Related papers: Homogenization of locally stationary diffusions wi…
Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion…
This article mainly proves the existence of stationary correctors under space-time spectral gap conditions, which exhibit different properties from those of elliptic operator correctors. Additionally, new flux correctors and their…
The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in $\R^n$. Our primary contribution is a stochastic homogenization result that characterizes the effective…
We study stochastic homogenization of a quasilinear parabolic PDE with nonlinear microscopic Robin conditions on a perforated domain. The focus of our work lies on the underlying geometry that does not allow standard homogenization…
In this article, basing upon probabilistic methods, we discuss periodic homogenization of a class of weakly coupled systems of linear elliptic and parabolic partial differential equations. Under the assumption that the systems have rapidly…
As amorphous materials get jammed, both geometric and dynamic heterogeneity are observed. We investigate the correlation between the local geometric heterogeneity and local rearrangements in a slowly compressed bidisperse…
The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous piezoelectric structures saturated by Newtonian fluids. The flow is propelled by peristaltic deformation of microchannels which is induced due…
We study a diffusion process with random space-time dependent coefficients. Moreover the diffusion matrix is allowed to degenerate. An invariance principle is proved provided that the diffusion coefficient is controlled by a time…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard…
We use the local orthogonal decomposition technique to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale diffusion coefficient. We consider nonsmooth initial data and a backward…
This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation. In [11] rate of convergence results in…
We study suspensions of solid particles in a viscous incompressible fluid in the presence of highly oscillatory velocity-dependent surface forces. The flow at a small Reynolds number is modeled by the Stokes equations coupled with the…
The focus of our work is dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g.~functionally-graded) media endowed with periodic microstructure. For this class of quasi-periodic medium…
We study the local scaling properties associated with straight line periodic orbits in homogeneous Hamiltonian systems, whose stability undergoes repeated oscillations as a function of one parameter. We give strong evidence of local scaling…
We study a class of second-order degenerate linear parabolic equations in divergence form in $(-\infty, T) \times \mathbb R^d_+$ with homogeneous Dirichlet boundary condition on $(-\infty, T) \times \partial \mathbb R^d_+$, where $\mathbb…
We study the homogenization problem for a system of stochastic differential equation with local time terms that models a multivariate diffusion in presence of semipermeable hyperplane interfaces with oblique penetration. We show that this…
We prove the two-scale transformation method which allows rigorous homogenisation of problems defined on locally periodic domains by transformation on periodic domains. The idea to consider periodic substitute problems was originally…
The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…
We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chain generator. Our approximations achieve a higher degree of…