Related papers: Convergence along mean flows
This article is on the simultaneous diffusion approximation and homogenization of the linear Boltzmann equation when both the mean free path $\varepsilon$ and the heterogeneity length scale $\eta$ vanish. No periodicity assumption is made…
The issue of analytical derivation of the mean velocity profile in a near-wall turbulent flow is revisited in the context of a two-dimensional channel flow. An approach based on the use of dispersion relations for the flow velocity is…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
The main goal of this work is to establish quantitative nondivergence estimates for flows on homogeneous spaces of products of real and $p$-adic Lie groups. These results have applications both to ergodic theory and to Diophantine…
We consider the mean curvature flow of compact convex surfaces in Euclidean $3$-space with free boundary lying on an arbitrary convex barrier surface with bounded geometry. When the initial surface is sufficiently convex, depending only on…
We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension $3$ and higher and for coefficients having a finite range of dependence, we prove a pointwise version of…
The possibility to derive an equation for the mean velocity field in turbulent flow by using classical statistical mechanics is investigated. An application of projection operator technique available in the literature is used for this…
We consider elliptic diffusion problems with a random anisotropic diffusion coefficient, where, in a notable direction given by a random vector field, the diffusion strength differs from the diffusion strength perpendicular to this notable…
The paper addresses the numerical approximation of two variants of hyperbolic mean curvature flow of surfaces in $\mathbb R^3$. For each evolution law we propose both a finite element method, as well as a finite difference scheme in the…
We investigate the large-scale transport properties of quasi-neutrally-buoyant inertial particles carried by incompressible zero-mean periodic or steady ergodic flows. We show how to compute large-scale indicators such as the…
We study diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of manifolds (surfaces or points) in $\mathbb{R}^d$ and small perturbations of such processes. Assuming certain ergodic properties at and near the…
We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of…
This paper presents a new multiphase flow code, cast under an open-source GNU license. The main characteristics of the different flow models are given, then the numerical method used is briefly presented: it includes temporal flow solvers,…
In this paper we get a version of mean value inequality for generalized self-expander type submanifolds in Euclidean space. As the application, we prove that if mean curvature flow $M(t)$ on the self-expander in Euclidean space subconverges…
Lying between traditional parabolic and hyperbolic equations, time-fractional wave equations of order $\alpha\in(1,2)$ in time inherit both decaying and oscillating properties. In this article, we establish a long-time asymptotic estimate…
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…
In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter $\epsilon$ such that, for every fixed value of the slow variable, the fast dynamics are sufficiently chaotic with…
A tracer particle is called anomalously diffusive if its mean squared displacement grows approximately as $\sigma^2 t^{\alpha}$ as a function of time $t$ for some constant $\sigma^2$, where the diffusion exponent satisfies $\alpha \neq 1$.…
Consider a fast-slow system of ordinary differential equations of the form $\dot x=a(x,y)+\varepsilon^{-1}b(x,y)$, $\dot y=\varepsilon^{-2}g(y)$, where it is assumed that $b$ averages to zero under the fast flow generated by $g$. We give…