Vibrations in materials with granularity

Abstract

This thesis concerns the vibrational properties of different classical disordered condensed matter systems. In the first part we focus on materials that exhibit a rigidity transition as their density is increased. By introducing a new method into the field, we were able to look into the localization behavior of vibrational modes of jammed packings of soft spherical particles, both in the localized regime where the localization length is much less and in the regime where it is grater than the linear system size. We also analyze the nature of vibrational modes of jammed packings of soft elliptical particles, where we uncover the change of the structure of the spectrum, compared to the simplest model of sphere packings, due to the rotational degrees of freedom of the particles. In the second part of this thesis we explore the localization properties of collective modes and response to uniform driving of bubble clouds. We find that the response is often very different from that of a typical mode because the frequency response of each mode is sufficiently wide that many modes are excited when the cloud is driven by an ultrasound.