Asymptotic expansions in perforated media with a periodic structure

Separation of scales and almost-periodic effects in the asymptotic behaviour of perforated periodic media

Asymptotic analysis of periodically-perforated nonlinear media

A well-known result on the asymptotic behaviour of Dirichlet problems in perforated domains shows the appearance of a ‘strange’ extra term as the period of the perforation tends to 0. In a paper by Cioranescu and Murat [10] (see also e.g. earlier work by Marchenko Khrushlov [17]) the following result (among others) is proved. Let Ω be a bounded open set in R, n ≥ 3 and for all δ > 0 let Ωδ be t...

Asymptotic Expansions for Transmission Eigenvalues for Media with Small Inhomogeneities

We consider the transmission eigenvalue problem for an inhomogeneous medium containing a finite number of diametrically small inhomogeneities of different refractive index. We prove a convergence result for the transmission eigenvalues and eigenvectors corresponding to media with small homogeneities as the diameter of small inhomogeneities goes to zero. In addition we derive rigorously a formul...

Matching of Asymptotic Expansions for Wave Propagation in Media with Thin Slots I: The Asymptotic Expansion

In this series of two articles, we consider the propagation of a time harmonic wave in a medium made of the junction a half-space (containing possibly scatterers) with a thin slot. The Neumann boundary condition is considered along the boundary on the propagation domain, which authorizes the propagation of the wave inside the slot, even if the width of the slot is very small. We perform a compl...

A field expansions method for scattering by periodic multilayered media.

The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein described is...