In this paper we extend the homogenization method to the optimization of the position of fuel assemblies in a nuclear reactor core. For this type of problem the state equation is a system of diffusion equations for the neutron flux. Homogenization theory allows to relax a truly discrete optimization problem into a continuous and well-posed optimization problem. The latter one is solved by using...

These Lecture Notes contain the abstract of ve lectures conceived as an introduction to -convergence methods in the theory of Homogenization, and delivered on September 8{10, 1993 as part of the \School on Homogenization" at the ICTP, Trieste. Their content is strictly linked and complementary to the subject of the courses held at the same School by A. Defranceschi and G. Buttazzo. Prerequisite...

The aim of upscaling is to determine equivalent homogeneous parameters at a coarse-scale from a spatially oscillating fine-scale parameter distribution. A large variety of upscaling methods is available, among which the homogenization method plays an important role. This paper presents an extension of the classical homogenization method to nonlinear problems as they occur while upscaling parame...

This paper is concerned with the approximation of effective coefficients in homogenization of linear elliptic equations. One common drawback among numerical homogenization methods is the presence of the so-called resonance error, which roughly speaking is a function of the ratio ε/η, where η is a typical macroscopic lengthscale and ε is the typical size of the heterogeneities. In the present wo...

A new Multiscale Enrichment method based on the Partition of Unity (MEPU) method is presented. It is a synthesis of mathematical homogenization theory and the Partition of Unity method. Its primary objective is to extend the range of applicability of mathematical homogenization theory to problems where scale separation may not be possible. MEPU is perfectly suited for enriching the coarse scale...

The effect of damage due to particle debonding on the constitutive response of highly filled composites is investigated using two multiscale homogenization schemes: one based on a closed-form micromechanics solution, and the other on the finite element implementation of the mathematical theory of homogenization. In both cases, the particle debonding process is modeled using a bilinear cohesive ...

We present here the homogenization of the equations for the initial modulational (large scale) perturbations of stationary solutions of the two-dimensional Navier–Stokes equations with a time-independent periodic rapidly oscillating forcing. The stationary solutions are cellular flows and they are determined by the stream function φ = sinx1/ sinx2/ + δ cosx1/ cosx2/ , 0 ≤ δ ≤ 1. Two results are...

1.Current Ecological and Social Problems in South America 1.1. Antagonism between Conservation and Development 1.2. The Blindness of Macroeconomic Parameters 2.Diversity and Homogenization in Southern South America since European Colonization 2.1. Three Waves of Eco-Cultural Homogenization: The Case of Southern Chile 2.1.1. European Conquerors (1500–1800) 2.1.2. Independence and Modernization (...

In this paper we consider numerical homogenization and correctors for nonlinear elliptic equations. The numerical correctors are constructed for operators with homogeneous random coefficients. The construction employs two scales, one a physical scale and the other a numerical scale. A numerical homogenization technique is proposed and analyzed. This procedure is developed within finite element ...

The periodic unfolding method was introduced in [4] by D. Cioranescu, A. Damlamian and G. Griso for the study of classical periodic homogenization. The main tools are the unfolding operator and a macro-micro decomposition of functions which allows to separate the macroscopic and microscopic scales. In this paper, we extend this method to the homogenization in domains with holes, introducing the...