epsilon\equiv D/(T_0\lambda)=1$ between the diffusion…
In this work we study the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise. We give exact formulas for the drift and diffusion coefficients for the case…
In this paper, we are interested in the propagation of convexity by the strong solution to a one-dimensional Brownian stochastic differential equation with coefficients Lipschitz in the spatial variable uniformly in the time variable and in…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
We extend the ideas of (Barbour 1990) and use Stein's method to obtain a bound on the distance between a scaled time-changed random walk and a time-changed Brownian Motion. We then apply this result to bound the distance between a…
We introduce a continuous Galerkin finite element discretization of the non-hydrostatic Boussinesq approximation of the Navier-Stokes equations, suitable for various applications such as coastal ocean dynamics and ice-ocean interactions,…
We study nonequilibrium steady states in the Lorentz gas of periodic scatterers when an external field is applied and the particle kinetic energy is held fixed by a ``thermostat'' constructed according to Gauss' principle of least…
Anisotropic diffusion processes emerge in various fields such as transport in biological tissue and diffusion in liquid crystals. In such systems, the motion is described by a diffusion tensor. For a proper characterization of processes…
A model for diffusion in liquids that couples the dynamics of tracer particles to a fluctuating Stokes equation for the fluid is investigated in the limit of large Schmidt number. In this limit, the concentration of tracers is shown to…
Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system, are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by…
We investigate the construction of diffusions consisting of infinitely numerous Brownian particles moving in $\mathbb{R}^d$ and interacting via logarithmic functions (two-dimensional Coulomb potentials). These potentials are very strong and…
We find explicit upper bounds for the density of marginals of continuous diffusions where we assume that the diffusion coefficient is constant and the drift is solely assumed to be progressively measurable and locally bounded. In one…
Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random…
In this work, we are concerned with existence and uniqueness of invariant measures for path-dependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment…
We derive the incompressible Euler equations with heat convection with the no-penetration boundary condition from the Boltzmann equation with the diffuse boundary in the hydrodynamic limit for the scale of large Reynold number. Inspired by…
We investigate the extreme value statistics of a one-dimensional Brownian motion (with the diffusion constant $D$) during a time interval $\left[0, t \right]$ in the presence of a reflective boundary at the origin, starting from a positive…
The scattering of inertia-gravity waves by large-scale geostrophic turbulence in a rapidly rotating, strongly stratified fluid leads to the diffusion of wave energy on the constant-frequency cone in wavenumber space. We derive the…
We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation…
We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the Central Limit Theorems formally established for their marginal empirical…