진학프로석·박사 채용 접수 플랫폼

This project focuses on the modelling of the propagation of (acoustic or elastic) wave fields in a medium with heterogeneous properties (randomly-fluctuating density and compressibility for instance). In general, the solution of such an equation displays two phases: (i) a coherent wave, somewhat similar to a wave propagating in a homogeneous medium, and (ii) an incoherent wave, seemingly more random. In some very heterogeneous media, like concrete or the Earth, that second phase of the solution is the most prominent, and the transport of energy is better modeled by diffusion than by wave propagation. If the level of heterogeneity is large enough, transport can be stopped altogether. This phenomenon is called Anderson localization, and has already been observed experimentally in granular media. The main objective of the project is to understand precisely the transition between diffusion and localization in randomly-fluctuating heterogeneous media. 

The main theoretical tool will be asymptotic analysis, as in classical homogenization in mechanics, but considering quadratic observables. Numerical analysis and tools may also be required, depending on the background of the candidate. Initially, waveguides (for instance surface waves in a 2D half-space) may be considered since the 1D setting allows for easier analysis but the objective of this project is precisely to tackle higher dimensional problems, which are essential for applications. Alternatively, and depending on the background of the candidate, the project will concentrate on the extension to realistic engineering applications of the localization landscape method, a numerical technique developed recently to identify the onset of localization. Within a larger project, interactions are expected with colleagues from the railway industry, that will provide measurements of wave propagation through barriers made of crushed stones.