Homogenization for advection-diffusion in a perforated domain

The volume of a Wiener sausage constructed from a diffusion process with periodic, mean-zero, divergence-free velocity field, in dimension 3 or more, is shown to have a non-random and positive asymptotic rate of growth. This is used to establish the existence of a homogenized limit for such a diffusion when subject to Dirichlet conditions on the boundaries of a sparse and independent array of obstacles. There is a constant effective long-time loss rate at the obstacles. The dependence of this rate on the form and intensity of the obstacles and on the velocity field is investigated. A Monte Carlo algorithm for the computation of the volume growth rate of the sausage is introduced and some numerical results are presented for the Taylor–Green velocity field

Multiscale model reduction methods for flow in heterogeneous porous media

In this paper we provide a general framework for model reduction methods applied to fluid flow in porous media. Using reduced basis and numerical homogenization techniques we show that the complexity of the numerical approximation of Stokes flow in heterogeneous media can be drastically reduced. The use of such a computational framework is illustrated at several model problems such as two and three scale porous media

Analytic regularity and polynomial approximation of stochastic, parametric elliptic multiscale PDEs

A class of second order, elliptic PDEs in divergence form with stochastic and anisotropic conductivity coefficients and $n$ known, separated microscopic length scales $\epsilon_i$, $i=1,...,n$ in a bounded domain $D\subset R^d$ is considered. Neither stationarity nor ergodicity of these coefficients is assumed. Sufficient conditions are given for the random solution to converge $P$-a.s, as $\epsilon_i\rightarrow 0$, to a stochastic, elliptic one-scale limit problem in a tensorized domain of dimension $(n+1)d$. It is shown that this stochastic limit problem admits best $N$-term "polynomial chaos" type approximations which converge at a rate $\sigma>0$ that is determined by the summability of the random inputs' Karhúnen-Loève expansion. The convergence of the polynomial chaos expansion is shown to hold $P$-a.s. and uniformly with respect to the scale parameters $\epsilon_i$. Regularity results for the stochastic, one-scale limiting problem are established. An error bound for the approximation of the random solution at finite, positive values of the scale parameters $\epsilon_i$ is established in the case of two scales, and in the case of $n>2$ scales convergence is shown, albeit without giving a convergence rate in this case

Enhancing livelihoods of poor livestock keepers through increasing use of fodder: Vietnam Report on Project Output 1— Mechanisms for strengthening and/or establishing multi-stakeholder alliances that enable scaling up and out of fodder technologies

Presentation prepared to the FAP End of Project Workshop, Luang Prabang, Laos, 15-19 November 2010

Study of tribological behaviour of fresh mortar against a rigid plane wall

International audienc