相关论文: On microscopic derivation of a fractional stochast…
We introduce and study the inhomogeneous exponential jump model - an integrable stochastic interacting particle system on the continuous half line evolving in continuous time. An important feature of the system is the presence of arbitrary…
We consider the interplay of thermal fluctuations and shear on the surface of the domains in various systems coarsening under an imposed shear flow. These include systems with nonconserved and conserved dynamics, and a conserved order…
We discuss the generation and statistics of the density fluctuations in highly compressible polytropic turbulence, based on a simple model and one-dimensional numerical simulations. Observing that density structures tend to form in a…
We revisit the one-dimensional Burgers equation in the inviscid limit for white-noise initial velocity. We derive the probability distributions of velocity and Lagrangian increments, measured on intervals of any length $x$. This also gives…
We study the fluctuations of a random surface in a stochastic growth model on a system of interlacing particles placed on a two dimensional lattice. There are two different types of particles, one with a low jump rate and the other with a…
We demonstrate that numerical solutions of Burgers' equation can be obtained by a scale-totality algorithm for fluids of small viscosity (down to one billionth). Two sets of initial data, modelling simple shears and wall boundary layers,…
We consider one-dimensional infinite chains of harmonic oscillators with stochastic perturbations and long-range interactions which have polynomial decay rate $|x|^{-\theta}, x \to \infty, \theta > 1$, where $x \in \mathbb{Z}$ is the…
An important result in classical stochastic thermodynamics is the work fluctuation--dissipation relation (FDR), which states that the dissipated work done along a slow process is proportional to the resulting work fluctuations. Here we show…
In this paper, we consider the averaging principle for one dimensional stochastic Burgers equation with slow and fast time-scales. Under some suitable conditions, we show that the slow component strongly converges to the solution of the…
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…
This paper develops a two-stage stochastic model to investigate evolution of random fields on the unit sphere $\bS^2$ in $\R^3$. The model is defined by a time-fractional stochastic diffusion equation on $\bS^2$ governed by a diffusion…
We review the formulation of the stochastic Burgers equation as a martingale problem. One way of understanding the difficulty in making sense of the equation is to note that it is a stochastic PDE with distributional drift, so we first…
We consider the one-dimensional Burgers equation perturbed by a stochastic forcing, which is assumed to be white in time and localised and low-dimensional in space. We establish a mixing property for the Markov process associated with the…
The fluctuation-dissipation theorem, in the Kubo original formulation, is based on the decomposition of the thermal agitation forces into a dissipative contribution and a stochastically fluctuating term. This decomposition can be avoided by…
We study a hard sphere gas at equilibrium, and prove that in the low density limit, the fluctuations converge to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times. The method of…
A fundamental problem of non-equilibrium statistical mechanics is the derivation of macroscopic transport equations in the hydrodynamic limit. The rigorous study of such limits requires detailed information about rates of convergence to…
We consider the stochastic heat equation on $\mathbb R^d$ with multiplicative space-time white noise noise smoothed in space. For $d\geq 3$ and small noise intensity, the solution is known to converge to a strictly positive random variable…
The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale. A stochastic model for a mesoscopic cell…
We present a theoretical framework to analyze the violation of fluctuation-response relation (FRR) for any observable from a finite Markov system with two well-separated time scales. We find that, generally for both slow and fast…
We investigate a boundary-driven Ginzburg-Landau dynamics with long-range interactions. In the hydrodynamic limit, the macroscopic evolution is governed by a fractional heat equation with Dirichlet boundary conditions, while the…