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Boundary layer correctors and generalized polarization tensor for periodic rough thin layers. A review for the conductivity problem

Clair Poignard (2012)

ESAIM: Proceedings

We study the behaviour of the steady-state voltage potential in a material composed of a two-dimensional object surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be εα–periodic, ε being the magnitude of the mean thickness of the layer, and α a positive parameter describing the degree of roughness. For ε tending to zero, we determine the appropriate boundary layer correctors which lead to approximate transmission conditions equivalent to...

Boundary layer tails in periodic homogenization

Grégoire Allaire, Micol Amar (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper focus on the properties of boundary layers in periodic homogenization in rectangular domains which are either fixed or have an oscillating boundary. Such boundary layers are highly oscillating near the boundary and decay exponentially fast in the interior to a non-zero limit that we call boundary layer tail. The influence of these boundary layer tails on interior error estimates is emphasized. They mainly have two effects (at first order with respect to the period ε): first, they add...

Bounds and estimates on the effective properties for nonlinear composites

Peter Wall (2000)

Applications of Mathematics

In this paper we derive lower bounds and upper bounds on the effective properties for nonlinear heterogeneous systems. The key result to obtain these bounds is to derive a variational principle, which generalizes the variational principle by P. Ponte Castaneda from 1992. In general, when the Ponte Castaneda variational principle is used one only gets either a lower or an upper bound depending on the growth conditions. In this paper we overcome this problem by using our new variational principle...

Bounds and numerical results for homogenized degenerated p -Poisson equations

Johan Byström, Jonas Engström, Peter Wall (2004)

Applications of Mathematics

In this paper we derive upper and lower bounds on the homogenized energy density functional corresponding to degenerated p -Poisson equations. Moreover, we give some non-trivial examples where the bounds are tight and thus can be used as good approximations of the homogenized properties. We even present some cases where the bounds coincide and also compare them with some numerical results.

Conditions aux limites approchées pour les couches minces périodiques

Habib Ammari, Chiraz Latiri-Grouz (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Nous écrivons et nous justifions des conditions aux limites approchées pour des couches minces périodiques recouvrant un objet parfaitement conducteur en polarisation transverse électrique et transverse magnétique.

Corrector results for a parabolic problem with a memory effect

Patrizia Donato, Editha C. Jose (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to provide the correctors associated to the homogenization of a parabolic problem describing the heat transfer. The results here complete the earlier study in [Jose, Rev. Roumaine Math. Pures Appl.54 (2009) 189–222] on the asymptotic behaviour of a problem in a domain with two components separated by an ε-periodic interface. The physical model established in [Carslaw and Jaeger, The Clarendon Press, Oxford (1947)] prescribes on the interface the condition that the flux...

Derivation of a homogenized two-temperature model from the heat equation

Laurent Desvillettes, François Golse, Valeria Ricci (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat,...

Currently displaying 41 – 60 of 284