Localization of waves and vibrations in complex systems

Localization of waves plays a major role in the behavior of numerous physical systems, whether they are of acoustical, mechanical, optical, or quantum nature. This localization can be the result of a complex medium, of the geometry of the vibrating structure, or even due to the presence of disorder. It is for instance responsible for the metal-insulator transition in several disordered alloys. In mechanics, a marked localization of steady vibrations can be achieved in rectangular clamped plates by blocking only one interior point [1]. In this talk, we will quickly overview several manifestations of wave localization, and then show that this phenomenon can be explained within a general theory of localization applying to all vibratory systems whose wave equation derive from an energy form. The main tool of this theory, the localization landscape, controls the amplitude of the stationary vibrations, and predicts the spatial regions where vibrations will be localized as well as the frequencies above which a delocalization transition occurs [2].
We will present comparisons between numerical simulations and experimental measurements of wave localization in thin clamped plates, proving that it possible to directly observe the localization landscape in real devices. We will provide an example where the landscape can be used as a “design” tool by defining the positions of blocked points inside the plate in order to obtain specific spatial vibrating patterns. Finally we will briefly sketch the current developments of the theory as well as some of its applications.