Guy Bouchitté

Singular perturbations of variational problems arising from a two-phase transition model

AbstractGiven thatα, β are two Lipschitz continuous functions of Ω to ℝ+ and thatf(x, u, p) is a continuous function of

Theory of mesoscopic magnetism in photonic crystals

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Homogenization of Maxwell's Equations in a Split Ring Geometry

× ℝ × ℝN to [0, + ∞[ such that, for everyx, f(x,·, 0) reaches its minimum value 0 at exactly two pointsα(x) andβ(x), we prove the convergence ofFε(u) = (1/ε)∫Ωf (x, u, εDu) dx when the perturbation parameterε goes to zero. A formula is given for the limit functional and a general minimal interface criterium is deduced for a wide class of two-phase transition models. Earlier results of [19], [21], and [22] are extended with new proofs.

Negative refraction in periodic and random photonic crystals

Abstract In duality pairs such as (Mb, C0) and (W−1,p′, W01,P), a convex integral functional on the space of functions has a polar which admits an integral representation. This representation is the sum of a first term involving the absolutely continuous component of the measure and of a second one which is a positively homogeneous function of the singular part. The duality is useful in plasticity theory. In the Sobolev case the study of non-parametric integrands is new. A description of the sub-differential is obtained.

HOMOGENIZATION OF A WIRE PHOTONIC CRYSTAL: THE CASE OF SMALL VOLUME FRACTION*

We provide a rigorous theoretical basis for the artificial magnetic activity of metamaterials near resonances. Our approach is a renormalization-based scheme that authorizes a completely general theory. The major result is an explicit expression of the effective permeability, in terms of resonant frequencies. The theoretical results are checked numerically, and we give applications of our theory to left-handed media and to the solution of the Pokrovski-Efros paradox.

Homogenization of Maxwell’s equations with split rings

To the aim of studying the homogenization of low-dimensional periodic structures, we identify each of them with a periodic positive measure

Left-handed media and homogenization of photonic crystals.

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Homogenization, Plasticity and Yield Design

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