相关论文: Asymptotic flux across hypersurfaces for diffusion…

In turbulent flows, energy flux refers to the transfer of kinetic energy across different scales of motion, a concept that is a cornerstone of turbulence theory. The direction of net energy flux is prescribed by the dimensionality of the…

We use confocal microscopy to directly visualize the spatial fluctuations in fluid flow through a three-dimensional porous medium. We find that the velocity magnitudes and the velocity components both along and transverse to the imposed…

Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the…

We consider for a small parameter $\varepsilon >0$ a parabolic convection-diffusion problem with P\'eclet number of order $\mathcal{O}(\varepsilon^{-1})$ in a three-dimensional graph-like junction consisting of thin curvilinear cylinders…

We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…

A Type-I model of a multicomponent system of fluids with non-constant temperature is derived as the high-friction limit of a Type-II model via a Chapman-Enskog expansion. The asymptotic model is shown to fit into the general theory of…

The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…

This work is an extended version of the paper arXiv:0803.2669v1[math-ph], in which the main results were announced. We consider certain classical diffusion process for a wave function on the phase space. It is shown that at the time of…

We consider a diffusion process $X$ in a random potential $\V$ of the form $\V_x = \S_x -\delta x$ where $\delta$ is a positive drift and $\S$ is a strictly stable process of index $\alpha\in (1,2)$ with positive jumps. Then the diffusion…

We study the asymptotic behaviour of a real-valued diffusion whose non-regular drift is given as a sum of a dissipative term and a bounded measurable one. We prove that two trajectories of that diffusion converge a.s. to one another at an…

Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…

In a theoretical analysis, we generalise well known asymptotic results to obtain expressions for the rate of transfer of material from the surface of an arbitrary, rigid particle suspended in an open pathline flow at large P\'eclet number,…

We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…

We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…

Significant advancements have emerged in the theory of asymptotic stability of shear flows in stably stratified fluids. In this comprehensive review, we spotlight these recent developments, with particular emphasis on novel approaches that…

We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…

We consider the limiting behavior of fluctuations of small noise diffusions with multiple scales around their homogenized deterministic limit. We allow full dependence of the coefficients on the slow and fast motion. These processes arise…

This paper establishes the global asymptotic equivalence, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models…

We derive the vorticity equation for an incompressible fluid on a 2-dimensional surface with arbitrary topology embedded in 3-dimensional Euclidean space by using a tailored Clebsch parametrization of the flow. In the inviscid limit, we…

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…