Waves in disordered particulate materials: transmission and inter-particle correlations

At its core, this dissertation not only contributes to a deeper understanding of wave propagation in particulate materials but also opens new avenues for innovative engineering solutions in fields such as acoustic and electromagnetic material sensing and design. For instance, it contributes to the development of materials for specific wave-manipulation applications such as selectively blocking or absorbing specific wave frequencies. It challenges the standard approach that on average, a wave propagates through random particulate materials with a single effective wavenumber, demonstrating instead the presence of multiple effective wavenumbers due to strong multiple scattering phenomena. This finding is surprising, considering the homogeneous and isotropic nature of the medium and our focus on scalar waves. To confirm these predictions, we conduct high-fidelity Monte-Carlo simulations, avoiding any statistical assumptions and providing the first clear evidence that there is indeed more than one effective wavenumber. However, when performing simulations we came across another unresolved gap in the theory concerning the incident wave that encounters a material with random microstructure. It is well known that any incident wave will eventually be completely replaced by some sort of effective transmitted wave. This is often referred to as the extinction of the incident wave. What was not clear is how far does the incident wave travel before being replaced by an effective wave? In disordered particulate materials we prove that the incident wave does not propagate within the material more than the correlation length between particles. In more detail, the extinction length is exactly equal to the maximum distance at which two particles are still correlated. This result not only helps perform numerical simulations, but is important to know in any experimental measurement, or even when designing materials to control wave propagation. A further challenge we encountered when comparing Monte-Carlo simulations, of thousands of particles, with theoretical predictions, is that the typically used pair-correlations g(r) - where r is the distance between the particles - did not match exactly the pair-correlations from our Monte-Carlo simulations. This naturally led us to investigate the discrepancy between theoretical pair-correlation functions and those derived from our Monte-Carlo simulations. This motivated our research on the realizability problem – whether a specific particle configuration can be calculated to match a given pair-correlation. Recognising the significant role of pair-correlations in fields like chemistry and materials science, we demonstrate a way to formulate the realizability problem as a smooth optimisation problem, where the gradients can be easily calculated. This approach, relying on gradient-based methods, promises more efficient solutions compared to traditional brute-force, non-gradient-based techniques.