Homogenization and Bloch waves
By: Cristian Barbarosie
From: Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Universidade de Lisboa, Portugal
At: Building C2, room 2.4.16
[2026-05-07]
Homogenization theory describes the effective (macroscopic) behaviour of media with microscopic inhomogeneities such as composite materials or crystal lattices. Homogenization theory is mainly directed to static or quasi-static phenomena like thermal conduction, elastic equilibrium, fluid flow through porous media. It can also model the propagation of slow waves, whose wavelength is much larger than the periodicity cell of the inhomogeneities.
In order to model the propagation of waves whose wavelength is of the same order of magnitude as the periodicity cell, a different approach is needed, based on the notion of Bloch wave. This approach is useful in describing the propagation of waves through periodic media (e.g. crystalline structures). An interesting possibility is the appearance of band gaps, that is, ranges of frequencies where the propagation of the wave is forbidden. Obtaining such band gaps leads to the design of acoustic or electromagnetic filters.