Anomalous diffusion of acoustic waves in 2D periodic media: Radiative transport and renormalization analysis.

Abstract

This work investigates the occurrence of anomalous transport of acoustic waves propagating in two-dimensional (2D) perfectly periodic media and presents dedicated analysis tools to explore and understand the properties of the medium controlling the transitions between different transport regimes. By leveraging a two-fold approach that combines both radiative transport and renormalization theory, the propagation properties of the inhomogeneous medium can be characterized both near and at the transition from normal to anomalous diffusion. The proposed approach builds upon the classical radiative transfer theory of bulk materials, and it is specifically designed to study 2D systems. The ability to simulate and interpret the field quantities that describe such transport mechanisms can play a significant role in the development of wave-based imaging technology for highly inhomogeneous and scattering media.