Soft-mode and Anderson-like localization in two-phase disordered media

TL;DR

This paper provides a continuum perspective on wave localization in two-phase disordered elastic media, revealing how soft modes and Anderson-like localization emerge at different frequencies due to disorder in modulus and density.

Contribution

It introduces a continuum approach to study wave localization, connecting soft modes and Anderson localization in elastic media with implications for material design.

Findings

Soft modes arise from disordered elastic modulus at low frequencies.

Anderson-like localization occurs at high frequencies due to disorder in density or modulus.

Vibrational dynamics transition from plane waves to diffusons with increasing frequency.

Abstract

Wave localization is ubiquitous in disordered media -- from amorphous materials, where soft-mode localization is closely related to materials failure, to semi-conductors, where Anderson localization leads to metal-insulator transition. Our main understanding, though, is based on discrete models. Here, we provide a continuum perspective on the wave localization in two-phase disordered elastic media by studying the scalar wave equation with heterogeneous modulus and/or density. At low frequencies, soft modes arise as a result of disordered elastic modulus, which can also be predicted by the localization landscape. At high frequencies, Anderson-like localization occurs due to disorder either in density or modulus. For the latter case, we demonstrate how the vibrational dynamics changes from plane waves to diffusons with increasing frequency. Finally, we discuss the implications of our findings on the design of architected soft materials.