Weak scattering in phononic crystals

In recent decades, there has been a significant advancement in the field of phononic crystals, thanks to the development of innovative techniques for controlling waves in complex media. One area of particular interest involves materials comprising a host medium with an array of point scatterers. Hyperuniform and stealth disordered materials are especially noteworthy, as they enable the identification of point scatterers that mitigate scattering within a certain frequency range while exhibiting heterogeneity in another range. The Born hypothesis plays a crucial role in connecting the design of hyperuniform materials to wave propagation characteristics. In this seminar, we will delve into a comprehensive methodology for modeling various types of scatterers in 1D waveguides. Furthermore, we will establish the mathematical correlation between the point distribution and propagation properties to ensure that we are dealing with weak scattering phenomena. To validate this methodology, we will present numerical examples and provide physical interpretations for the mathematical findings.