We study the homogenization of a Schrödinger equation with a large periodic potential:
denoting by∈ the period, the potential is scaled as∈− 2. We obtain a rigorous derivation of …

This paper is concerned with the high-frequency homogenization of bubbly phononic
crystals. It is a follow-up of the work [H. Ammari et al., J. Differential Equations, 263 (2017) …

This paper deals with the homogenization of a second order parabolic operator with a large
nonlinear potential and periodically oscillating coefficients of both spatial and temporal …

We consider a family of-periodic Schrödinger operators with rapidly oscillating potentials on,
where is a Bravais lattice of, the two-scale potential is-periodic with zero mean with respect …

In this paper the effective mass approximation and the k· p multi-band models, describing
quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to …

We study the homogenization and singular perturbation of the wave equation in a periodic
media for long times of the order of the inverse of the period. We consider initial data that are …

We consider the homogenization of both the parabolic and eigenvalue problems for a
singularly perturbed convection-diffusion equation in a periodic medium. All coefficients of …

The goal of this course is to give an introduction to periodic homogenization theory with an
emphasis on applications to Schrödinger equation. We review the formal method of two …

We consider time-dependent nonlinear Schrödinger equations subject to smooth lattice-
periodic potentials plus additional confining potentials, slowly varying on the lattice scale …

We find effective, or homogenized, material parameters for Maxwell's equations when the
microscopic scale becomes small compared to the scale induced by the frequencies of the …